Applies an activation function element-wise to the input. The following activation functions are supported: - `relu`: Rectified Linear Unit, :math:`y = max(x, 0)` - `sigmoid`: :math:`y = \frac{1}{1 + exp(-x)}` - `tanh`: Hyperbolic tangent, :math:`y = \frac{exp(x) - exp(-x)}{exp(x) + exp(-x)}` - `softrelu`: Soft ReLU, or SoftPlus, :math:`y = log(1 + exp(x))` - `softsign`: :math:`y = \frac{x}{1 + abs(x)}` Defined in src/operator/nn/activation.cc:L168
The input array.
Activation function to be applied.
org.apache.mxnet.Symbol
Batch normalization. Normalizes a data batch by mean and variance, and applies a scale ``gamma`` as well as offset ``beta``. Assume the input has more than one dimension and we normalize along axis 1. We first compute the mean and variance along this axis: .. math:: data\_mean[i] = mean(data[:,i,:,...]) \\ data\_var[i] = var(data[:,i,:,...]) Then compute the normalized output, which has the same shape as input, as following: .. math:: out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i] Both *mean* and *var* returns a scalar by treating the input as a vector. Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta`` have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and the inverse of ``data_var``, which are needed for the backward pass. Note that gradient of these two outputs are blocked. Besides the inputs and the outputs, this operator accepts two auxiliary states, ``moving_mean`` and ``moving_var``, which are *k*-length vectors. They are global statistics for the whole dataset, which are updated by:: moving_mean = moving_mean * momentum + data_mean * (1 - momentum) moving_var = moving_var * momentum + data_var * (1 - momentum) If ``use_global_stats`` is set to be true, then ``moving_mean`` and ``moving_var`` are used instead of ``data_mean`` and ``data_var`` to compute the output. It is often used during inference. The parameter ``axis`` specifies which axis of the input shape denotes the 'channel' (separately normalized groups). The default is 1. Specifying -1 sets the channel axis to be the last item in the input shape. Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is true, then set ``gamma`` to 1 and its gradient to 0. .. Note:: When ``fix_gamma`` is set to True, no sparse support is provided. If ``fix_gamma is`` set to False, the sparse tensors will fallback. Defined in src/operator/nn/batch_norm.cc:L571
Input data to batch normalization
gamma array
beta array
running mean of input
running variance of input
Epsilon to prevent div 0. Must be no less than CUDNN_BN_MIN_EPSILON defined in cudnn.h when using cudnn (usually 1e-5)
Momentum for moving average
Fix gamma while training
Whether use global moving statistics instead of local batch-norm. This will force change batch-norm into a scale shift operator.
Output the mean and inverse std
Specify which shape axis the channel is specified
Do not select CUDNN operator, if available
The minimum scalar value in the form of float32 obtained through calibration. If present, it will be used to by quantized batch norm op to calculate primitive scale.Note: this calib_range is to calib bn output.
The maximum scalar value in the form of float32 obtained through calibration. If present, it will be used to by quantized batch norm op to calculate primitive scale.Note: this calib_range is to calib bn output.
org.apache.mxnet.Symbol
Batch normalization. This operator is DEPRECATED. Perform BatchNorm on the input. Normalizes a data batch by mean and variance, and applies a scale ``gamma`` as well as offset ``beta``. Assume the input has more than one dimension and we normalize along axis 1. We first compute the mean and variance along this axis: .. math:: data\_mean[i] = mean(data[:,i,:,...]) \\ data\_var[i] = var(data[:,i,:,...]) Then compute the normalized output, which has the same shape as input, as following: .. math:: out[:,i,:,...] = \frac{data[:,i,:,...] - data\_mean[i]}{\sqrt{data\_var[i]+\epsilon}} * gamma[i] + beta[i] Both *mean* and *var* returns a scalar by treating the input as a vector. Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta`` have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and ``data_var`` as well, which are needed for the backward pass. Besides the inputs and the outputs, this operator accepts two auxiliary states, ``moving_mean`` and ``moving_var``, which are *k*-length vectors. They are global statistics for the whole dataset, which are updated by:: moving_mean = moving_mean * momentum + data_mean * (1 - momentum) moving_var = moving_var * momentum + data_var * (1 - momentum) If ``use_global_stats`` is set to be true, then ``moving_mean`` and ``moving_var`` are used instead of ``data_mean`` and ``data_var`` to compute the output. It is often used during inference. Both ``gamma`` and ``beta`` are learnable parameters. But if ``fix_gamma`` is true, then set ``gamma`` to 1 and its gradient to 0. There's no sparse support for this operator, and it will exhibit problematic behavior if used with sparse tensors. Defined in src/operator/batch_norm_v1.cc:L95
Input data to batch normalization
gamma array
beta array
Epsilon to prevent div 0
Momentum for moving average
Fix gamma while training
Whether use global moving statistics instead of local batch-norm. This will force change batch-norm into a scale shift operator.
Output All,normal mean and var
org.apache.mxnet.Symbol
Applies bilinear sampling to input feature map.
Bilinear Sampling is the key of [NIPS2015] \"Spatial Transformer Networks\". The usage of the operator is very similar to remap function in OpenCV,
except that the operator has the backward pass.
Given :math:`data` and :math:`grid`, then the output is computed by
.. math::
x_{src} = grid[batch, 0, y_{dst}, x_{dst}] \\
y_{src} = grid[batch, 1, y_{dst}, x_{dst}] \\
output[batch, channel, y_{dst}, x_{dst}] = G(data[batch, channel, y_{src}, x_{src})
:math:`x_{dst}`, :math:`y_{dst}` enumerate all spatial locations in :math:`output`, and :math:`G()` denotes the bilinear interpolation kernel.
The out-boundary points will be padded with zeros.The shape of the output will be (data.shape[0], data.shape[1], grid.shape[2], grid.shape[3]).
The operator assumes that :math:`data` has 'NCHW' layout and :math:`grid` has been normalized to [-1, 1].
BilinearSampler often cooperates with GridGenerator which generates sampling grids for BilinearSampler.
GridGenerator supports two kinds of transformation: ``affine`` and ``warp``.
If users want to design a CustomOp to manipulate :math:`grid`, please firstly refer to the code of GridGenerator.
Example 1::
## Zoom out data two times
data = array(`[ [`[ [1, 4, 3, 6],
[1, 8, 8, 9],
[0, 4, 1, 5],
[1, 0, 1, 3] ] ] ])
affine_matrix = array(`[ [2, 0, 0],
[0, 2, 0] ])
affine_matrix = reshape(affine_matrix, shape=(1, 6))
grid = GridGenerator(data=affine_matrix, transform_type='affine', target_shape=(4, 4))
out = BilinearSampler(data, grid)
out
`[ [`[ [ 0, 0, 0, 0],
[ 0, 3.5, 6.5, 0],
[ 0, 1.25, 2.5, 0],
[ 0, 0, 0, 0] ] ]
Example 2::
## shift data horizontally by -1 pixel
data = array(`[ [`[ [1, 4, 3, 6],
[1, 8, 8, 9],
[0, 4, 1, 5],
[1, 0, 1, 3] ] ] ])
warp_maxtrix = array(`[ [`[ [1, 1, 1, 1],
[1, 1, 1, 1],
[1, 1, 1, 1],
[1, 1, 1, 1] ],
`[ [0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0] ] ] ])
grid = GridGenerator(data=warp_matrix, transform_type='warp')
out = BilinearSampler(data, grid)
out
`[ [`[ [ 4, 3, 6, 0],
[ 8, 8, 9, 0],
[ 4, 1, 5, 0],
[ 0, 1, 3, 0] ] ]
Defined in src/operator/bilinear_sampler.cc:L256
Input data to the BilinearsamplerOp.
Input grid to the BilinearsamplerOp.grid has two channels: x_src, y_src
whether to turn cudnn off
org.apache.mxnet.Symbol
Stops gradient computation. Stops the accumulated gradient of the inputs from flowing through this operator in the backward direction. In other words, this operator prevents the contribution of its inputs to be taken into account for computing gradients. Example:: v1 = [1, 2] v2 = [0, 1] a = Variable('a') b = Variable('b') b_stop_grad = stop_gradient(3 * b) loss = MakeLoss(b_stop_grad + a) executor = loss.simple_bind(ctx=cpu(), a=(1,2), b=(1,2)) executor.forward(is_train=True, a=v1, b=v2) executor.outputs [ 1. 5.] executor.backward() executor.grad_arrays [ 0. 0.] [ 1. 1.] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L327
The input array.
org.apache.mxnet.Symbol
Connectionist Temporal Classification Loss. .. note:: The existing alias ``contrib_CTCLoss`` is deprecated. The shapes of the inputs and outputs: - **data**: `(sequence_length, batch_size, alphabet_size)` - **label**: `(batch_size, label_sequence_length)` - **out**: `(batch_size)` The `data` tensor consists of sequences of activation vectors (without applying softmax), with i-th channel in the last dimension corresponding to i-th label for i between 0 and alphabet_size-1 (i.e always 0-indexed). Alphabet size should include one additional value reserved for blank label. When `blank_label` is ``"first"``, the ``0``-th channel is be reserved for activation of blank label, or otherwise if it is "last", ``(alphabet_size-1)``-th channel should be reserved for blank label. ``label`` is an index matrix of integers. When `blank_label` is ``"first"``, the value 0 is then reserved for blank label, and should not be passed in this matrix. Otherwise, when `blank_label` is ``"last"``, the value `(alphabet_size-1)` is reserved for blank label. If a sequence of labels is shorter than *label_sequence_length*, use the special padding value at the end of the sequence to conform it to the correct length. The padding value is `0` when `blank_label` is ``"first"``, and `-1` otherwise. For example, suppose the vocabulary is `[a, b, c]`, and in one batch we have three sequences 'ba', 'cbb', and 'abac'. When `blank_label` is ``"first"``, we can index the labels as `{'a': 1, 'b': 2, 'c': 3}`, and we reserve the 0-th channel for blank label in data tensor. The resulting `label` tensor should be padded to be:: `[ [2, 1, 0, 0], [3, 2, 2, 0], [1, 2, 1, 3] ] When `blank_label` is ``"last"``, we can index the labels as `{'a': 0, 'b': 1, 'c': 2}`, and we reserve the channel index 3 for blank label in data tensor. The resulting `label` tensor should be padded to be:: `[ [1, 0, -1, -1], [2, 1, 1, -1], [0, 1, 0, 2] ] ``out`` is a list of CTC loss values, one per example in the batch. See *Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks*, A. Graves *et al*. for more information on the definition and the algorithm. Defined in src/operator/nn/ctc_loss.cc:L100
Input ndarray
Ground-truth labels for the loss.
Lengths of data for each of the samples. Only required when use_data_lengths is true.
Lengths of labels for each of the samples. Only required when use_label_lengths is true.
Whether the data lenghts are decided by data_lengths
. If false, the lengths are equal to the max sequence length.
Whether the label lenghts are decided by label_lengths
, or derived from padding_mask
. If false, the lengths are derived from the first occurrence of the value of padding_mask
. The value of padding_mask
is
when first CTC label is reserved for blank, and 0
when last label is reserved for blank. See -1
blank_label
.
Set the label that is reserved for blank label.If "first", 0-th label is reserved, and label values for tokens in the vocabulary are between
and 1
, and the padding mask is alphabet_size-1
. If "last", last label value -1
is reserved for blank label instead, and label values for tokens in the vocabulary are between alphabet_size-1
and 0
, and the padding mask is alphabet_size-2
.0
org.apache.mxnet.Symbol
Casts all elements of the input to a new type. .. note:: ``Cast`` is deprecated. Use ``cast`` instead. Example:: cast([0.9, 1.3], dtype='int32') = [0, 1] cast([1e20, 11.1], dtype='float16') = [inf, 11.09375] cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L665
The input.
Output data type.
org.apache.mxnet.Symbol
Joins input arrays along a given axis. .. note:: `Concat` is deprecated. Use `concat` instead. The dimensions of the input arrays should be the same except the axis along which they will be concatenated. The dimension of the output array along the concatenated axis will be equal to the sum of the corresponding dimensions of the input arrays. The storage type of ``concat`` output depends on storage types of inputs - concat(csr, csr, ..., csr, dim=0) = csr - otherwise, ``concat`` generates output with default storage Example:: x = `[ [1,1],[2,2] ] y = `[ [3,3],[4,4],[5,5] ] z = `[ [6,6], [7,7],[8,8] ] concat(x,y,z,dim=0) = `[ [ 1., 1.], [ 2., 2.], [ 3., 3.], [ 4., 4.], [ 5., 5.], [ 6., 6.], [ 7., 7.], [ 8., 8.] ] Note that you cannot concat x,y,z along dimension 1 since dimension 0 is not the same for all the input arrays. concat(y,z,dim=1) = `[ [ 3., 3., 6., 6.], [ 4., 4., 7., 7.], [ 5., 5., 8., 8.] ] Defined in src/operator/nn/concat.cc:L383
List of arrays to concatenate
Number of inputs to be concated.
the dimension to be concated.
org.apache.mxnet.Symbol
Compute *N*-D convolution on *(N+2)*-D input. In the 2-D convolution, given input data with shape *(batch_size, channel, height, width)*, the output is computed by .. math:: out[n,i,:,:] = bias[i] + \sum_{j=0}^{channel} data[n,j,:,:] \star weight[i,j,:,:] where :math:`\star` is the 2-D cross-correlation operator. For general 2-D convolution, the shapes are - **data**: *(batch_size, channel, height, width)* - **weight**: *(num_filter, channel, kernel[0], kernel[1])* - **bias**: *(num_filter,)* - **out**: *(batch_size, num_filter, out_height, out_width)*. Define:: f(x,k,p,s,d) = floor((x+2*p-d*(k-1)-1)/s)+1 then we have:: out_height=f(height, kernel[0], pad[0], stride[0], dilate[0]) out_width=f(width, kernel[1], pad[1], stride[1], dilate[1]) If ``no_bias`` is set to be true, then the ``bias`` term is ignored. The default data ``layout`` is *NCHW*, namely *(batch_size, channel, height, width)*. We can choose other layouts such as *NWC*. If ``num_group`` is larger than 1, denoted by *g*, then split the input ``data`` evenly into *g* parts along the channel axis, and also evenly split ``weight`` along the first dimension. Next compute the convolution on the *i*-th part of the data with the *i*-th weight part. The output is obtained by concatenating all the *g* results. 1-D convolution does not have *height* dimension but only *width* in space. - **data**: *(batch_size, channel, width)* - **weight**: *(num_filter, channel, kernel[0])* - **bias**: *(num_filter,)* - **out**: *(batch_size, num_filter, out_width)*. 3-D convolution adds an additional *depth* dimension besides *height* and *width*. The shapes are - **data**: *(batch_size, channel, depth, height, width)* - **weight**: *(num_filter, channel, kernel[0], kernel[1], kernel[2])* - **bias**: *(num_filter,)* - **out**: *(batch_size, num_filter, out_depth, out_height, out_width)*. Both ``weight`` and ``bias`` are learnable parameters. There are other options to tune the performance. - **cudnn_tune**: enable this option leads to higher startup time but may give faster speed. Options are - **off**: no tuning - **limited_workspace**:run test and pick the fastest algorithm that doesn't exceed workspace limit. - **fastest**: pick the fastest algorithm and ignore workspace limit. - **None** (default): the behavior is determined by environment variable ``MXNET_CUDNN_AUTOTUNE_DEFAULT``. 0 for off, 1 for limited workspace (default), 2 for fastest. - **workspace**: A large number leads to more (GPU) memory usage but may improve the performance. Defined in src/operator/nn/convolution.cc:L473
Input data to the ConvolutionOp.
Weight matrix.
Bias parameter.
Convolution kernel size: (w,), (h, w) or (d, h, w)
Convolution stride: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension.
Convolution dilate: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension.
Zero pad for convolution: (w,), (h, w) or (d, h, w). Defaults to no padding.
Convolution filter(channel) number
Number of group partitions.
Maximum temporary workspace allowed (MB) in convolution.This parameter has two usages. When CUDNN is not used, it determines the effective batch size of the convolution kernel. When CUDNN is used, it controls the maximum temporary storage used for tuning the best CUDNN kernel when limited_workspace
strategy is used.
Whether to disable bias parameter.
Whether to pick convolution algo by running performance test.
Turn off cudnn for this layer.
Set layout for input, output and weight. Empty for default layout: NCW for 1d, NCHW for 2d and NCDHW for 3d.NHWC and NDHWC are only supported on GPU.
org.apache.mxnet.Symbol
This operator is DEPRECATED. Apply convolution to input then add a bias.
Input data to the ConvolutionV1Op.
Weight matrix.
Bias parameter.
convolution kernel size: (h, w) or (d, h, w)
convolution stride: (h, w) or (d, h, w)
convolution dilate: (h, w) or (d, h, w)
pad for convolution: (h, w) or (d, h, w)
convolution filter(channel) number
Number of group partitions. Equivalent to slicing input into num_group partitions, apply convolution on each, then concatenate the results
Maximum temporary workspace allowed for convolution (MB).This parameter determines the effective batch size of the convolution kernel, which may be smaller than the given batch size. Also, the workspace will be automatically enlarged to make sure that we can run the kernel with batch_size=1
Whether to disable bias parameter.
Whether to pick convolution algo by running performance test. Leads to higher startup time but may give faster speed. Options are: 'off': no tuning 'limited_workspace': run test and pick the fastest algorithm that doesn't exceed workspace limit. 'fastest': pick the fastest algorithm and ignore workspace limit. If set to None (default), behavior is determined by environment variable MXNET_CUDNN_AUTOTUNE_DEFAULT: 0 for off, 1 for limited workspace (default), 2 for fastest.
Turn off cudnn for this layer.
Set layout for input, output and weight. Empty for default layout: NCHW for 2d and NCDHW for 3d.
org.apache.mxnet.Symbol
Applies correlation to inputs. The correlation layer performs multiplicative patch comparisons between two feature maps. Given two multi-channel feature maps :math:`f_{1}, f_{2}`, with :math:`w`, :math:`h`, and :math:`c` being their width, height, and number of channels, the correlation layer lets the network compare each patch from :math:`f_{1}` with each patch from :math:`f_{2}`. For now we consider only a single comparison of two patches. The 'correlation' of two patches centered at :math:`x_{1}` in the first map and :math:`x_{2}` in the second map is then defined as: .. math:: c(x_{1}, x_{2}) = \sum_{o \in [-k,k] \times [-k,k]} <f_{1}(x_{1} + o), f_{2}(x_{2} + o)> for a square patch of size :math:`K:=2k+1`. Note that the equation above is identical to one step of a convolution in neural networks, but instead of convolving data with a filter, it convolves data with other data. For this reason, it has no training weights. Computing :math:`c(x_{1}, x_{2})` involves :math:`c * K^{2}` multiplications. Comparing all patch combinations involves :math:`w^{2}*h^{2}` such computations. Given a maximum displacement :math:`d`, for each location :math:`x_{1}` it computes correlations :math:`c(x_{1}, x_{2})` only in a neighborhood of size :math:`D:=2d+1`, by limiting the range of :math:`x_{2}`. We use strides :math:`s_{1}, s_{2}`, to quantize :math:`x_{1}` globally and to quantize :math:`x_{2}` within the neighborhood centered around :math:`x_{1}`. The final output is defined by the following expression: .. math:: out[n, q, i, j] = c(x_{i, j}, x_{q}) where :math:`i` and :math:`j` enumerate spatial locations in :math:`f_{1}`, and :math:`q` denotes the :math:`q^{th}` neighborhood of :math:`x_{i,j}`. Defined in src/operator/correlation.cc:L198
Input data1 to the correlation.
Input data2 to the correlation.
kernel size for Correlation must be an odd number
Max displacement of Correlation
stride1 quantize data1 globally
stride2 quantize data2 within the neighborhood centered around data1
pad for Correlation
operation type is either multiplication or subduction
org.apache.mxnet.Symbol
.. note:: `Crop` is deprecated. Use `slice` instead. Crop the 2nd and 3rd dim of input data, with the corresponding size of h_w or with width and height of the second input symbol, i.e., with one input, we need h_w to specify the crop height and width, otherwise the second input symbol's size will be used Defined in src/operator/crop.cc:L50
Tensor or List of Tensors, the second input will be used as crop_like shape reference
Number of inputs for crop, if equals one, then we will use the h_wfor crop height and width, else if equals two, then we will use the heightand width of the second input symbol, we name crop_like here
crop offset coordinate: (y, x)
crop height and width: (h, w)
If set to true, then it will use be the center_crop,or it will crop using the shape of crop_like
org.apache.mxnet.Symbol
Computes 1D or 2D transposed convolution (aka fractionally strided convolution) of the input tensor. This operation can be seen as the gradient of Convolution operation with respect to its input. Convolution usually reduces the size of the input. Transposed convolution works the other way, going from a smaller input to a larger output while preserving the connectivity pattern.
Input tensor to the deconvolution operation.
Weights representing the kernel.
Bias added to the result after the deconvolution operation.
Deconvolution kernel size: (w,), (h, w) or (d, h, w). This is same as the kernel size used for the corresponding convolution
The stride used for the corresponding convolution: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension.
Dilation factor for each dimension of the input: (w,), (h, w) or (d, h, w). Defaults to 1 for each dimension.
The amount of implicit zero padding added during convolution for each dimension of the input: (w,), (h, w) or (d, h, w).
is usually a good choice. If (kernel-1)/2
target_shape
is set, pad
will be ignored and a padding that will generate the target shape will be used. Defaults to no padding.
Adjustment for output shape: (w,), (h, w) or (d, h, w). If target_shape
is set, adj
will be ignored and computed accordingly.
Shape of the output tensor: (w,), (h, w) or (d, h, w).
Number of output filters.
Number of groups partition.
Maximum temporary workspace allowed (MB) in deconvolution.This parameter has two usages. When CUDNN is not used, it determines the effective batch size of the deconvolution kernel. When CUDNN is used, it controls the maximum temporary storage used for tuning the best CUDNN kernel when limited_workspace
strategy is used.
Whether to disable bias parameter.
Whether to pick convolution algorithm by running performance test.
Turn off cudnn for this layer.
Set layout for input, output and weight. Empty for default layout, NCW for 1d, NCHW for 2d and NCDHW for 3d.NHWC and NDHWC are only supported on GPU.
org.apache.mxnet.Symbol
Applies dropout operation to input array. - During training, each element of the input is set to zero with probability p. The whole array is rescaled by :math:`1/(1-p)` to keep the expected sum of the input unchanged. - During testing, this operator does not change the input if mode is 'training'. If mode is 'always', the same computaion as during training will be applied. Example:: random.seed(998) input_array = array(`[ [3., 0.5, -0.5, 2., 7.], [2., -0.4, 7., 3., 0.2] ]) a = symbol.Variable('a') dropout = symbol.Dropout(a, p = 0.2) executor = dropout.simple_bind(a = input_array.shape) ## If training executor.forward(is_train = True, a = input_array) executor.outputs `[ [ 3.75 0.625 -0. 2.5 8.75 ] [ 2.5 -0.5 8.75 3.75 0. ] ] ## If testing executor.forward(is_train = False, a = input_array) executor.outputs `[ [ 3. 0.5 -0.5 2. 7. ] [ 2. -0.4 7. 3. 0.2 ] ] Defined in src/operator/nn/dropout.cc:L96
Input array to which dropout will be applied.
Fraction of the input that gets dropped out during training time.
Whether to only turn on dropout during training or to also turn on for inference.
Axes for variational dropout kernel.
Whether to turn off cudnn in dropout operator. This option is ignored if axes is specified.
org.apache.mxnet.Symbol
Adds all input arguments element-wise. .. math:: add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n ``add_n`` is potentially more efficient than calling ``add`` by `n` times. The storage type of ``add_n`` output depends on storage types of inputs - add_n(row_sparse, row_sparse, ..) = row_sparse - add_n(default, csr, default) = default - add_n(any input combinations longer than 4 (>4) with at least one default type) = default - otherwise, ``add_n`` falls all inputs back to default storage and generates default storage Defined in src/operator/tensor/elemwise_sum.cc:L155
Positional input arguments
org.apache.mxnet.Symbol
Maps integer indices to vector representations (embeddings). This operator maps words to real-valued vectors in a high-dimensional space, called word embeddings. These embeddings can capture semantic and syntactic properties of the words. For example, it has been noted that in the learned embedding spaces, similar words tend to be close to each other and dissimilar words far apart. For an input array of shape (d1, ..., dK), the shape of an output array is (d1, ..., dK, output_dim). All the input values should be integers in the range [0, input_dim). If the input_dim is ip0 and output_dim is op0, then shape of the embedding weight matrix must be (ip0, op0). When "sparse_grad" is False, if any index mentioned is too large, it is replaced by the index that addresses the last vector in an embedding matrix. When "sparse_grad" is True, an error will be raised if invalid indices are found. Examples:: input_dim = 4 output_dim = 5 // Each row in weight matrix y represents a word. So, y = (w0,w1,w2,w3) y = `[ [ 0., 1., 2., 3., 4.], [ 5., 6., 7., 8., 9.], [ 10., 11., 12., 13., 14.], [ 15., 16., 17., 18., 19.] ] // Input array x represents n-grams(2-gram). So, x = [(w1,w3), (w0,w2)] x = `[ [ 1., 3.], [ 0., 2.] ] // Mapped input x to its vector representation y. Embedding(x, y, 4, 5) = `[ `[ [ 5., 6., 7., 8., 9.], [ 15., 16., 17., 18., 19.] ], `[ [ 0., 1., 2., 3., 4.], [ 10., 11., 12., 13., 14.] ] ] The storage type of weight can be either row_sparse or default. .. Note:: If "sparse_grad" is set to True, the storage type of gradient w.r.t weights will be "row_sparse". Only a subset of optimizers support sparse gradients, including SGD, AdaGrad and Adam. Note that by default lazy updates is turned on, which may perform differently from standard updates. For more details, please check the Optimization API at: https://mxnet.incubator.apache.org/api/python/optimization/optimization.html Defined in src/operator/tensor/indexing_op.cc:L539
The input array to the embedding operator.
The embedding weight matrix.
Vocabulary size of the input indices.
Dimension of the embedding vectors.
Data type of weight.
Compute row sparse gradient in the backward calculation. If set to True, the grad's storage type is row_sparse.
org.apache.mxnet.Symbol
Flattens the input array into a 2-D array by collapsing the higher dimensions. .. note:: `Flatten` is deprecated. Use `flatten` instead. For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes the input array into an output array of shape ``(d1, d2*...*dk)``. Note that the behavior of this function is different from numpy.ndarray.flatten, which behaves similar to mxnet.ndarray.reshape((-1,)). Example:: x = `[ [ [1,2,3], [4,5,6], [7,8,9] ], [ [1,2,3], [4,5,6], [7,8,9] ] ], flatten(x) = `[ [ 1., 2., 3., 4., 5., 6., 7., 8., 9.], [ 1., 2., 3., 4., 5., 6., 7., 8., 9.] ] Defined in src/operator/tensor/matrix_op.cc:L250
Input array.
org.apache.mxnet.Symbol
Applies a linear transformation: :math:`Y = XW^T + b`. If ``flatten`` is set to be true, then the shapes are: - **data**: `(batch_size, x1, x2, ..., xn)` - **weight**: `(num_hidden, x1 * x2 * ... * xn)` - **bias**: `(num_hidden,)` - **out**: `(batch_size, num_hidden)` If ``flatten`` is set to be false, then the shapes are: - **data**: `(x1, x2, ..., xn, input_dim)` - **weight**: `(num_hidden, input_dim)` - **bias**: `(num_hidden,)` - **out**: `(x1, x2, ..., xn, num_hidden)` The learnable parameters include both ``weight`` and ``bias``. If ``no_bias`` is set to be true, then the ``bias`` term is ignored. .. Note:: The sparse support for FullyConnected is limited to forward evaluation with `row_sparse` weight and bias, where the length of `weight.indices` and `bias.indices` must be equal to `num_hidden`. This could be useful for model inference with `row_sparse` weights trained with importance sampling or noise contrastive estimation. To compute linear transformation with 'csr' sparse data, sparse.dot is recommended instead of sparse.FullyConnected. Defined in src/operator/nn/fully_connected.cc:L291
Input data.
Weight matrix.
Bias parameter.
Number of hidden nodes of the output.
Whether to disable bias parameter.
Whether to collapse all but the first axis of the input data tensor.
org.apache.mxnet.Symbol
Generates 2D sampling grid for bilinear sampling.
Input data to the function.
The type of transformation. For affine
, input data should be an affine matrix of size (batch, 6). For warp
, input data should be an optical flow of size (batch, 2, h, w).
Specifies the output shape (H, W). This is required if transformation type is affine
. If transformation type is warp
, this parameter is ignored.
org.apache.mxnet.Symbol
Group normalization. The input channels are separated into ``num_groups`` groups, each containing ``num_channels / num_groups`` channels. The mean and standard-deviation are calculated separately over the each group. .. math:: data = data.reshape((N, num_groups, C // num_groups, ...)) out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma + beta Both ``gamma`` and ``beta`` are learnable parameters. Defined in src/operator/nn/group_norm.cc:L77
Input data
gamma array
beta array
Total number of groups.
An epsilon
parameter to prevent division by 0.
Output the mean and std calculated along the given axis.
org.apache.mxnet.Symbol
Apply a sparse regularization to the output a sigmoid activation function.
Input data.
The sparseness target
The tradeoff parameter for the sparseness penalty
The momentum for running average
org.apache.mxnet.Symbol
Applies instance normalization to the n-dimensional input array. This operator takes an n-dimensional input array where (n>2) and normalizes the input using the following formula: .. math:: out = \frac{x - mean[data]}{ \sqrt{Var[data]} + \epsilon} * gamma + beta This layer is similar to batch normalization layer (`BatchNorm`) with two differences: first, the normalization is carried out per example (instance), not over a batch. Second, the same normalization is applied both at test and train time. This operation is also known as `contrast normalization`. If the input data is of shape [batch, channel, spacial_dim1, spacial_dim2, ...], `gamma` and `beta` parameters must be vectors of shape [channel]. This implementation is based on this paper [1]_ .. [1] Instance Normalization: The Missing Ingredient for Fast Stylization, D. Ulyanov, A. Vedaldi, V. Lempitsky, 2016 (arXiv:1607.08022v2). Examples:: // Input of shape (2,1,2) x = `[ `[ [ 1.1, 2.2] ], `[ [ 3.3, 4.4] ] ] // gamma parameter of length 1 gamma = [1.5] // beta parameter of length 1 beta = [0.5] // Instance normalization is calculated with the above formula InstanceNorm(x,gamma,beta) = `[ `[ [-0.997527 , 1.99752665] ], `[ [-0.99752653, 1.99752724] ] ] Defined in src/operator/instance_norm.cc:L95
An n-dimensional input array (n > 2) of the form [batch, channel, spatial_dim1, spatial_dim2, ...].
A vector of length 'channel', which multiplies the normalized input.
A vector of length 'channel', which is added to the product of the normalized input and the weight.
An epsilon
parameter to prevent division by 0.
org.apache.mxnet.Symbol
Normalize the input array using the L2 norm. For 1-D NDArray, it computes:: out = data / sqrt(sum(data ** 2) + eps) For N-D NDArray, if the input array has shape (N, N, ..., N), with ``mode`` = ``instance``, it normalizes each instance in the multidimensional array by its L2 norm.:: for i in 0...N out[i,:,:,...,:] = data[i,:,:,...,:] / sqrt(sum(data[i,:,:,...,:] ** 2) + eps) with ``mode`` = ``channel``, it normalizes each channel in the array by its L2 norm.:: for i in 0...N out[:,i,:,...,:] = data[:,i,:,...,:] / sqrt(sum(data[:,i,:,...,:] ** 2) + eps) with ``mode`` = ``spatial``, it normalizes the cross channel norm for each position in the array by its L2 norm.:: for dim in 2...N for i in 0...N out[.....,i,...] = take(out, indices=i, axis=dim) / sqrt(sum(take(out, indices=i, axis=dim) ** 2) + eps) -dim- Example:: x = `[ `[ [1,2], [3,4] ], `[ [2,2], [5,6] ] ] L2Normalization(x, mode='instance') =`[ `[ [ 0.18257418 0.36514837] [ 0.54772252 0.73029673] ] `[ [ 0.24077171 0.24077171] [ 0.60192931 0.72231513] ] ] L2Normalization(x, mode='channel') =`[ `[ [ 0.31622776 0.44721359] [ 0.94868326 0.89442718] ] `[ [ 0.37139067 0.31622776] [ 0.92847669 0.94868326] ] ] L2Normalization(x, mode='spatial') =`[ `[ [ 0.44721359 0.89442718] [ 0.60000002 0.80000001] ] `[ [ 0.70710677 0.70710677] [ 0.6401844 0.76822126] ] ] Defined in src/operator/l2_normalization.cc:L196
Input array to normalize.
A small constant for numerical stability.
Specify the dimension along which to compute L2 norm.
org.apache.mxnet.Symbol
Applies local response normalization to the input. The local response normalization layer performs "lateral inhibition" by normalizing over local input regions. If :math:`a_{x,y}^{i}` is the activity of a neuron computed by applying kernel :math:`i` at position :math:`(x, y)` and then applying the ReLU nonlinearity, the response-normalized activity :math:`b_{x,y}^{i}` is given by the expression: .. math:: b_{x,y}^{i} = \frac{a_{x,y}^{i}}{\Bigg({k + \frac{\alpha}{n} \sum_{j=max(0, i-\frac{n}{2})}^{min(N-1, i+\frac{n}{2})} (a_{x,y}^{j})^{2}}\Bigg)^{\beta}} where the sum runs over :math:`n` "adjacent" kernel maps at the same spatial position, and :math:`N` is the total number of kernels in the layer. Defined in src/operator/nn/lrn.cc:L164
Input data to LRN
The variance scaling parameter :math:lpha
in the LRN expression.
The power parameter :math:eta
in the LRN expression.
The parameter :math:k
in the LRN expression.
normalization window width in elements.
org.apache.mxnet.Symbol
Layer normalization. Normalizes the channels of the input tensor by mean and variance, and applies a scale ``gamma`` as well as offset ``beta``. Assume the input has more than one dimension and we normalize along axis 1. We first compute the mean and variance along this axis and then compute the normalized output, which has the same shape as input, as following: .. math:: out = \frac{data - mean(data, axis)}{\sqrt{var(data, axis) + \epsilon}} * gamma + beta Both ``gamma`` and ``beta`` are learnable parameters. Unlike BatchNorm and InstanceNorm, the *mean* and *var* are computed along the channel dimension. Assume the input has size *k* on axis 1, then both ``gamma`` and ``beta`` have shape *(k,)*. If ``output_mean_var`` is set to be true, then outputs both ``data_mean`` and ``data_std``. Note that no gradient will be passed through these two outputs. The parameter ``axis`` specifies which axis of the input shape denotes the 'channel' (separately normalized groups). The default is -1, which sets the channel axis to be the last item in the input shape. Defined in src/operator/nn/layer_norm.cc:L156
Input data to layer normalization
gamma array
beta array
The axis to perform layer normalization. Usually, this should be be axis of the channel dimension. Negative values means indexing from right to left.
An epsilon
parameter to prevent division by 0.
Output the mean and std calculated along the given axis.
org.apache.mxnet.Symbol
Applies Leaky rectified linear unit activation element-wise to the input. Leaky ReLUs attempt to fix the "dying ReLU" problem by allowing a small `slope` when the input is negative and has a slope of one when input is positive. The following modified ReLU Activation functions are supported: - *elu*: Exponential Linear Unit. `y = x > 0 ? x : slope * (exp(x)-1)` - *selu*: Scaled Exponential Linear Unit. `y = lambda * (x > 0 ? x : alpha * (exp(x) - 1))` where *lambda = 1.0507009873554804934193349852946* and *alpha = 1.6732632423543772848170429916717*. - *leaky*: Leaky ReLU. `y = x > 0 ? x : slope * x` - *prelu*: Parametric ReLU. This is same as *leaky* except that `slope` is learnt during training. - *rrelu*: Randomized ReLU. same as *leaky* but the `slope` is uniformly and randomly chosen from *[lower_bound, upper_bound)* for training, while fixed to be *(lower_bound+upper_bound)/2* for inference. Defined in src/operator/leaky_relu.cc:L161
Input data to activation function.
Input data to activation function.
Activation function to be applied.
Init slope for the activation. (For leaky and elu only)
Lower bound of random slope. (For rrelu only)
Upper bound of random slope. (For rrelu only)
org.apache.mxnet.Symbol
Computes and optimizes for squared loss during backward propagation. Just outputs ``data`` during forward propagation. If :math:`\hat{y}_i` is the predicted value of the i-th sample, and :math:`y_i` is the corresponding target value, then the squared loss estimated over :math:`n` samples is defined as :math:`\text{SquaredLoss}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert \textbf{y}_i - \hat{\textbf{y}}_i \rVert_2` .. note:: Use the LinearRegressionOutput as the final output layer of a net. The storage type of ``label`` can be ``default`` or ``csr`` - LinearRegressionOutput(default, default) = default - LinearRegressionOutput(default, csr) = default By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example. The parameter `grad_scale` can be used to change this scale to `grad_scale/m`. Defined in src/operator/regression_output.cc:L92
Input data to the function.
Input label to the function.
Scale the gradient by a float factor
org.apache.mxnet.Symbol
Applies a logistic function to the input. The logistic function, also known as the sigmoid function, is computed as :math:`\frac{1}{1+exp(-\textbf{x})}`. Commonly, the sigmoid is used to squash the real-valued output of a linear model :math:`wTx+b` into the [0,1] range so that it can be interpreted as a probability. It is suitable for binary classification or probability prediction tasks. .. note:: Use the LogisticRegressionOutput as the final output layer of a net. The storage type of ``label`` can be ``default`` or ``csr`` - LogisticRegressionOutput(default, default) = default - LogisticRegressionOutput(default, csr) = default The loss function used is the Binary Cross Entropy Loss: :math:`-{(y\log(p) + (1 - y)\log(1 - p))}` Where `y` is the ground truth probability of positive outcome for a given example, and `p` the probability predicted by the model. By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example. The parameter `grad_scale` can be used to change this scale to `grad_scale/m`. Defined in src/operator/regression_output.cc:L152
Input data to the function.
Input label to the function.
Scale the gradient by a float factor
org.apache.mxnet.Symbol
Computes mean absolute error of the input. MAE is a risk metric corresponding to the expected value of the absolute error. If :math:`\hat{y}_i` is the predicted value of the i-th sample, and :math:`y_i` is the corresponding target value, then the mean absolute error (MAE) estimated over :math:`n` samples is defined as :math:`\text{MAE}(\textbf{Y}, \hat{\textbf{Y}} ) = \frac{1}{n} \sum_{i=0}^{n-1} \lVert \textbf{y}_i - \hat{\textbf{y}}_i \rVert_1` .. note:: Use the MAERegressionOutput as the final output layer of a net. The storage type of ``label`` can be ``default`` or ``csr`` - MAERegressionOutput(default, default) = default - MAERegressionOutput(default, csr) = default By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example. The parameter `grad_scale` can be used to change this scale to `grad_scale/m`. Defined in src/operator/regression_output.cc:L120
Input data to the function.
Input label to the function.
Scale the gradient by a float factor
org.apache.mxnet.Symbol
Make your own loss function in network construction. This operator accepts a customized loss function symbol as a terminal loss and the symbol should be an operator with no backward dependency. The output of this function is the gradient of loss with respect to the input data. For example, if you are a making a cross entropy loss function. Assume ``out`` is the predicted output and ``label`` is the true label, then the cross entropy can be defined as:: cross_entropy = label * log(out) + (1 - label) * log(1 - out) loss = MakeLoss(cross_entropy) We will need to use ``MakeLoss`` when we are creating our own loss function or we want to combine multiple loss functions. Also we may want to stop some variables' gradients from backpropagation. See more detail in ``BlockGrad`` or ``stop_gradient``. In addition, we can give a scale to the loss by setting ``grad_scale``, so that the gradient of the loss will be rescaled in the backpropagation. .. note:: This operator should be used as a Symbol instead of NDArray. Defined in src/operator/make_loss.cc:L71
Input array.
Gradient scale as a supplement to unary and binary operators
clip each element in the array to 0 when it is less than
. This is used when valid_thresh
is set to normalization
.'valid'
If this is set to null, the output gradient will not be normalized. If this is set to batch, the output gradient will be divided by the batch size. If this is set to valid, the output gradient will be divided by the number of valid input elements.
org.apache.mxnet.Symbol
Pads an input array with a constant or edge values of the array. .. note:: `Pad` is deprecated. Use `pad` instead. .. note:: Current implementation only supports 4D and 5D input arrays with padding applied only on axes 1, 2 and 3. Expects axes 4 and 5 in `pad_width` to be zero. This operation pads an input array with either a `constant_value` or edge values along each axis of the input array. The amount of padding is specified by `pad_width`. `pad_width` is a tuple of integer padding widths for each axis of the format ``(before_1, after_1, ... , before_N, after_N)``. The `pad_width` should be of length ``2*N`` where ``N`` is the number of dimensions of the array. For dimension ``N`` of the input array, ``before_N`` and ``after_N`` indicates how many values to add before and after the elements of the array along dimension ``N``. The widths of the higher two dimensions ``before_1``, ``after_1``, ``before_2``, ``after_2`` must be 0. Example:: x = `[ [`[ [ 1. 2. 3.] [ 4. 5. 6.] ] `[ [ 7. 8. 9.] [ 10. 11. 12.] ] ] `[ `[ [ 11. 12. 13.] [ 14. 15. 16.] ] `[ [ 17. 18. 19.] [ 20. 21. 22.] ] ] ] pad(x,mode="edge", pad_width=(0,0,0,0,1,1,1,1)) = `[ [`[ [ 1. 1. 2. 3. 3.] [ 1. 1. 2. 3. 3.] [ 4. 4. 5. 6. 6.] [ 4. 4. 5. 6. 6.] ] `[ [ 7. 7. 8. 9. 9.] [ 7. 7. 8. 9. 9.] [ 10. 10. 11. 12. 12.] [ 10. 10. 11. 12. 12.] ] ] `[ `[ [ 11. 11. 12. 13. 13.] [ 11. 11. 12. 13. 13.] [ 14. 14. 15. 16. 16.] [ 14. 14. 15. 16. 16.] ] `[ [ 17. 17. 18. 19. 19.] [ 17. 17. 18. 19. 19.] [ 20. 20. 21. 22. 22.] [ 20. 20. 21. 22. 22.] ] ] ] pad(x, mode="constant", constant_value=0, pad_width=(0,0,0,0,1,1,1,1)) = `[ [`[ [ 0. 0. 0. 0. 0.] [ 0. 1. 2. 3. 0.] [ 0. 4. 5. 6. 0.] [ 0. 0. 0. 0. 0.] ] `[ [ 0. 0. 0. 0. 0.] [ 0. 7. 8. 9. 0.] [ 0. 10. 11. 12. 0.] [ 0. 0. 0. 0. 0.] ] ] `[ `[ [ 0. 0. 0. 0. 0.] [ 0. 11. 12. 13. 0.] [ 0. 14. 15. 16. 0.] [ 0. 0. 0. 0. 0.] ] `[ [ 0. 0. 0. 0. 0.] [ 0. 17. 18. 19. 0.] [ 0. 20. 21. 22. 0.] [ 0. 0. 0. 0. 0.] ] ] ] Defined in src/operator/pad.cc:L766
An n-dimensional input array.
Padding type to use. "constant" pads with constant_value
"edge" pads using the edge values of the input array "reflect" pads by reflecting values with respect to the edges.
Widths of the padding regions applied to the edges of each axis. It is a tuple of integer padding widths for each axis of the format
. It should be of length (before_1, after_1, ... , before_N, after_N)
where 2*N
is the number of dimensions of the array.This is equivalent to pad_width in numpy.pad, but flattened.N
The value used for padding when mode
is "constant".
org.apache.mxnet.Symbol
Performs pooling on the input. The shapes for 1-D pooling are - **data** and **out**: *(batch_size, channel, width)* (NCW layout) or *(batch_size, width, channel)* (NWC layout), The shapes for 2-D pooling are - **data** and **out**: *(batch_size, channel, height, width)* (NCHW layout) or *(batch_size, height, width, channel)* (NHWC layout), out_height = f(height, kernel[0], pad[0], stride[0]) out_width = f(width, kernel[1], pad[1], stride[1]) The definition of *f* depends on ``pooling_convention``, which has two options: - **valid** (default):: f(x, k, p, s) = floor((x+2*p-k)/s)+1 - **full**, which is compatible with Caffe:: f(x, k, p, s) = ceil((x+2*p-k)/s)+1 When ``global_pool`` is set to be true, then global pooling is performed. It will reset ``kernel=(height, width)`` and set the appropiate padding to 0. Three pooling options are supported by ``pool_type``: - **avg**: average pooling - **max**: max pooling - **sum**: sum pooling - **lp**: Lp pooling For 3-D pooling, an additional *depth* dimension is added before *height*. Namely the input data and output will have shape *(batch_size, channel, depth, height, width)* (NCDHW layout) or *(batch_size, depth, height, width, channel)* (NDHWC layout). Notes on Lp pooling: Lp pooling was first introduced by this paper: https://arxiv.org/pdf/1204.3968.pdf. L-1 pooling is simply sum pooling, while L-inf pooling is simply max pooling. We can see that Lp pooling stands between those two, in practice the most common value for p is 2. For each window ``X``, the mathematical expression for Lp pooling is: :math:`f(X) = \sqrt[p]{\sum_{x}^{X} x^p}` Defined in src/operator/nn/pooling.cc:L417
Input data to the pooling operator.
Pooling kernel size: (y, x) or (d, y, x)
Pooling type to be applied.
Ignore kernel size, do global pooling based on current input feature map.
Turn off cudnn pooling and use MXNet pooling operator.
Pooling convention to be applied.
Stride: for pooling (y, x) or (d, y, x). Defaults to 1 for each dimension.
Pad for pooling: (y, x) or (d, y, x). Defaults to no padding.
Value of p for Lp pooling, can be 1 or 2, required for Lp Pooling.
Only used for AvgPool, specify whether to count padding elements for averagecalculation. For example, with a 5*5 kernel on a 3*3 corner of a image,the sum of the 9 valid elements will be divided by 25 if this is set to true,or it will be divided by 9 if this is set to false. Defaults to true.
Set layout for input and output. Empty for default layout: NCW for 1d, NCHW for 2d and NCDHW for 3d.
org.apache.mxnet.Symbol
This operator is DEPRECATED. Perform pooling on the input. The shapes for 2-D pooling is - **data**: *(batch_size, channel, height, width)* - **out**: *(batch_size, num_filter, out_height, out_width)*, with:: out_height = f(height, kernel[0], pad[0], stride[0]) out_width = f(width, kernel[1], pad[1], stride[1]) The definition of *f* depends on ``pooling_convention``, which has two options: - **valid** (default):: f(x, k, p, s) = floor((x+2*p-k)/s)+1 - **full**, which is compatible with Caffe:: f(x, k, p, s) = ceil((x+2*p-k)/s)+1 But ``global_pool`` is set to be true, then do a global pooling, namely reset ``kernel=(height, width)``. Three pooling options are supported by ``pool_type``: - **avg**: average pooling - **max**: max pooling - **sum**: sum pooling 1-D pooling is special case of 2-D pooling with *weight=1* and *kernel[1]=1*. For 3-D pooling, an additional *depth* dimension is added before *height*. Namely the input data will have shape *(batch_size, channel, depth, height, width)*. Defined in src/operator/pooling_v1.cc:L104
Input data to the pooling operator.
pooling kernel size: (y, x) or (d, y, x)
Pooling type to be applied.
Ignore kernel size, do global pooling based on current input feature map.
Pooling convention to be applied.
stride: for pooling (y, x) or (d, y, x)
pad for pooling: (y, x) or (d, y, x)
org.apache.mxnet.Symbol
Applies recurrent layers to input data. Currently, vanilla RNN, LSTM and GRU are implemented, with both multi-layer and bidirectional support. When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use pseudo-float16 precision (float32 math with float16 I/O) precision in order to use Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups. **Vanilla RNN** Applies a single-gate recurrent layer to input X. Two kinds of activation function are supported: ReLU and Tanh. With ReLU activation function: .. math:: h_t = relu(W_{ih} * x_t + b_{ih} + W_{hh} * h_{(t-1)} + b_{hh}) With Tanh activtion function: .. math:: h_t = \tanh(W_{ih} * x_t + b_{ih} + W_{hh} * h_{(t-1)} + b_{hh}) Reference paper: Finding structure in time - Elman, 1988. https://crl.ucsd.edu/~elman/Papers/fsit.pdf **LSTM** Long Short-Term Memory - Hochreiter, 1997. http://www.bioinf.jku.at/publications/older/2604.pdf .. math:: \begin{array}{ll} i_t = \mathrm{sigmoid}(W_{ii} x_t + b_{ii} + W_{hi} h_{(t-1)} + b_{hi}) \\ f_t = \mathrm{sigmoid}(W_{if} x_t + b_{if} + W_{hf} h_{(t-1)} + b_{hf}) \\ g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hc} h_{(t-1)} + b_{hg}) \\ o_t = \mathrm{sigmoid}(W_{io} x_t + b_{io} + W_{ho} h_{(t-1)} + b_{ho}) \\ c_t = f_t * c_{(t-1)} + i_t * g_t \\ h_t = o_t * \tanh(c_t) \end{array} **GRU** Gated Recurrent Unit - Cho et al. 2014. http://arxiv.org/abs/1406.1078 The definition of GRU here is slightly different from paper but compatible with CUDNN. .. math:: \begin{array}{ll} r_t = \mathrm{sigmoid}(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \\ z_t = \mathrm{sigmoid}(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \\ n_t = \tanh(W_{in} x_t + b_{in} + r_t * (W_{hn} h_{(t-1)}+ b_{hn})) \\ h_t = (1 - z_t) * n_t + z_t * h_{(t-1)} \\ \end{array} Defined in src/operator/rnn.cc:L354
Input data to RNN
Vector of all RNN trainable parameters concatenated
initial hidden state of the RNN
initial cell state for LSTM networks (only for LSTM)
Vector of valid sequence lengths for each element in batch. (Only used if use_sequence_length kwarg is True)
size of the state for each layer
number of stacked layers
whether to use bidirectional recurrent layers
the type of RNN to compute
drop rate of the dropout on the outputs of each RNN layer, except the last layer.
Whether to have the states as symbol outputs.
size of project size
Minimum clip value of LSTM states. This option must be used together with lstm_state_clip_max.
Maximum clip value of LSTM states. This option must be used together with lstm_state_clip_min.
Whether to stop NaN from propagating in state by clipping it to min/max. If clipping range is not specified, this option is ignored.
If set to true, this layer takes in an extra input parameter sequence_length
to specify variable length sequence
org.apache.mxnet.Symbol
Performs region of interest(ROI) pooling on the input array. ROI pooling is a variant of a max pooling layer, in which the output size is fixed and region of interest is a parameter. Its purpose is to perform max pooling on the inputs of non-uniform sizes to obtain fixed-size feature maps. ROI pooling is a neural-net layer mostly used in training a `Fast R-CNN` network for object detection. This operator takes a 4D feature map as an input array and region proposals as `rois`, then it pools over sub-regions of input and produces a fixed-sized output array regardless of the ROI size. To crop the feature map accordingly, you can resize the bounding box coordinates by changing the parameters `rois` and `spatial_scale`. The cropped feature maps are pooled by standard max pooling operation to a fixed size output indicated by a `pooled_size` parameter. batch_size will change to the number of region bounding boxes after `ROIPooling`. The size of each region of interest doesn't have to be perfectly divisible by the number of pooling sections(`pooled_size`). Example:: x = `[ [`[ [ 0., 1., 2., 3., 4., 5.], [ 6., 7., 8., 9., 10., 11.], [ 12., 13., 14., 15., 16., 17.], [ 18., 19., 20., 21., 22., 23.], [ 24., 25., 26., 27., 28., 29.], [ 30., 31., 32., 33., 34., 35.], [ 36., 37., 38., 39., 40., 41.], [ 42., 43., 44., 45., 46., 47.] ] ] ] // region of interest i.e. bounding box coordinates. y = `[ [0,0,0,4,4] ] // returns array of shape (2,2) according to the given roi with max pooling. ROIPooling(x, y, (2,2), 1.0) = `[ [`[ [ 14., 16.], [ 26., 28.] ] ] ] // region of interest is changed due to the change in `spacial_scale` parameter. ROIPooling(x, y, (2,2), 0.7) = `[ [`[ [ 7., 9.], [ 19., 21.] ] ] ] Defined in src/operator/roi_pooling.cc:L225
The input array to the pooling operator, a 4D Feature maps
Bounding box coordinates, a 2D array of [ [batch_index, x1, y1, x2, y2] ], where (x1, y1) and (x2, y2) are top left and bottom right corners of designated region of interest.
batch_index indicates the index of corresponding image in the input array
ROI pooling output shape (h,w)
Ratio of input feature map height (or w) to raw image height (or w). Equals the reciprocal of total stride in convolutional layers
org.apache.mxnet.Symbol
Reshapes the input array. .. note:: ``Reshape`` is deprecated, use ``reshape`` Given an array and a shape, this function returns a copy of the array in the new shape. The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array. Example:: reshape([1,2,3,4], shape=(2,2)) = `[ [1,2], [3,4] ] Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below: - ``0`` copy this dimension from the input to the output shape. Example:: - input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2) - input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4) - ``-1`` infers the dimension of the output shape by using the remainder of the input dimensions keeping the size of the new array same as that of the input array. At most one dimension of shape can be -1. Example:: - input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4) - input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8) - input shape = (2,3,4), shape=(-1,), output shape = (24,) - ``-2`` copy all/remainder of the input dimensions to the output shape. Example:: - input shape = (2,3,4), shape = (-2,), output shape = (2,3,4) - input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4) - input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1) - ``-3`` use the product of two consecutive dimensions of the input shape as the output dimension. Example:: - input shape = (2,3,4), shape = (-3,4), output shape = (6,4) - input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20) - input shape = (2,3,4), shape = (0,-3), output shape = (2,12) - input shape = (2,3,4), shape = (-3,-2), output shape = (6,4) - ``-4`` split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1). Example:: - input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4) - input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4) If the argument `reverse` is set to 1, then the special values are inferred from right to left. Example:: - without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5) - with reverse=1, output shape will be (50,4). Defined in src/operator/tensor/matrix_op.cc:L175
Input data to reshape.
The target shape
If true then the special values are inferred from right to left
(Deprecated! Use
instead.) Target new shape. One and only one dim can be 0, in which case it will be inferred from the rest of dimsshape
(Deprecated! Use
instead.) Whether keep the highest dim unchanged.If set to true, then the first dim in target_shape is ignored,and always fixed as inputshape
org.apache.mxnet.Symbol
Computes support vector machine based transformation of the input. This tutorial demonstrates using SVM as output layer for classification instead of softmax: https://github.com/dmlc/mxnet/tree/master/example/svm_mnist.
Input data for SVM transformation.
Class label for the input data.
The loss function penalizes outputs that lie outside this margin. Default margin is 1.
Regularization parameter for the SVM. This balances the tradeoff between coefficient size and error.
Whether to use L1-SVM objective. L2-SVM objective is used by default.
org.apache.mxnet.Symbol
Takes the last element of a sequence. This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] and returns a (n-1)-dimensional array of the form [batch_size, other_feature_dims]. Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length` should be an input array of positive ints of dimension [batch_size]. To use this parameter, set `use_sequence_length` to `True`, otherwise each example in the batch is assumed to have the max sequence length. .. note:: Alternatively, you can also use `take` operator. Example:: x = `[ `[ [ 1., 2., 3.], [ 4., 5., 6.], [ 7., 8., 9.] ], `[ [ 10., 11., 12.], [ 13., 14., 15.], [ 16., 17., 18.] ], `[ [ 19., 20., 21.], [ 22., 23., 24.], [ 25., 26., 27.] ] ] // returns last sequence when sequence_length parameter is not used SequenceLast(x) = `[ [ 19., 20., 21.], [ 22., 23., 24.], [ 25., 26., 27.] ] // sequence_length is used SequenceLast(x, sequence_length=[1,1,1], use_sequence_length=True) = `[ [ 1., 2., 3.], [ 4., 5., 6.], [ 7., 8., 9.] ] // sequence_length is used SequenceLast(x, sequence_length=[1,2,3], use_sequence_length=True) = `[ [ 1., 2., 3.], [ 13., 14., 15.], [ 25., 26., 27.] ] Defined in src/operator/sequence_last.cc:L106
n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] where n>2
vector of sequence lengths of the form [batch_size]
If set to true, this layer takes in an extra input parameter sequence_length
to specify variable length sequence
The sequence axis. Only values of 0 and 1 are currently supported.
org.apache.mxnet.Symbol
Sets all elements outside the sequence to a constant value. This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] and returns an array of the same shape. Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length` should be an input array of positive ints of dimension [batch_size]. To use this parameter, set `use_sequence_length` to `True`, otherwise each example in the batch is assumed to have the max sequence length and this operator works as the `identity` operator. Example:: x = `[ `[ [ 1., 2., 3.], [ 4., 5., 6.] ], `[ [ 7., 8., 9.], [ 10., 11., 12.] ], `[ [ 13., 14., 15.], [ 16., 17., 18.] ] ] // Batch 1 B1 = `[ [ 1., 2., 3.], [ 7., 8., 9.], [ 13., 14., 15.] ] // Batch 2 B2 = `[ [ 4., 5., 6.], [ 10., 11., 12.], [ 16., 17., 18.] ] // works as identity operator when sequence_length parameter is not used SequenceMask(x) = `[ `[ [ 1., 2., 3.], [ 4., 5., 6.] ], `[ [ 7., 8., 9.], [ 10., 11., 12.] ], `[ [ 13., 14., 15.], [ 16., 17., 18.] ] ] // sequence_length [1,1] means 1 of each batch will be kept // and other rows are masked with default mask value = 0 SequenceMask(x, sequence_length=[1,1], use_sequence_length=True) = `[ `[ [ 1., 2., 3.], [ 4., 5., 6.] ], `[ [ 0., 0., 0.], [ 0., 0., 0.] ], `[ [ 0., 0., 0.], [ 0., 0., 0.] ] ] // sequence_length [2,3] means 2 of batch B1 and 3 of batch B2 will be kept // and other rows are masked with value = 1 SequenceMask(x, sequence_length=[2,3], use_sequence_length=True, value=1) = `[ `[ [ 1., 2., 3.], [ 4., 5., 6.] ], `[ [ 7., 8., 9.], [ 10., 11., 12.] ], `[ [ 1., 1., 1.], [ 16., 17., 18.] ] ] Defined in src/operator/sequence_mask.cc:L186
n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] where n>2
vector of sequence lengths of the form [batch_size]
If set to true, this layer takes in an extra input parameter sequence_length
to specify variable length sequence
The value to be used as a mask.
The sequence axis. Only values of 0 and 1 are currently supported.
org.apache.mxnet.Symbol
Reverses the elements of each sequence. This function takes an n-dimensional input array of the form [max_sequence_length, batch_size, other_feature_dims] and returns an array of the same shape. Parameter `sequence_length` is used to handle variable-length sequences. `sequence_length` should be an input array of positive ints of dimension [batch_size]. To use this parameter, set `use_sequence_length` to `True`, otherwise each example in the batch is assumed to have the max sequence length. Example:: x = `[ `[ [ 1., 2., 3.], [ 4., 5., 6.] ], `[ [ 7., 8., 9.], [ 10., 11., 12.] ], `[ [ 13., 14., 15.], [ 16., 17., 18.] ] ] // Batch 1 B1 = `[ [ 1., 2., 3.], [ 7., 8., 9.], [ 13., 14., 15.] ] // Batch 2 B2 = `[ [ 4., 5., 6.], [ 10., 11., 12.], [ 16., 17., 18.] ] // returns reverse sequence when sequence_length parameter is not used SequenceReverse(x) = `[ `[ [ 13., 14., 15.], [ 16., 17., 18.] ], `[ [ 7., 8., 9.], [ 10., 11., 12.] ], `[ [ 1., 2., 3.], [ 4., 5., 6.] ] ] // sequence_length [2,2] means 2 rows of // both batch B1 and B2 will be reversed. SequenceReverse(x, sequence_length=[2,2], use_sequence_length=True) = `[ `[ [ 7., 8., 9.], [ 10., 11., 12.] ], `[ [ 1., 2., 3.], [ 4., 5., 6.] ], `[ [ 13., 14., 15.], [ 16., 17., 18.] ] ] // sequence_length [2,3] means 2 of batch B2 and 3 of batch B3 // will be reversed. SequenceReverse(x, sequence_length=[2,3], use_sequence_length=True) = `[ `[ [ 7., 8., 9.], [ 16., 17., 18.] ], `[ [ 1., 2., 3.], [ 10., 11., 12.] ], `[ [ 13., 14, 15.], [ 4., 5., 6.] ] ] Defined in src/operator/sequence_reverse.cc:L122
n-dimensional input array of the form [max_sequence_length, batch_size, other dims] where n>2
vector of sequence lengths of the form [batch_size]
If set to true, this layer takes in an extra input parameter sequence_length
to specify variable length sequence
The sequence axis. Only 0 is currently supported.
org.apache.mxnet.Symbol
Splits an array along a particular axis into multiple sub-arrays. .. note:: ``SliceChannel`` is deprecated. Use ``split`` instead. **Note** that `num_outputs` should evenly divide the length of the axis along which to split the array. Example:: x = `[ `[ [ 1.] [ 2.] ] `[ [ 3.] [ 4.] ] `[ [ 5.] [ 6.] ] ] x.shape = (3, 2, 1) y = split(x, axis=1, num_outputs=2) // a list of 2 arrays with shape (3, 1, 1) y = `[ `[ [ 1.] ] `[ [ 3.] ] `[ [ 5.] ] ] `[ `[ [ 2.] ] `[ [ 4.] ] `[ [ 6.] ] ] y[0].shape = (3, 1, 1) z = split(x, axis=0, num_outputs=3) // a list of 3 arrays with shape (1, 2, 1) z = `[ `[ [ 1.] [ 2.] ] ] `[ `[ [ 3.] [ 4.] ] ] `[ `[ [ 5.] [ 6.] ] ] z[0].shape = (1, 2, 1) `squeeze_axis=1` removes the axis with length 1 from the shapes of the output arrays. **Note** that setting `squeeze_axis` to ``1`` removes axis with length 1 only along the `axis` which it is split. Also `squeeze_axis` can be set to true only if ``input.shape[axis] == num_outputs``. Example:: z = split(x, axis=0, num_outputs=3, squeeze_axis=1) // a list of 3 arrays with shape (2, 1) z = `[ [ 1.] [ 2.] ] `[ [ 3.] [ 4.] ] `[ [ 5.] [ 6.] ] z[0].shape = (2 ,1 ) Defined in src/operator/slice_channel.cc:L107
The input
Number of splits. Note that this should evenly divide the length of the axis
.
Axis along which to split.
If true, Removes the axis with length 1 from the shapes of the output arrays. **Note** that setting squeeze_axis
to
removes axis with length 1 only along the true
axis
which it is split. Also squeeze_axis
can be set to
only if true
.input.shape[axis] == num_outputs
org.apache.mxnet.Symbol
Computes the gradient of cross entropy loss with respect to softmax output. - This operator computes the gradient in two steps. The cross entropy loss does not actually need to be computed. - Applies softmax function on the input array. - Computes and returns the gradient of cross entropy loss w.r.t. the softmax output. - The softmax function, cross entropy loss and gradient is given by: - Softmax Function: .. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)} - Cross Entropy Function: .. math:: \text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i) - The gradient of cross entropy loss w.r.t softmax output: .. math:: \text{gradient} = \text{output} - \text{label} - During forward propagation, the softmax function is computed for each instance in the input array. For general *N*-D input arrays with shape :math:`(d_1, d_2, ..., d_n)`. The size is :math:`s=d_1 \cdot d_2 \cdot \cdot \cdot d_n`. We can use the parameters `preserve_shape` and `multi_output` to specify the way to compute softmax: - By default, `preserve_shape` is ``false``. This operator will reshape the input array into a 2-D array with shape :math:`(d_1, \frac{s}{d_1})` and then compute the softmax function for each row in the reshaped array, and afterwards reshape it back to the original shape :math:`(d_1, d_2, ..., d_n)`. - If `preserve_shape` is ``true``, the softmax function will be computed along the last axis (`axis` = ``-1``). - If `multi_output` is ``true``, the softmax function will be computed along the second axis (`axis` = ``1``). - During backward propagation, the gradient of cross-entropy loss w.r.t softmax output array is computed. The provided label can be a one-hot label array or a probability label array. - If the parameter `use_ignore` is ``true``, `ignore_label` can specify input instances with a particular label to be ignored during backward propagation. **This has no effect when softmax `output` has same shape as `label`**. Example:: data = `[ [1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4] ] label = [1,0,2,3] ignore_label = 1 SoftmaxOutput(data=data, label = label,\ multi_output=true, use_ignore=true,\ ignore_label=ignore_label) ## forward softmax output `[ [ 0.0320586 0.08714432 0.23688284 0.64391428] [ 0.25 0.25 0.25 0.25 ] [ 0.25 0.25 0.25 0.25 ] [ 0.25 0.25 0.25 0.25 ] ] ## backward gradient output `[ [ 0. 0. 0. 0. ] [-0.75 0.25 0.25 0.25] [ 0.25 0.25 -0.75 0.25] [ 0.25 0.25 0.25 -0.75] ] ## notice that the first row is all 0 because label[0] is 1, which is equal to ignore_label. - The parameter `grad_scale` can be used to rescale the gradient, which is often used to give each loss function different weights. - This operator also supports various ways to normalize the gradient by `normalization`, The `normalization` is applied if softmax output has different shape than the labels. The `normalization` mode can be set to the followings: - ``'null'``: do nothing. - ``'batch'``: divide the gradient by the batch size. - ``'valid'``: divide the gradient by the number of instances which are not ignored. Defined in src/operator/softmax_output.cc:L231
Input array.
Ground truth label.
Scales the gradient by a float factor.
The instances whose labels
== ignore_label
will be ignored during backward, if use_ignore
is set to
).true
If set to
, the softmax function will be computed along axis true
. This is applied when the shape of input array differs from the shape of label array.1
If set to
, the true
ignore_label
value will not contribute to the backward gradient.
If set to
, the softmax function will be computed along the last axis (true
).-1
Normalizes the gradient.
Multiplies gradient with output gradient element-wise.
Constant for computing a label smoothed version of cross-entropyfor the backwards pass. This constant gets subtracted from theone-hot encoding of the gold label and distributed uniformly toall other labels.
org.apache.mxnet.Symbol
Applies softmax activation to input. This is intended for internal layers. .. note:: This operator has been deprecated, please use `softmax`. If `mode` = ``instance``, this operator will compute a softmax for each instance in the batch. This is the default mode. If `mode` = ``channel``, this operator will compute a k-class softmax at each position of each instance, where `k` = ``num_channel``. This mode can only be used when the input array has at least 3 dimensions. This can be used for `fully convolutional network`, `image segmentation`, etc. Example:: >>> input_array = mx.nd.array(`[ [3., 0.5, -0.5, 2., 7.], >>> [2., -.4, 7., 3., 0.2] ]) >>> softmax_act = mx.nd.SoftmaxActivation(input_array) >>> print softmax_act.asnumpy() `[ [ 1.78322066e-02 1.46375655e-03 5.38485940e-04 6.56010211e-03 9.73605454e-01] [ 6.56221947e-03 5.95310994e-04 9.73919690e-01 1.78379621e-02 1.08472735e-03] ] Defined in src/operator/nn/softmax_activation.cc:L59
The input array.
Specifies how to compute the softmax. If set to
, it computes softmax for each instance. If set to instance
, It computes cross channel softmax for each position of each instance.channel
org.apache.mxnet.Symbol
Computes the gradient of cross entropy loss with respect to softmax output. - This operator computes the gradient in two steps. The cross entropy loss does not actually need to be computed. - Applies softmax function on the input array. - Computes and returns the gradient of cross entropy loss w.r.t. the softmax output. - The softmax function, cross entropy loss and gradient is given by: - Softmax Function: .. math:: \text{softmax}(x)_i = \frac{exp(x_i)}{\sum_j exp(x_j)} - Cross Entropy Function: .. math:: \text{CE(label, output)} = - \sum_i \text{label}_i \log(\text{output}_i) - The gradient of cross entropy loss w.r.t softmax output: .. math:: \text{gradient} = \text{output} - \text{label} - During forward propagation, the softmax function is computed for each instance in the input array. For general *N*-D input arrays with shape :math:`(d_1, d_2, ..., d_n)`. The size is :math:`s=d_1 \cdot d_2 \cdot \cdot \cdot d_n`. We can use the parameters `preserve_shape` and `multi_output` to specify the way to compute softmax: - By default, `preserve_shape` is ``false``. This operator will reshape the input array into a 2-D array with shape :math:`(d_1, \frac{s}{d_1})` and then compute the softmax function for each row in the reshaped array, and afterwards reshape it back to the original shape :math:`(d_1, d_2, ..., d_n)`. - If `preserve_shape` is ``true``, the softmax function will be computed along the last axis (`axis` = ``-1``). - If `multi_output` is ``true``, the softmax function will be computed along the second axis (`axis` = ``1``). - During backward propagation, the gradient of cross-entropy loss w.r.t softmax output array is computed. The provided label can be a one-hot label array or a probability label array. - If the parameter `use_ignore` is ``true``, `ignore_label` can specify input instances with a particular label to be ignored during backward propagation. **This has no effect when softmax `output` has same shape as `label`**. Example:: data = `[ [1,2,3,4],[2,2,2,2],[3,3,3,3],[4,4,4,4] ] label = [1,0,2,3] ignore_label = 1 SoftmaxOutput(data=data, label = label,\ multi_output=true, use_ignore=true,\ ignore_label=ignore_label) ## forward softmax output `[ [ 0.0320586 0.08714432 0.23688284 0.64391428] [ 0.25 0.25 0.25 0.25 ] [ 0.25 0.25 0.25 0.25 ] [ 0.25 0.25 0.25 0.25 ] ] ## backward gradient output `[ [ 0. 0. 0. 0. ] [-0.75 0.25 0.25 0.25] [ 0.25 0.25 -0.75 0.25] [ 0.25 0.25 0.25 -0.75] ] ## notice that the first row is all 0 because label[0] is 1, which is equal to ignore_label. - The parameter `grad_scale` can be used to rescale the gradient, which is often used to give each loss function different weights. - This operator also supports various ways to normalize the gradient by `normalization`, The `normalization` is applied if softmax output has different shape than the labels. The `normalization` mode can be set to the followings: - ``'null'``: do nothing. - ``'batch'``: divide the gradient by the batch size. - ``'valid'``: divide the gradient by the number of instances which are not ignored. Defined in src/operator/softmax_output.cc:L231
Input array.
Ground truth label.
Scales the gradient by a float factor.
The instances whose labels
== ignore_label
will be ignored during backward, if use_ignore
is set to
).true
If set to
, the softmax function will be computed along axis true
. This is applied when the shape of input array differs from the shape of label array.1
If set to
, the true
ignore_label
value will not contribute to the backward gradient.
If set to
, the softmax function will be computed along the last axis (true
).-1
Normalizes the gradient.
Multiplies gradient with output gradient element-wise.
Constant for computing a label smoothed version of cross-entropyfor the backwards pass. This constant gets subtracted from theone-hot encoding of the gold label and distributed uniformly toall other labels.
org.apache.mxnet.Symbol
Applies a spatial transformer to input feature map.
Input data to the SpatialTransformerOp.
localisation net, the output dim should be 6 when transform_type is affine. You shold initialize the weight and bias with identity tranform.
output shape(h, w) of spatial transformer: (y, x)
transformation type
sampling type
whether to turn cudnn off
org.apache.mxnet.Symbol
Interchanges two axes of an array. Examples:: x = `[ [1, 2, 3] ]) swapaxes(x, 0, 1) = `[ [ 1], [ 2], [ 3] ] x = `[ `[ [ 0, 1], [ 2, 3] ], `[ [ 4, 5], [ 6, 7] ] ] // (2,2,2) array swapaxes(x, 0, 2) = `[ `[ [ 0, 4], [ 2, 6] ], `[ [ 1, 5], [ 3, 7] ] ] Defined in src/operator/swapaxis.cc:L70
Input array.
the first axis to be swapped.
the second axis to be swapped.
org.apache.mxnet.Symbol
Upsamples the given input data. Two algorithms (``sample_type``) are available for upsampling: - Nearest Neighbor - Bilinear **Nearest Neighbor Upsampling** Input data is expected to be NCHW. Example:: x = `[ [`[ [1. 1. 1.] [1. 1. 1.] [1. 1. 1.] ] ] ] UpSampling(x, scale=2, sample_type='nearest') = `[ [`[ [1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1.] [1. 1. 1. 1. 1. 1.] ] ] ] **Bilinear Upsampling** Uses `deconvolution` algorithm under the hood. You need provide both input data and the kernel. Input data is expected to be NCHW. `num_filter` is expected to be same as the number of channels. Example:: x = `[ [`[ [1. 1. 1.] [1. 1. 1.] [1. 1. 1.] ] ] ] w = `[ [`[ [1. 1. 1. 1.] [1. 1. 1. 1.] [1. 1. 1. 1.] [1. 1. 1. 1.] ] ] ] UpSampling(x, w, scale=2, sample_type='bilinear', num_filter=1) = `[ [`[ [1. 2. 2. 2. 2. 1.] [2. 4. 4. 4. 4. 2.] [2. 4. 4. 4. 4. 2.] [2. 4. 4. 4. 4. 2.] [2. 4. 4. 4. 4. 2.] [1. 2. 2. 2. 2. 1.] ] ] ] Defined in src/operator/nn/upsampling.cc:L173
Array of tensors to upsample. For bilinear upsampling, there should be 2 inputs - 1 data and 1 weight.
Up sampling scale
Input filter. Only used by bilinear sample_type.Since bilinear upsampling uses deconvolution, num_filters is set to the number of channels.
upsampling method
How to handle multiple input. concat means concatenate upsampled images along the channel dimension. sum means add all images together, only available for nearest neighbor upsampling.
Number of inputs to be upsampled. For nearest neighbor upsampling, this can be 1-N; the size of output will be(scale*h_0,scale*w_0) and all other inputs will be upsampled to thesame size. For bilinear upsampling this must be 2; 1 input and 1 weight.
Tmp workspace for deconvolution (MB)
org.apache.mxnet.Symbol
Returns element-wise absolute value of the input. Example:: abs([-2, 0, 3]) = [2, 0, 3] The storage type of ``abs`` output depends upon the input storage type: - abs(default) = default - abs(row_sparse) = row_sparse - abs(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L721
The input array.
org.apache.mxnet.Symbol
Update function for Adam optimizer. Adam is seen as a generalization of AdaGrad. Adam update consists of the following steps, where g represents gradient and m, v are 1st and 2nd order moment estimates (mean and variance). .. math:: g_t = \nabla J(W_{t-1})\\ m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t\\ v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\ W_t = W_{t-1} - \alpha \frac{ m_t }{ \sqrt{ v_t } + \epsilon } It updates the weights using:: m = beta1*m + (1-beta1)*grad v = beta2*v + (1-beta2)*(grad**2) w += - learning_rate * m / (sqrt(v) + epsilon) However, if grad's storage type is ``row_sparse``, ``lazy_update`` is True and the storage type of weight is the same as those of m and v, only the row slices whose indices appear in grad.indices are updated (for w, m and v):: for row in grad.indices: m[row] = beta1*m[row] + (1-beta1)*grad[row] v[row] = beta2*v[row] + (1-beta2)*(grad[row]**2) w[row] += - learning_rate * m[row] / (sqrt(v[row]) + epsilon) Defined in src/operator/optimizer_op.cc:L688
Weight
Gradient
Moving mean
Moving variance
Learning rate
The decay rate for the 1st moment estimates.
The decay rate for the 2nd moment estimates.
A small constant for numerical stability.
Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
If true, lazy updates are applied if gradient's stype is row_sparse and all of w, m and v have the same stype
org.apache.mxnet.Symbol
Adds all input arguments element-wise. .. math:: add\_n(a_1, a_2, ..., a_n) = a_1 + a_2 + ... + a_n ``add_n`` is potentially more efficient than calling ``add`` by `n` times. The storage type of ``add_n`` output depends on storage types of inputs - add_n(row_sparse, row_sparse, ..) = row_sparse - add_n(default, csr, default) = default - add_n(any input combinations longer than 4 (>4) with at least one default type) = default - otherwise, ``add_n`` falls all inputs back to default storage and generates default storage Defined in src/operator/tensor/elemwise_sum.cc:L155
Positional input arguments
org.apache.mxnet.Symbol
Check if all the float numbers in the array are finite (used for AMP) Defined in src/operator/contrib/all_finite.cc:L101
Array
Initialize output to 1.
org.apache.mxnet.Symbol
Cast function between low precision float/FP32 used by AMP. It casts only between low precision float/FP32 and does not do anything for other types. Defined in src/operator/tensor/amp_cast.cc:L37
The input.
Output data type.
org.apache.mxnet.Symbol
Cast function used by AMP, that casts its inputs to the common widest type. It casts only between low precision float/FP32 and does not do anything for other types. Defined in src/operator/tensor/amp_cast.cc:L71
Weights
Number of input/output pairs to be casted to the widest type.
Whether to cast to the narrowest type
org.apache.mxnet.Symbol
Returns element-wise inverse cosine of the input array. The input should be in range `[-1, 1]`. The output is in the closed interval :math:`[0, \pi]` .. math:: arccos([-1, -.707, 0, .707, 1]) = [\pi, 3\pi/4, \pi/2, \pi/4, 0] The storage type of ``arccos`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L206
The input array.
org.apache.mxnet.Symbol
Returns the element-wise inverse hyperbolic cosine of the input array, \
computed element-wise.
The storage type of ``arccosh`` output is always dense
Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L474
The input array.
org.apache.mxnet.Symbol
Returns element-wise inverse sine of the input array. The input should be in the range `[-1, 1]`. The output is in the closed interval of [:math:`-\pi/2`, :math:`\pi/2`]. .. math:: arcsin([-1, -.707, 0, .707, 1]) = [-\pi/2, -\pi/4, 0, \pi/4, \pi/2] The storage type of ``arcsin`` output depends upon the input storage type: - arcsin(default) = default - arcsin(row_sparse) = row_sparse - arcsin(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L187
The input array.
org.apache.mxnet.Symbol
Returns the element-wise inverse hyperbolic sine of the input array, \ computed element-wise. The storage type of ``arcsinh`` output depends upon the input storage type: - arcsinh(default) = default - arcsinh(row_sparse) = row_sparse - arcsinh(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L436
The input array.
org.apache.mxnet.Symbol
Returns element-wise inverse tangent of the input array. The output is in the closed interval :math:`[-\pi/2, \pi/2]` .. math:: arctan([-1, 0, 1]) = [-\pi/4, 0, \pi/4] The storage type of ``arctan`` output depends upon the input storage type: - arctan(default) = default - arctan(row_sparse) = row_sparse - arctan(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L227
The input array.
org.apache.mxnet.Symbol
Returns the element-wise inverse hyperbolic tangent of the input array, \ computed element-wise. The storage type of ``arctanh`` output depends upon the input storage type: - arctanh(default) = default - arctanh(row_sparse) = row_sparse - arctanh(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L515
The input array.
org.apache.mxnet.Symbol
Returns indices of the maximum values along an axis. In the case of multiple occurrences of maximum values, the indices corresponding to the first occurrence are returned. Examples:: x = `[ [ 0., 1., 2.], [ 3., 4., 5.] ] // argmax along axis 0 argmax(x, axis=0) = [ 1., 1., 1.] // argmax along axis 1 argmax(x, axis=1) = [ 2., 2.] // argmax along axis 1 keeping same dims as an input array argmax(x, axis=1, keepdims=True) = `[ [ 2.], [ 2.] ] Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L52
The input
The axis along which to perform the reduction. Negative values means indexing from right to left. Requires axis to be set as int, because global reduction is not supported yet.
If this is set to True
, the reduced axis is left in the result as dimension with size one.
org.apache.mxnet.Symbol
Returns argmax indices of each channel from the input array. The result will be an NDArray of shape (num_channel,). In case of multiple occurrences of the maximum values, the indices corresponding to the first occurrence are returned. Examples:: x = `[ [ 0., 1., 2.], [ 3., 4., 5.] ] argmax_channel(x) = [ 2., 2.] Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L97
The input array
org.apache.mxnet.Symbol
Returns indices of the minimum values along an axis. In the case of multiple occurrences of minimum values, the indices corresponding to the first occurrence are returned. Examples:: x = `[ [ 0., 1., 2.], [ 3., 4., 5.] ] // argmin along axis 0 argmin(x, axis=0) = [ 0., 0., 0.] // argmin along axis 1 argmin(x, axis=1) = [ 0., 0.] // argmin along axis 1 keeping same dims as an input array argmin(x, axis=1, keepdims=True) = `[ [ 0.], [ 0.] ] Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L77
The input
The axis along which to perform the reduction. Negative values means indexing from right to left. Requires axis to be set as int, because global reduction is not supported yet.
If this is set to True
, the reduced axis is left in the result as dimension with size one.
org.apache.mxnet.Symbol
Returns the indices that would sort an input array along the given axis. This function performs sorting along the given axis and returns an array of indices having same shape as an input array that index data in sorted order. Examples:: x = `[ [ 0.3, 0.2, 0.4], [ 0.1, 0.3, 0.2] ] // sort along axis -1 argsort(x) = `[ [ 1., 0., 2.], [ 0., 2., 1.] ] // sort along axis 0 argsort(x, axis=0) = `[ [ 1., 0., 1.] [ 0., 1., 0.] ] // flatten and then sort argsort(x, axis=None) = [ 3., 1., 5., 0., 4., 2.] Defined in src/operator/tensor/ordering_op.cc:L183
The input array
Axis along which to sort the input tensor. If not given, the flattened array is used. Default is -1.
Whether to sort in ascending or descending order.
DType of the output indices. It is only valid when ret_typ is "indices" or "both". An error will be raised if the selected data type cannot precisely represent the indices.
org.apache.mxnet.Symbol
Batchwise dot product. ``batch_dot`` is used to compute dot product of ``x`` and ``y`` when ``x`` and ``y`` are data in batch, namely N-D (N >= 3) arrays in shape of `(B0, ..., B_i, :, :)`. For example, given ``x`` with shape `(B_0, ..., B_i, N, M)` and ``y`` with shape `(B_0, ..., B_i, M, K)`, the result array will have shape `(B_0, ..., B_i, N, K)`, which is computed by:: batch_dot(x,y)[b_0, ..., b_i, :, :] = dot(x[b_0, ..., b_i, :, :], y[b_0, ..., b_i, :, :]) Defined in src/operator/tensor/dot.cc:L127
The first input
The second input
If true then transpose the first input before dot.
If true then transpose the second input before dot.
The desired storage type of the forward output given by user, if thecombination of input storage types and this hint does not matchany implemented ones, the dot operator will perform fallback operationand still produce an output of the desired storage type.
org.apache.mxnet.Symbol
Takes elements from a data batch. .. note:: `batch_take` is deprecated. Use `pick` instead. Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be an output array of shape ``(i0,)`` with:: output[i] = input[i, indices[i] ] Examples:: x = `[ [ 1., 2.], [ 3., 4.], [ 5., 6.] ] // takes elements with specified indices batch_take(x, [0,1,0]) = [ 1. 4. 5.] Defined in src/operator/tensor/indexing_op.cc:L777
The input array
The index array
org.apache.mxnet.Symbol
Returns element-wise sum of the input arrays with broadcasting. `broadcast_plus` is an alias to the function `broadcast_add`. Example:: x = `[ [ 1., 1., 1.], [ 1., 1., 1.] ] y = `[ [ 0.], [ 1.] ] broadcast_add(x, y) = `[ [ 1., 1., 1.], [ 2., 2., 2.] ] broadcast_plus(x, y) = `[ [ 1., 1., 1.], [ 2., 2., 2.] ] Supported sparse operations: broadcast_add(csr, dense(1D)) = dense broadcast_add(dense(1D), csr) = dense Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Broadcasts the input array over particular axes. Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes. `broadcast_axes` is an alias to the function `broadcast_axis`. Example:: // given x of shape (1,2,1) x = `[ `[ [ 1.], [ 2.] ] ] // broadcast x on on axis 2 broadcast_axis(x, axis=2, size=3) = `[ `[ [ 1., 1., 1.], [ 2., 2., 2.] ] ] // broadcast x on on axes 0 and 2 broadcast_axis(x, axis=(0,2), size=(2,3)) = `[ `[ [ 1., 1., 1.], [ 2., 2., 2.] ], `[ [ 1., 1., 1.], [ 2., 2., 2.] ] ] Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L58
The input
The axes to perform the broadcasting.
Target sizes of the broadcasting axes.
org.apache.mxnet.Symbol
Broadcasts the input array over particular axes. Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes. `broadcast_axes` is an alias to the function `broadcast_axis`. Example:: // given x of shape (1,2,1) x = `[ `[ [ 1.], [ 2.] ] ] // broadcast x on on axis 2 broadcast_axis(x, axis=2, size=3) = `[ `[ [ 1., 1., 1.], [ 2., 2., 2.] ] ] // broadcast x on on axes 0 and 2 broadcast_axis(x, axis=(0,2), size=(2,3)) = `[ `[ [ 1., 1., 1.], [ 2., 2., 2.] ], `[ [ 1., 1., 1.], [ 2., 2., 2.] ] ] Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L58
The input
The axes to perform the broadcasting.
Target sizes of the broadcasting axes.
org.apache.mxnet.Symbol
Returns element-wise division of the input arrays with broadcasting. Example:: x = `[ [ 6., 6., 6.], [ 6., 6., 6.] ] y = `[ [ 2.], [ 3.] ] broadcast_div(x, y) = `[ [ 3., 3., 3.], [ 2., 2., 2.] ] Supported sparse operations: broadcast_div(csr, dense(1D)) = csr Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L187
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Returns the result of element-wise **equal to** (==) comparison operation with broadcasting. Example:: x = `[ [ 1., 1., 1.], [ 1., 1., 1.] ] y = `[ [ 0.], [ 1.] ] broadcast_equal(x, y) = `[ [ 0., 0., 0.], [ 1., 1., 1.] ] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L46
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Returns the result of element-wise **greater than** (>) comparison operation with broadcasting. Example:: x = `[ [ 1., 1., 1.], [ 1., 1., 1.] ] y = `[ [ 0.], [ 1.] ] broadcast_greater(x, y) = `[ [ 1., 1., 1.], [ 0., 0., 0.] ] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L82
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Returns the result of element-wise **greater than or equal to** (>=) comparison operation with broadcasting. Example:: x = `[ [ 1., 1., 1.], [ 1., 1., 1.] ] y = `[ [ 0.], [ 1.] ] broadcast_greater_equal(x, y) = `[ [ 1., 1., 1.], [ 1., 1., 1.] ] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L100
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Returns the hypotenuse of a right angled triangle, given its "legs" with broadcasting. It is equivalent to doing :math:`sqrt(x_1^2 + x_2^2)`. Example:: x = `[ [ 3., 3., 3.] ] y = `[ [ 4.], [ 4.] ] broadcast_hypot(x, y) = `[ [ 5., 5., 5.], [ 5., 5., 5.] ] z = `[ [ 0.], [ 4.] ] broadcast_hypot(x, z) = `[ [ 3., 3., 3.], [ 5., 5., 5.] ] Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L158
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Returns the result of element-wise **lesser than** (<) comparison operation with broadcasting. Example:: x = `[ [ 1., 1., 1.], [ 1., 1., 1.] ] y = `[ [ 0.], [ 1.] ] broadcast_lesser(x, y) = `[ [ 0., 0., 0.], [ 0., 0., 0.] ] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L118
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Returns the result of element-wise **lesser than or equal to** (<=) comparison operation with broadcasting. Example:: x = `[ [ 1., 1., 1.], [ 1., 1., 1.] ] y = `[ [ 0.], [ 1.] ] broadcast_lesser_equal(x, y) = `[ [ 0., 0., 0.], [ 1., 1., 1.] ] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L136
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Broadcasts lhs to have the same shape as rhs. Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations with arrays of different shapes efficiently without creating multiple copies of arrays. Also see, `Broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>`_ for more explanation. Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes. For example:: broadcast_like(`[ [1,2,3] ], `[ [5,6,7],[7,8,9] ]) = `[ [ 1., 2., 3.], [ 1., 2., 3.] ]) broadcast_like([9], [1,2,3,4,5], lhs_axes=(0,), rhs_axes=(-1,)) = [9,9,9,9,9] Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L135
First input.
Second input.
Axes to perform broadcast on in the first input array
Axes to copy from the second input array
org.apache.mxnet.Symbol
Returns the result of element-wise **logical and** with broadcasting. Example:: x = `[ [ 1., 1., 1.], [ 1., 1., 1.] ] y = `[ [ 0.], [ 1.] ] broadcast_logical_and(x, y) = `[ [ 0., 0., 0.], [ 1., 1., 1.] ] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L154
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Returns the result of element-wise **logical or** with broadcasting. Example:: x = `[ [ 1., 1., 0.], [ 1., 1., 0.] ] y = `[ [ 1.], [ 0.] ] broadcast_logical_or(x, y) = `[ [ 1., 1., 1.], [ 1., 1., 0.] ] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L172
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Returns the result of element-wise **logical xor** with broadcasting. Example:: x = `[ [ 1., 1., 0.], [ 1., 1., 0.] ] y = `[ [ 1.], [ 0.] ] broadcast_logical_xor(x, y) = `[ [ 0., 0., 1.], [ 1., 1., 0.] ] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L190
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Returns element-wise maximum of the input arrays with broadcasting. This function compares two input arrays and returns a new array having the element-wise maxima. Example:: x = `[ [ 1., 1., 1.], [ 1., 1., 1.] ] y = `[ [ 0.], [ 1.] ] broadcast_maximum(x, y) = `[ [ 1., 1., 1.], [ 1., 1., 1.] ] Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L81
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Returns element-wise minimum of the input arrays with broadcasting. This function compares two input arrays and returns a new array having the element-wise minima. Example:: x = `[ [ 1., 1., 1.], [ 1., 1., 1.] ] y = `[ [ 0.], [ 1.] ] broadcast_maximum(x, y) = `[ [ 0., 0., 0.], [ 1., 1., 1.] ] Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L117
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Returns element-wise difference of the input arrays with broadcasting. `broadcast_minus` is an alias to the function `broadcast_sub`. Example:: x = `[ [ 1., 1., 1.], [ 1., 1., 1.] ] y = `[ [ 0.], [ 1.] ] broadcast_sub(x, y) = `[ [ 1., 1., 1.], [ 0., 0., 0.] ] broadcast_minus(x, y) = `[ [ 1., 1., 1.], [ 0., 0., 0.] ] Supported sparse operations: broadcast_sub/minus(csr, dense(1D)) = dense broadcast_sub/minus(dense(1D), csr) = dense Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Returns element-wise modulo of the input arrays with broadcasting. Example:: x = `[ [ 8., 8., 8.], [ 8., 8., 8.] ] y = `[ [ 2.], [ 3.] ] broadcast_mod(x, y) = `[ [ 0., 0., 0.], [ 2., 2., 2.] ] Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L222
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Returns element-wise product of the input arrays with broadcasting. Example:: x = `[ [ 1., 1., 1.], [ 1., 1., 1.] ] y = `[ [ 0.], [ 1.] ] broadcast_mul(x, y) = `[ [ 0., 0., 0.], [ 1., 1., 1.] ] Supported sparse operations: broadcast_mul(csr, dense(1D)) = csr Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L146
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Returns the result of element-wise **not equal to** (!=) comparison operation with broadcasting. Example:: x = `[ [ 1., 1., 1.], [ 1., 1., 1.] ] y = `[ [ 0.], [ 1.] ] broadcast_not_equal(x, y) = `[ [ 1., 1., 1.], [ 0., 0., 0.] ] Defined in src/operator/tensor/elemwise_binary_broadcast_op_logic.cc:L64
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Returns element-wise sum of the input arrays with broadcasting. `broadcast_plus` is an alias to the function `broadcast_add`. Example:: x = `[ [ 1., 1., 1.], [ 1., 1., 1.] ] y = `[ [ 0.], [ 1.] ] broadcast_add(x, y) = `[ [ 1., 1., 1.], [ 2., 2., 2.] ] broadcast_plus(x, y) = `[ [ 1., 1., 1.], [ 2., 2., 2.] ] Supported sparse operations: broadcast_add(csr, dense(1D)) = dense broadcast_add(dense(1D), csr) = dense Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L58
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Returns result of first array elements raised to powers from second array, element-wise with broadcasting. Example:: x = `[ [ 1., 1., 1.], [ 1., 1., 1.] ] y = `[ [ 0.], [ 1.] ] broadcast_power(x, y) = `[ [ 2., 2., 2.], [ 4., 4., 4.] ] Defined in src/operator/tensor/elemwise_binary_broadcast_op_extended.cc:L45
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Returns element-wise difference of the input arrays with broadcasting. `broadcast_minus` is an alias to the function `broadcast_sub`. Example:: x = `[ [ 1., 1., 1.], [ 1., 1., 1.] ] y = `[ [ 0.], [ 1.] ] broadcast_sub(x, y) = `[ [ 1., 1., 1.], [ 0., 0., 0.] ] broadcast_minus(x, y) = `[ [ 1., 1., 1.], [ 0., 0., 0.] ] Supported sparse operations: broadcast_sub/minus(csr, dense(1D)) = dense broadcast_sub/minus(dense(1D), csr) = dense Defined in src/operator/tensor/elemwise_binary_broadcast_op_basic.cc:L106
First input to the function
Second input to the function
org.apache.mxnet.Symbol
Broadcasts the input array to a new shape. Broadcasting is a mechanism that allows NDArrays to perform arithmetic operations with arrays of different shapes efficiently without creating multiple copies of arrays. Also see, `Broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>`_ for more explanation. Broadcasting is allowed on axes with size 1, such as from `(2,1,3,1)` to `(2,8,3,9)`. Elements will be duplicated on the broadcasted axes. For example:: broadcast_to(`[ [1,2,3] ], shape=(2,3)) = `[ [ 1., 2., 3.], [ 1., 2., 3.] ]) The dimension which you do not want to change can also be kept as `0` which means copy the original value. So with `shape=(2,0)`, we will obtain the same result as in the above example. Defined in src/operator/tensor/broadcast_reduce_op_value.cc:L82
The input
The shape of the desired array. We can set the dim to zero if it's same as the original. E.g A = broadcast_to(B, shape=(10, 0, 0))
has the same meaning as A = broadcast_axis(B, axis=0, size=10)
.
org.apache.mxnet.Symbol
Casts all elements of the input to a new type. .. note:: ``Cast`` is deprecated. Use ``cast`` instead. Example:: cast([0.9, 1.3], dtype='int32') = [0, 1] cast([1e20, 11.1], dtype='float16') = [inf, 11.09375] cast([300, 11.1, 10.9, -1, -3], dtype='uint8') = [44, 11, 10, 255, 253] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L665
The input.
Output data type.
org.apache.mxnet.Symbol
Casts tensor storage type to the new type. When an NDArray with default storage type is cast to csr or row_sparse storage, the result is compact, which means: - for csr, zero values will not be retained - for row_sparse, row slices of all zeros will not be retained The storage type of ``cast_storage`` output depends on stype parameter: - cast_storage(csr, 'default') = default - cast_storage(row_sparse, 'default') = default - cast_storage(default, 'csr') = csr - cast_storage(default, 'row_sparse') = row_sparse - cast_storage(csr, 'csr') = csr - cast_storage(row_sparse, 'row_sparse') = row_sparse Example:: dense = `[ [ 0., 1., 0.], [ 2., 0., 3.], [ 0., 0., 0.], [ 0., 0., 0.] ] # cast to row_sparse storage type rsp = cast_storage(dense, 'row_sparse') rsp.indices = [0, 1] rsp.values = `[ [ 0., 1., 0.], [ 2., 0., 3.] ] # cast to csr storage type csr = cast_storage(dense, 'csr') csr.indices = [1, 0, 2] csr.values = [ 1., 2., 3.] csr.indptr = [0, 1, 3, 3, 3] Defined in src/operator/tensor/cast_storage.cc:L71
The input.
Output storage type.
org.apache.mxnet.Symbol
Returns element-wise cube-root value of the input. .. math:: cbrt(x) = \sqrt[3]{x} Example:: cbrt([1, 8, -125]) = [1, 2, -5] The storage type of ``cbrt`` output depends upon the input storage type: - cbrt(default) = default - cbrt(row_sparse) = row_sparse - cbrt(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L216
The input array.
org.apache.mxnet.Symbol
Returns element-wise ceiling of the input. The ceil of the scalar x is the smallest integer i, such that i >= x. Example:: ceil([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-2., -1., 2., 2., 3.] The storage type of ``ceil`` output depends upon the input storage type: - ceil(default) = default - ceil(row_sparse) = row_sparse - ceil(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L818
The input array.
org.apache.mxnet.Symbol
Picks elements from an input array according to the input indices along the given axis. Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be an output array of shape ``(i0,)`` with:: output[i] = input[i, indices[i] ] By default, if any index mentioned is too large, it is replaced by the index that addresses the last element along an axis (the `clip` mode). This function supports n-dimensional input and (n-1)-dimensional indices arrays. Examples:: x = `[ [ 1., 2.], [ 3., 4.], [ 5., 6.] ] // picks elements with specified indices along axis 0 pick(x, y=[0,1], 0) = [ 1., 4.] // picks elements with specified indices along axis 1 pick(x, y=[0,1,0], 1) = [ 1., 4., 5.] y = `[ [ 1.], [ 0.], [ 2.] ] // picks elements with specified indices along axis 1 using 'wrap' mode // to place indicies that would normally be out of bounds pick(x, y=[2,-1,-2], 1, mode='wrap') = [ 1., 4., 5.] y = `[ [ 1.], [ 0.], [ 2.] ] // picks elements with specified indices along axis 1 and dims are maintained pick(x,y, 1, keepdims=True) = `[ [ 2.], [ 3.], [ 6.] ] Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L155
The input array
The index array
int or None. The axis to picking the elements. Negative values means indexing from right to left. If is None
, the elements in the index w.r.t the flattened input will be picked.
If true, the axis where we pick the elements is left in the result as dimension with size one.
Specify how out-of-bound indices behave. Default is "clip". "clip" means clip to the range. So, if all indices mentioned are too large, they are replaced by the index that addresses the last element along an axis. "wrap" means to wrap around.
org.apache.mxnet.Symbol
Clips (limits) the values in an array. Given an interval, values outside the interval are clipped to the interval edges. Clipping ``x`` between `a_min` and `a_max` would be:: .. math:: clip(x, a_min, a_max) = \max(\min(x, a_max), a_min)) Example:: x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] clip(x,1,8) = [ 1., 1., 2., 3., 4., 5., 6., 7., 8., 8.] The storage type of ``clip`` output depends on storage types of inputs and the a_min, a_max \ parameter values: - clip(default) = default - clip(row_sparse, a_min <= 0, a_max >= 0) = row_sparse - clip(csr, a_min <= 0, a_max >= 0) = csr - clip(row_sparse, a_min < 0, a_max < 0) = default - clip(row_sparse, a_min > 0, a_max > 0) = default - clip(csr, a_min < 0, a_max < 0) = csr - clip(csr, a_min > 0, a_max > 0) = csr Defined in src/operator/tensor/matrix_op.cc:L677
Input array.
Minimum value
Maximum value
org.apache.mxnet.Symbol
Joins input arrays along a given axis. .. note:: `Concat` is deprecated. Use `concat` instead. The dimensions of the input arrays should be the same except the axis along which they will be concatenated. The dimension of the output array along the concatenated axis will be equal to the sum of the corresponding dimensions of the input arrays. The storage type of ``concat`` output depends on storage types of inputs - concat(csr, csr, ..., csr, dim=0) = csr - otherwise, ``concat`` generates output with default storage Example:: x = `[ [1,1],[2,2] ] y = `[ [3,3],[4,4],[5,5] ] z = `[ [6,6], [7,7],[8,8] ] concat(x,y,z,dim=0) = `[ [ 1., 1.], [ 2., 2.], [ 3., 3.], [ 4., 4.], [ 5., 5.], [ 6., 6.], [ 7., 7.], [ 8., 8.] ] Note that you cannot concat x,y,z along dimension 1 since dimension 0 is not the same for all the input arrays. concat(y,z,dim=1) = `[ [ 3., 3., 6., 6.], [ 4., 4., 7., 7.], [ 5., 5., 8., 8.] ] Defined in src/operator/nn/concat.cc:L383
List of arrays to concatenate
Number of inputs to be concated.
the dimension to be concated.
org.apache.mxnet.Symbol
Computes the element-wise cosine of the input array. The input should be in radians (:math:`2\pi` rad equals 360 degrees). .. math:: cos([0, \pi/4, \pi/2]) = [1, 0.707, 0] The storage type of ``cos`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L90
The input array.
org.apache.mxnet.Symbol
Returns the hyperbolic cosine of the input array, computed element-wise. .. math:: cosh(x) = 0.5\times(exp(x) + exp(-x)) The storage type of ``cosh`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L351
The input array.
org.apache.mxnet.Symbol
Slices a region of the array. .. note:: ``crop`` is deprecated. Use ``slice`` instead. This function returns a sliced array between the indices given by `begin` and `end` with the corresponding `step`. For an input array of ``shape=(d_0, d_1, ..., d_n-1)``, slice operation with ``begin=(b_0, b_1...b_m-1)``, ``end=(e_0, e_1, ..., e_m-1)``, and ``step=(s_0, s_1, ..., s_m-1)``, where m <= n, results in an array with the shape ``(|e_0-b_0|/|s_0|, ..., |e_m-1-b_m-1|/|s_m-1|, d_m, ..., d_n-1)``. The resulting array's *k*-th dimension contains elements from the *k*-th dimension of the input array starting from index ``b_k`` (inclusive) with step ``s_k`` until reaching ``e_k`` (exclusive). If the *k*-th elements are `None` in the sequence of `begin`, `end`, and `step`, the following rule will be used to set default values. If `s_k` is `None`, set `s_k=1`. If `s_k > 0`, set `b_k=0`, `e_k=d_k`; else, set `b_k=d_k-1`, `e_k=-1`. The storage type of ``slice`` output depends on storage types of inputs - slice(csr) = csr - otherwise, ``slice`` generates output with default storage .. note:: When input data storage type is csr, it only supports step=(), or step=(None,), or step=(1,) to generate a csr output. For other step parameter values, it falls back to slicing a dense tensor. Example:: x = `[ [ 1., 2., 3., 4.], [ 5., 6., 7., 8.], [ 9., 10., 11., 12.] ] slice(x, begin=(0,1), end=(2,4)) = `[ [ 2., 3., 4.], [ 6., 7., 8.] ] slice(x, begin=(None, 0), end=(None, 3), step=(-1, 2)) = `[ [9., 11.], [5., 7.], [1., 3.] ] Defined in src/operator/tensor/matrix_op.cc:L482
Source input
starting indices for the slice operation, supports negative indices.
ending indices for the slice operation, supports negative indices.
step for the slice operation, supports negative values.
org.apache.mxnet.Symbol
Connectionist Temporal Classification Loss. .. note:: The existing alias ``contrib_CTCLoss`` is deprecated. The shapes of the inputs and outputs: - **data**: `(sequence_length, batch_size, alphabet_size)` - **label**: `(batch_size, label_sequence_length)` - **out**: `(batch_size)` The `data` tensor consists of sequences of activation vectors (without applying softmax), with i-th channel in the last dimension corresponding to i-th label for i between 0 and alphabet_size-1 (i.e always 0-indexed). Alphabet size should include one additional value reserved for blank label. When `blank_label` is ``"first"``, the ``0``-th channel is be reserved for activation of blank label, or otherwise if it is "last", ``(alphabet_size-1)``-th channel should be reserved for blank label. ``label`` is an index matrix of integers. When `blank_label` is ``"first"``, the value 0 is then reserved for blank label, and should not be passed in this matrix. Otherwise, when `blank_label` is ``"last"``, the value `(alphabet_size-1)` is reserved for blank label. If a sequence of labels is shorter than *label_sequence_length*, use the special padding value at the end of the sequence to conform it to the correct length. The padding value is `0` when `blank_label` is ``"first"``, and `-1` otherwise. For example, suppose the vocabulary is `[a, b, c]`, and in one batch we have three sequences 'ba', 'cbb', and 'abac'. When `blank_label` is ``"first"``, we can index the labels as `{'a': 1, 'b': 2, 'c': 3}`, and we reserve the 0-th channel for blank label in data tensor. The resulting `label` tensor should be padded to be:: `[ [2, 1, 0, 0], [3, 2, 2, 0], [1, 2, 1, 3] ] When `blank_label` is ``"last"``, we can index the labels as `{'a': 0, 'b': 1, 'c': 2}`, and we reserve the channel index 3 for blank label in data tensor. The resulting `label` tensor should be padded to be:: `[ [1, 0, -1, -1], [2, 1, 1, -1], [0, 1, 0, 2] ] ``out`` is a list of CTC loss values, one per example in the batch. See *Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks*, A. Graves *et al*. for more information on the definition and the algorithm. Defined in src/operator/nn/ctc_loss.cc:L100
Input ndarray
Ground-truth labels for the loss.
Lengths of data for each of the samples. Only required when use_data_lengths is true.
Lengths of labels for each of the samples. Only required when use_label_lengths is true.
Whether the data lenghts are decided by data_lengths
. If false, the lengths are equal to the max sequence length.
Whether the label lenghts are decided by label_lengths
, or derived from padding_mask
. If false, the lengths are derived from the first occurrence of the value of padding_mask
. The value of padding_mask
is
when first CTC label is reserved for blank, and 0
when last label is reserved for blank. See -1
blank_label
.
Set the label that is reserved for blank label.If "first", 0-th label is reserved, and label values for tokens in the vocabulary are between
and 1
, and the padding mask is alphabet_size-1
. If "last", last label value -1
is reserved for blank label instead, and label values for tokens in the vocabulary are between alphabet_size-1
and 0
, and the padding mask is alphabet_size-2
.0
org.apache.mxnet.Symbol
Return the cumulative sum of the elements along a given axis. Defined in src/operator/numpy/np_cumsum.cc:L70
Input ndarray
Axis along which the cumulative sum is computed. The default (None) is to compute the cumsum over the flattened array.
Type of the returned array and of the accumulator in which the elements are summed. If dtype is not specified, it defaults to the dtype of a, unless a has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used.
org.apache.mxnet.Symbol
Converts each element of the input array from radians to degrees. .. math:: degrees([0, \pi/2, \pi, 3\pi/2, 2\pi]) = [0, 90, 180, 270, 360] The storage type of ``degrees`` output depends upon the input storage type: - degrees(default) = default - degrees(row_sparse) = row_sparse - degrees(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L274
The input array.
org.apache.mxnet.Symbol
Rearranges(permutes) data from depth into blocks of spatial data. Similar to ONNX DepthToSpace operator: https://github.com/onnx/onnx/blob/master/docs/Operators.md#DepthToSpace. The output is a new tensor where the values from depth dimension are moved in spatial blocks to height and width dimension. The reverse of this operation is ``space_to_depth``. .. math:: \begin{gather*} x \prime = reshape(x, [N, block\_size, block\_size, C / (block\_size ^ 2), H * block\_size, W * block\_size]) \\ x \prime \prime = transpose(x \prime, [0, 3, 4, 1, 5, 2]) \\ y = reshape(x \prime \prime, [N, C / (block\_size ^ 2), H * block\_size, W * block\_size]) \end{gather*} where :math:`x` is an input tensor with default layout as :math:`[N, C, H, W]`: [batch, channels, height, width] and :math:`y` is the output tensor of layout :math:`[N, C / (block\_size ^ 2), H * block\_size, W * block\_size]` Example:: x = `[ [`[ [0, 1, 2], [3, 4, 5] ], `[ [6, 7, 8], [9, 10, 11] ], `[ [12, 13, 14], [15, 16, 17] ], `[ [18, 19, 20], [21, 22, 23] ] ] ] depth_to_space(x, 2) = `[ [`[ [0, 6, 1, 7, 2, 8], [12, 18, 13, 19, 14, 20], [3, 9, 4, 10, 5, 11], [15, 21, 16, 22, 17, 23] ] ] ] Defined in src/operator/tensor/matrix_op.cc:L972
Input ndarray
Blocks of [block_size. block_size] are moved
org.apache.mxnet.Symbol
Extracts a diagonal or constructs a diagonal array. ``diag``'s behavior depends on the input array dimensions: - 1-D arrays: constructs a 2-D array with the input as its diagonal, all other elements are zero. - N-D arrays: extracts the diagonals of the sub-arrays with axes specified by ``axis1`` and ``axis2``. The output shape would be decided by removing the axes numbered ``axis1`` and ``axis2`` from the input shape and appending to the result a new axis with the size of the diagonals in question. For example, when the input shape is `(2, 3, 4, 5)`, ``axis1`` and ``axis2`` are 0 and 2 respectively and ``k`` is 0, the resulting shape would be `(3, 5, 2)`. Examples:: x = `[ [1, 2, 3], [4, 5, 6] ] diag(x) = [1, 5] diag(x, k=1) = [2, 6] diag(x, k=-1) = [4] x = [1, 2, 3] diag(x) = `[ [1, 0, 0], [0, 2, 0], [0, 0, 3] ] diag(x, k=1) = `[ [0, 1, 0], [0, 0, 2], [0, 0, 0] ] diag(x, k=-1) = `[ [0, 0, 0], [1, 0, 0], [0, 2, 0] ] x = `[ `[ [1, 2], [3, 4] ], `[ [5, 6], [7, 8] ] ] diag(x) = `[ [1, 7], [2, 8] ] diag(x, k=1) = `[ [3], [4] ] diag(x, axis1=-2, axis2=-1) = `[ [1, 4], [5, 8] ] Defined in src/operator/tensor/diag_op.cc:L87
Input ndarray
Diagonal in question. The default is 0. Use k>0 for diagonals above the main diagonal, and k<0 for diagonals below the main diagonal. If input has shape (S0 S1) k must be between -S0 and S1
The first axis of the sub-arrays of interest. Ignored when the input is a 1-D array.
The second axis of the sub-arrays of interest. Ignored when the input is a 1-D array.
org.apache.mxnet.Symbol
Dot product of two arrays. ``dot``'s behavior depends on the input array dimensions: - 1-D arrays: inner product of vectors - 2-D arrays: matrix multiplication - N-D arrays: a sum product over the last axis of the first input and the first axis of the second input For example, given 3-D ``x`` with shape `(n,m,k)` and ``y`` with shape `(k,r,s)`, the result array will have shape `(n,m,r,s)`. It is computed by:: dot(x,y)[i,j,a,b] = sum(x[i,j,:]*y[:,a,b]) Example:: x = reshape([0,1,2,3,4,5,6,7], shape=(2,2,2)) y = reshape([7,6,5,4,3,2,1,0], shape=(2,2,2)) dot(x,y)[0,0,1,1] = 0 sum(x[0,0,:]*y[:,1,1]) = 0 The storage type of ``dot`` output depends on storage types of inputs, transpose option and forward_stype option for output storage type. Implemented sparse operations include: - dot(default, default, transpose_a=True/False, transpose_b=True/False) = default - dot(csr, default, transpose_a=True) = default - dot(csr, default, transpose_a=True) = row_sparse - dot(csr, default) = default - dot(csr, row_sparse) = default - dot(default, csr) = csr (CPU only) - dot(default, csr, forward_stype='default') = default - dot(default, csr, transpose_b=True, forward_stype='default') = default If the combination of input storage types and forward_stype does not match any of the above patterns, ``dot`` will fallback and generate output with default storage. .. Note:: If the storage type of the lhs is "csr", the storage type of gradient w.r.t rhs will be "row_sparse". Only a subset of optimizers support sparse gradients, including SGD, AdaGrad and Adam. Note that by default lazy updates is turned on, which may perform differently from standard updates. For more details, please check the Optimization API at: https://mxnet.incubator.apache.org/api/python/optimization/optimization.html Defined in src/operator/tensor/dot.cc:L77
The first input
The second input
If true then transpose the first input before dot.
If true then transpose the second input before dot.
The desired storage type of the forward output given by user, if thecombination of input storage types and this hint does not matchany implemented ones, the dot operator will perform fallback operationand still produce an output of the desired storage type.
org.apache.mxnet.Symbol
Adds arguments element-wise. The storage type of ``elemwise_add`` output depends on storage types of inputs - elemwise_add(row_sparse, row_sparse) = row_sparse - elemwise_add(csr, csr) = csr - elemwise_add(default, csr) = default - elemwise_add(csr, default) = default - elemwise_add(default, rsp) = default - elemwise_add(rsp, default) = default - otherwise, ``elemwise_add`` generates output with default storage
first input
second input
org.apache.mxnet.Symbol
Divides arguments element-wise.
The storage type of ``elemwise_div`` output is always dense
first input
second input
org.apache.mxnet.Symbol
Multiplies arguments element-wise. The storage type of ``elemwise_mul`` output depends on storage types of inputs - elemwise_mul(default, default) = default - elemwise_mul(row_sparse, row_sparse) = row_sparse - elemwise_mul(default, row_sparse) = row_sparse - elemwise_mul(row_sparse, default) = row_sparse - elemwise_mul(csr, csr) = csr - otherwise, ``elemwise_mul`` generates output with default storage
first input
second input
org.apache.mxnet.Symbol
Subtracts arguments element-wise. The storage type of ``elemwise_sub`` output depends on storage types of inputs - elemwise_sub(row_sparse, row_sparse) = row_sparse - elemwise_sub(csr, csr) = csr - elemwise_sub(default, csr) = default - elemwise_sub(csr, default) = default - elemwise_sub(default, rsp) = default - elemwise_sub(rsp, default) = default - otherwise, ``elemwise_sub`` generates output with default storage
first input
second input
org.apache.mxnet.Symbol
Returns element-wise gauss error function of the input. Example:: erf([0, -1., 10.]) = [0., -0.8427, 1.] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L886
The input array.
org.apache.mxnet.Symbol
Returns element-wise inverse gauss error function of the input. Example:: erfinv([0, 0.5., -1.]) = [0., 0.4769, -inf] Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L907
The input array.
org.apache.mxnet.Symbol
Returns element-wise exponential value of the input. .. math:: exp(x) = e^x \approx 2.718^x Example:: exp([0, 1, 2]) = [1., 2.71828175, 7.38905621] The storage type of ``exp`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L63
The input array.
org.apache.mxnet.Symbol
Inserts a new axis of size 1 into the array shape For example, given ``x`` with shape ``(2,3,4)``, then ``expand_dims(x, axis=1)`` will return a new array with shape ``(2,1,3,4)``. Defined in src/operator/tensor/matrix_op.cc:L395
Source input
Position where new axis is to be inserted. Suppose that the input NDArray
's dimension is ndim
, the range of the inserted axis is [-ndim, ndim]
org.apache.mxnet.Symbol
Returns ``exp(x) - 1`` computed element-wise on the input. This function provides greater precision than ``exp(x) - 1`` for small values of ``x``. The storage type of ``expm1`` output depends upon the input storage type: - expm1(default) = default - expm1(row_sparse) = row_sparse - expm1(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L224
The input array.
org.apache.mxnet.Symbol
Fill one element of each line(row for python, column for R/Julia) in lhs according to index indicated by rhs and values indicated by mhs. This function assume rhs uses 0-based index.
Left operand to the function.
Middle operand to the function.
Right operand to the function.
org.apache.mxnet.Symbol
Returns element-wise rounded value to the nearest \ integer towards zero of the input. Example:: fix([-2.1, -1.9, 1.9, 2.1]) = [-2., -1., 1., 2.] The storage type of ``fix`` output depends upon the input storage type: - fix(default) = default - fix(row_sparse) = row_sparse - fix(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L875
The input array.
org.apache.mxnet.Symbol
Flattens the input array into a 2-D array by collapsing the higher dimensions. .. note:: `Flatten` is deprecated. Use `flatten` instead. For an input array with shape ``(d1, d2, ..., dk)``, `flatten` operation reshapes the input array into an output array of shape ``(d1, d2*...*dk)``. Note that the behavior of this function is different from numpy.ndarray.flatten, which behaves similar to mxnet.ndarray.reshape((-1,)). Example:: x = `[ [ [1,2,3], [4,5,6], [7,8,9] ], [ [1,2,3], [4,5,6], [7,8,9] ] ], flatten(x) = `[ [ 1., 2., 3., 4., 5., 6., 7., 8., 9.], [ 1., 2., 3., 4., 5., 6., 7., 8., 9.] ] Defined in src/operator/tensor/matrix_op.cc:L250
Input array.
org.apache.mxnet.Symbol
Reverses the order of elements along given axis while preserving array shape. Note: reverse and flip are equivalent. We use reverse in the following examples. Examples:: x = `[ [ 0., 1., 2., 3., 4.], [ 5., 6., 7., 8., 9.] ] reverse(x, axis=0) = `[ [ 5., 6., 7., 8., 9.], [ 0., 1., 2., 3., 4.] ] reverse(x, axis=1) = `[ [ 4., 3., 2., 1., 0.], [ 9., 8., 7., 6., 5.] ] Defined in src/operator/tensor/matrix_op.cc:L832
Input data array
The axis which to reverse elements.
org.apache.mxnet.Symbol
Returns element-wise floor of the input. The floor of the scalar x is the largest integer i, such that i <= x. Example:: floor([-2.1, -1.9, 1.5, 1.9, 2.1]) = [-3., -2., 1., 1., 2.] The storage type of ``floor`` output depends upon the input storage type: - floor(default) = default - floor(row_sparse) = row_sparse - floor(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L837
The input array.
org.apache.mxnet.Symbol
The FTML optimizer described in *FTML - Follow the Moving Leader in Deep Learning*, available at http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf. .. math:: g_t = \nabla J(W_{t-1})\\ v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2\\ d_t = \frac{ 1 - \beta_1^t }{ \eta_t } (\sqrt{ \frac{ v_t }{ 1 - \beta_2^t } } + \epsilon) \sigma_t = d_t - \beta_1 d_{t-1} z_t = \beta_1 z_{ t-1 } + (1 - \beta_1^t) g_t - \sigma_t W_{t-1} W_t = - \frac{ z_t }{ d_t } Defined in src/operator/optimizer_op.cc:L640
Weight
Gradient
Internal state d_t
Internal state v_t
Internal state z_t
Learning rate.
Generally close to 0.5.
Generally close to 1.
Epsilon to prevent div 0.
Number of update.
Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
org.apache.mxnet.Symbol
Update function for Ftrl optimizer. Referenced from *Ad Click Prediction: a View from the Trenches*, available at http://dl.acm.org/citation.cfm?id=2488200. It updates the weights using:: rescaled_grad = clip(grad * rescale_grad, clip_gradient) z += rescaled_grad - (sqrt(n + rescaled_grad**2) - sqrt(n)) * weight / learning_rate n += rescaled_grad**2 w = (sign(z) * lamda1 - z) / ((beta + sqrt(n)) / learning_rate + wd) * (abs(z) > lamda1) If w, z and n are all of ``row_sparse`` storage type, only the row slices whose indices appear in grad.indices are updated (for w, z and n):: for row in grad.indices: rescaled_grad[row] = clip(grad[row] * rescale_grad, clip_gradient) z[row] += rescaled_grad[row] - (sqrt(n[row] + rescaled_grad[row]**2) - sqrt(n[row])) * weight[row] / learning_rate n[row] += rescaled_grad[row]**2 w[row] = (sign(z[row]) * lamda1 - z[row]) / ((beta + sqrt(n[row])) / learning_rate + wd) * (abs(z[row]) > lamda1) Defined in src/operator/optimizer_op.cc:L876
Weight
Gradient
z
Square of grad
Learning rate
The L1 regularization coefficient.
Per-Coordinate Learning Rate beta.
Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
org.apache.mxnet.Symbol
Returns the gamma function (extension of the factorial function \
to the reals), computed element-wise on the input array.
The storage type of ``gamma`` output is always dense
The input array.
org.apache.mxnet.Symbol
Returns element-wise log of the absolute value of the gamma function \
of the input.
The storage type of ``gammaln`` output is always dense
The input array.
org.apache.mxnet.Symbol
Gather elements or slices from `data` and store to a tensor whose shape is defined by `indices`. Given `data` with shape `(X_0, X_1, ..., X_{N-1})` and indices with shape `(M, Y_0, ..., Y_{K-1})`, the output will have shape `(Y_0, ..., Y_{K-1}, X_M, ..., X_{N-1})`, where `M <= N`. If `M == N`, output shape will simply be `(Y_0, ..., Y_{K-1})`. The elements in output is defined as follows:: output[y_0, ..., y_{K-1}, x_M, ..., x_{N-1}] = data[indices[0, y_0, ..., y_{K-1}], ..., indices[M-1, y_0, ..., y_{K-1}], x_M, ..., x_{N-1}] Examples:: data = `[ [0, 1], [2, 3] ] indices = `[ [1, 1, 0], [0, 1, 0] ] gather_nd(data, indices) = [2, 3, 0] data = `[ `[ [1, 2], [3, 4] ], `[ [5, 6], [7, 8] ] ] indices = `[ [0, 1], [1, 0] ] gather_nd(data, indices) = `[ [3, 4], [5, 6] ]
data
indices
org.apache.mxnet.Symbol
Computes hard sigmoid of x element-wise. .. math:: y = max(0, min(1, alpha * x + beta)) Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L161
The input array.
Slope of hard sigmoid
Bias of hard sigmoid.
org.apache.mxnet.Symbol
Returns a copy of the input.
From:src/operator/tensor/elemwise_unary_op_basic.cc:246
The input array.
org.apache.mxnet.Symbol
Computes the Khatri-Rao product of the input matrices. Given a collection of :math:`n` input matrices, .. math:: A_1 \in \mathbb{R}^{M_1 \times M}, \ldots, A_n \in \mathbb{R}^{M_n \times N}, the (column-wise) Khatri-Rao product is defined as the matrix, .. math:: X = A_1 \otimes \cdots \otimes A_n \in \mathbb{R}^{(M_1 \cdots M_n) \times N}, where the :math:`k` th column is equal to the column-wise outer product :math:`{A_1}_k \otimes \cdots \otimes {A_n}_k` where :math:`{A_i}_k` is the kth column of the ith matrix. Example:: >>> A = mx.nd.array(`[ [1, -1], >>> [2, -3] ]) >>> B = mx.nd.array(`[ [1, 4], >>> [2, 5], >>> [3, 6] ]) >>> C = mx.nd.khatri_rao(A, B) >>> print(C.asnumpy()) `[ [ 1. -4.] [ 2. -5.] [ 3. -6.] [ 2. -12.] [ 4. -15.] [ 6. -18.] ] Defined in src/operator/contrib/krprod.cc:L108
Positional input matrices
org.apache.mxnet.Symbol
Phase I of lamb update it performs the following operations and returns g:. Link to paper: https://arxiv.org/pdf/1904.00962.pdf .. math:: \begin{gather*} grad = grad * rescale_grad if (grad < -clip_gradient) then grad = -clip_gradient if (grad > clip_gradient) then grad = clip_gradient mean = beta1 * mean + (1 - beta1) * grad; variance = beta2 * variance + (1. - beta2) * grad ^ 2; if (bias_correction) then mean_hat = mean / (1. - beta1^t); var_hat = var / (1 - beta2^t); g = mean_hat / (var_hat^(1/2) + epsilon) + wd * weight; else g = mean / (var_data^(1/2) + epsilon) + wd * weight; \end{gather*} Defined in src/operator/optimizer_op.cc:L953
Weight
Gradient
Moving mean
Moving variance
The decay rate for the 1st moment estimates.
The decay rate for the 2nd moment estimates.
A small constant for numerical stability.
Index update count.
Whether to use bias correction.
Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
org.apache.mxnet.Symbol
Phase II of lamb update it performs the following operations and updates grad. Link to paper: https://arxiv.org/pdf/1904.00962.pdf .. math:: \begin{gather*} if (lower_bound >= 0) then r1 = max(r1, lower_bound) if (upper_bound >= 0) then r1 = max(r1, upper_bound) if (r1 == 0 or r2 == 0) then lr = lr else lr = lr * (r1/r2) weight = weight - lr * g \end{gather*} Defined in src/operator/optimizer_op.cc:L992
Weight
Output of lamb_update_phase 1
r1
r2
Learning rate
Lower limit of norm of weight. If lower_bound <= 0, Lower limit is not set
Upper limit of norm of weight. If upper_bound <= 0, Upper limit is not set
org.apache.mxnet.Symbol
Compute the determinant of a matrix. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, *A* is a square matrix. We compute: *out* = *det(A)* If *n>2*, *det* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. .. note:: There is no gradient backwarded when A is non-invertible (which is equivalent to det(A) = 0) because zero is rarely hit upon in float point computation and the Jacobi's formula on determinant gradient is not computationally efficient when A is non-invertible. Examples:: Single matrix determinant A = `[ [1., 4.], [2., 3.] ] det(A) = [-5.] Batch matrix determinant A = `[ `[ [1., 4.], [2., 3.] ], `[ [2., 3.], [1., 4.] ] ] det(A) = [-5., 5.] Defined in src/operator/tensor/la_op.cc:L973
Tensor of square matrix
org.apache.mxnet.Symbol
Extracts the diagonal entries of a square matrix. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, then *A* represents a single square matrix which diagonal elements get extracted as a 1-dimensional tensor. If *n>2*, then *A* represents a batch of square matrices on the trailing two dimensions. The extracted diagonals are returned as an *n-1*-dimensional tensor. .. note:: The operator supports float32 and float64 data types only. Examples:: Single matrix diagonal extraction A = `[ [1.0, 2.0], [3.0, 4.0] ] extractdiag(A) = [1.0, 4.0] extractdiag(A, 1) = [2.0] Batch matrix diagonal extraction A = `[ `[ [1.0, 2.0], [3.0, 4.0] ], `[ [5.0, 6.0], [7.0, 8.0] ] ] extractdiag(A) = `[ [1.0, 4.0], [5.0, 8.0] ] Defined in src/operator/tensor/la_op.cc:L495
Tensor of square matrices
Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal.
org.apache.mxnet.Symbol
Extracts a triangular sub-matrix from a square matrix. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, then *A* represents a single square matrix from which a triangular sub-matrix is extracted as a 1-dimensional tensor. If *n>2*, then *A* represents a batch of square matrices on the trailing two dimensions. The extracted triangular sub-matrices are returned as an *n-1*-dimensional tensor. The *offset* and *lower* parameters determine the triangle to be extracted: - When *offset = 0* either the lower or upper triangle with respect to the main diagonal is extracted depending on the value of parameter *lower*. - When *offset = k > 0* the upper triangle with respect to the k-th diagonal above the main diagonal is extracted. - When *offset = k < 0* the lower triangle with respect to the k-th diagonal below the main diagonal is extracted. .. note:: The operator supports float32 and float64 data types only. Examples:: Single triagonal extraction A = `[ [1.0, 2.0], [3.0, 4.0] ] extracttrian(A) = [1.0, 3.0, 4.0] extracttrian(A, lower=False) = [1.0, 2.0, 4.0] extracttrian(A, 1) = [2.0] extracttrian(A, -1) = [3.0] Batch triagonal extraction A = `[ `[ [1.0, 2.0], [3.0, 4.0] ], `[ [5.0, 6.0], [7.0, 8.0] ] ] extracttrian(A) = `[ [1.0, 3.0, 4.0], [5.0, 7.0, 8.0] ] Defined in src/operator/tensor/la_op.cc:L605
Tensor of square matrices
Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal.
Refer to the lower triangular matrix if lower=true, refer to the upper otherwise. Only relevant when offset=0
org.apache.mxnet.Symbol
LQ factorization for general matrix. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, we compute the LQ factorization (LAPACK *gelqf*, followed by *orglq*). *A* must have shape *(x, y)* with *x <= y*, and must have full rank *=x*. The LQ factorization consists of *L* with shape *(x, x)* and *Q* with shape *(x, y)*, so that: *A* = *L* \* *Q* Here, *L* is lower triangular (upper triangle equal to zero) with nonzero diagonal, and *Q* is row-orthonormal, meaning that *Q* \* *Q*\ :sup:`T` is equal to the identity matrix of shape *(x, x)*. If *n>2*, *gelqf* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: Single LQ factorization A = `[ [1., 2., 3.], [4., 5., 6.] ] Q, L = gelqf(A) Q = `[ [-0.26726124, -0.53452248, -0.80178373], [0.87287156, 0.21821789, -0.43643578] ] L = `[ [-3.74165739, 0.], [-8.55235974, 1.96396101] ] Batch LQ factorization A = `[ `[ [1., 2., 3.], [4., 5., 6.] ], `[ [7., 8., 9.], [10., 11., 12.] ] ] Q, L = gelqf(A) Q = `[ `[ [-0.26726124, -0.53452248, -0.80178373], [0.87287156, 0.21821789, -0.43643578] ], `[ [-0.50257071, -0.57436653, -0.64616234], [0.7620735, 0.05862104, -0.64483142] ] ] L = `[ `[ [-3.74165739, 0.], [-8.55235974, 1.96396101] ], `[ [-13.92838828, 0.], [-19.09768702, 0.52758934] ] ] Defined in src/operator/tensor/la_op.cc:L798
Tensor of input matrices to be factorized
org.apache.mxnet.Symbol
Performs general matrix multiplication and accumulation. Input are tensors *A*, *B*, *C*, each of dimension *n >= 2* and having the same shape on the leading *n-2* dimensions. If *n=2*, the BLAS3 function *gemm* is performed: *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*) + *beta* \* *C* Here, *alpha* and *beta* are scalar parameters, and *op()* is either the identity or matrix transposition (depending on *transpose_a*, *transpose_b*). If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis* parameter. By default, the trailing two dimensions will be used for matrix encoding. For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes calls. For example let *A*, *B*, *C* be 5 dimensional tensors. Then gemm(*A*, *B*, *C*, axis=1) is equivalent to the following without the overhead of the additional swapaxis operations:: A1 = swapaxes(A, dim1=1, dim2=3) B1 = swapaxes(B, dim1=1, dim2=3) C = swapaxes(C, dim1=1, dim2=3) C = gemm(A1, B1, C) C = swapaxis(C, dim1=1, dim2=3) When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use pseudo-float16 precision (float32 math with float16 I/O) precision in order to use Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups. .. note:: The operator supports float32 and float64 data types only. Examples:: Single matrix multiply-add A = `[ [1.0, 1.0], [1.0, 1.0] ] B = `[ [1.0, 1.0], [1.0, 1.0], [1.0, 1.0] ] C = `[ [1.0, 1.0, 1.0], [1.0, 1.0, 1.0] ] gemm(A, B, C, transpose_b=True, alpha=2.0, beta=10.0) = `[ [14.0, 14.0, 14.0], [14.0, 14.0, 14.0] ] Batch matrix multiply-add A = `[ `[ [1.0, 1.0] ], `[ [0.1, 0.1] ] ] B = `[ `[ [1.0, 1.0] ], `[ [0.1, 0.1] ] ] C = `[ `[ [10.0] ], `[ [0.01] ] ] gemm(A, B, C, transpose_b=True, alpha=2.0 , beta=10.0) = `[ `[ [104.0] ], `[ [0.14] ] ] Defined in src/operator/tensor/la_op.cc:L89
Tensor of input matrices
Tensor of input matrices
Tensor of input matrices
Multiply with transposed of first input (A).
Multiply with transposed of second input (B).
Scalar factor multiplied with A*B.
Scalar factor multiplied with C.
Axis corresponding to the matrix rows.
org.apache.mxnet.Symbol
Performs general matrix multiplication. Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape on the leading *n-2* dimensions. If *n=2*, the BLAS3 function *gemm* is performed: *out* = *alpha* \* *op*\ (*A*) \* *op*\ (*B*) Here *alpha* is a scalar parameter and *op()* is either the identity or the matrix transposition (depending on *transpose_a*, *transpose_b*). If *n>2*, *gemm* is performed separately for a batch of matrices. The column indices of the matrices are given by the last dimensions of the tensors, the row indices by the axis specified with the *axis* parameter. By default, the trailing two dimensions will be used for matrix encoding. For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes calls. For example let *A*, *B* be 5 dimensional tensors. Then gemm(*A*, *B*, axis=1) is equivalent to the following without the overhead of the additional swapaxis operations:: A1 = swapaxes(A, dim1=1, dim2=3) B1 = swapaxes(B, dim1=1, dim2=3) C = gemm2(A1, B1) C = swapaxis(C, dim1=1, dim2=3) When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use pseudo-float16 precision (float32 math with float16 I/O) precision in order to use Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups. .. note:: The operator supports float32 and float64 data types only. Examples:: Single matrix multiply A = `[ [1.0, 1.0], [1.0, 1.0] ] B = `[ [1.0, 1.0], [1.0, 1.0], [1.0, 1.0] ] gemm2(A, B, transpose_b=True, alpha=2.0) = `[ [4.0, 4.0, 4.0], [4.0, 4.0, 4.0] ] Batch matrix multiply A = `[ `[ [1.0, 1.0] ], `[ [0.1, 0.1] ] ] B = `[ `[ [1.0, 1.0] ], `[ [0.1, 0.1] ] ] gemm2(A, B, transpose_b=True, alpha=2.0) = `[ `[ [4.0] ], `[ [0.04 ] ] ] Defined in src/operator/tensor/la_op.cc:L163
Tensor of input matrices
Tensor of input matrices
Multiply with transposed of first input (A).
Multiply with transposed of second input (B).
Scalar factor multiplied with A*B.
Axis corresponding to the matrix row indices.
org.apache.mxnet.Symbol
Compute the inverse of a matrix. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, *A* is a square matrix. We compute: *out* = *A*\ :sup:`-1` If *n>2*, *inverse* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: Single matrix inverse A = `[ [1., 4.], [2., 3.] ] inverse(A) = `[ [-0.6, 0.8], [0.4, -0.2] ] Batch matrix inverse A = `[ `[ [1., 4.], [2., 3.] ], `[ [1., 3.], [2., 4.] ] ] inverse(A) = `[ `[ [-0.6, 0.8], [0.4, -0.2] ], `[ [-2., 1.5], [1., -0.5] ] ] Defined in src/operator/tensor/la_op.cc:L919
Tensor of square matrix
org.apache.mxnet.Symbol
Constructs a square matrix with the input as diagonal. Input is a tensor *A* of dimension *n >= 1*. If *n=1*, then *A* represents the diagonal entries of a single square matrix. This matrix will be returned as a 2-dimensional tensor. If *n>1*, then *A* represents a batch of diagonals of square matrices. The batch of diagonal matrices will be returned as an *n+1*-dimensional tensor. .. note:: The operator supports float32 and float64 data types only. Examples:: Single diagonal matrix construction A = [1.0, 2.0] makediag(A) = `[ [1.0, 0.0], [0.0, 2.0] ] makediag(A, 1) = `[ [0.0, 1.0, 0.0], [0.0, 0.0, 2.0], [0.0, 0.0, 0.0] ] Batch diagonal matrix construction A = `[ [1.0, 2.0], [3.0, 4.0] ] makediag(A) = `[ `[ [1.0, 0.0], [0.0, 2.0] ], `[ [3.0, 0.0], [0.0, 4.0] ] ] Defined in src/operator/tensor/la_op.cc:L547
Tensor of diagonal entries
Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal.
org.apache.mxnet.Symbol
Constructs a square matrix with the input representing a specific triangular sub-matrix. This is basically the inverse of *linalg.extracttrian*. Input is a tensor *A* of dimension *n >= 1*. If *n=1*, then *A* represents the entries of a triangular matrix which is lower triangular if *offset<0* or *offset=0*, *lower=true*. The resulting matrix is derived by first constructing the square matrix with the entries outside the triangle set to zero and then adding *offset*-times an additional diagonal with zero entries to the square matrix. If *n>1*, then *A* represents a batch of triangular sub-matrices. The batch of corresponding square matrices is returned as an *n+1*-dimensional tensor. .. note:: The operator supports float32 and float64 data types only. Examples:: Single matrix construction A = [1.0, 2.0, 3.0] maketrian(A) = `[ [1.0, 0.0], [2.0, 3.0] ] maketrian(A, lower=false) = `[ [1.0, 2.0], [0.0, 3.0] ] maketrian(A, offset=1) = `[ [0.0, 1.0, 2.0], [0.0, 0.0, 3.0], [0.0, 0.0, 0.0] ] maketrian(A, offset=-1) = `[ [0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [2.0, 3.0, 0.0] ] Batch matrix construction A = `[ [1.0, 2.0, 3.0], [4.0, 5.0, 6.0] ] maketrian(A) = `[ `[ [1.0, 0.0], [2.0, 3.0] ], `[ [4.0, 0.0], [5.0, 6.0] ] ] maketrian(A, offset=1) = `[ `[ [0.0, 1.0, 2.0], [0.0, 0.0, 3.0], [0.0, 0.0, 0.0] ], `[ [0.0, 4.0, 5.0], [0.0, 0.0, 6.0], [0.0, 0.0, 0.0] ] ] Defined in src/operator/tensor/la_op.cc:L673
Tensor of triangular matrices stored as vectors
Offset of the diagonal versus the main diagonal. 0 corresponds to the main diagonal, a negative/positive value to diagonals below/above the main diagonal.
Refer to the lower triangular matrix if lower=true, refer to the upper otherwise. Only relevant when offset=0
org.apache.mxnet.Symbol
Performs Cholesky factorization of a symmetric positive-definite matrix. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, the Cholesky factor *B* of the symmetric, positive definite matrix *A* is computed. *B* is triangular (entries of upper or lower triangle are all zero), has positive diagonal entries, and: *A* = *B* \* *B*\ :sup:`T` if *lower* = *true* *A* = *B*\ :sup:`T` \* *B* if *lower* = *false* If *n>2*, *potrf* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: Single matrix factorization A = `[ [4.0, 1.0], [1.0, 4.25] ] potrf(A) = `[ [2.0, 0], [0.5, 2.0] ] Batch matrix factorization A = `[ `[ [4.0, 1.0], [1.0, 4.25] ], `[ [16.0, 4.0], [4.0, 17.0] ] ] potrf(A) = `[ `[ [2.0, 0], [0.5, 2.0] ], `[ [4.0, 0], [1.0, 4.0] ] ] Defined in src/operator/tensor/la_op.cc:L214
Tensor of input matrices to be decomposed
org.apache.mxnet.Symbol
Performs matrix inversion from a Cholesky factorization. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, *A* is a triangular matrix (entries of upper or lower triangle are all zero) with positive diagonal. We compute: *out* = *A*\ :sup:`-T` \* *A*\ :sup:`-1` if *lower* = *true* *out* = *A*\ :sup:`-1` \* *A*\ :sup:`-T` if *lower* = *false* In other words, if *A* is the Cholesky factor of a symmetric positive definite matrix *B* (obtained by *potrf*), then *out* = *B*\ :sup:`-1` If *n>2*, *potri* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. .. note:: Use this operator only if you are certain you need the inverse of *B*, and cannot use the Cholesky factor *A* (*potrf*), together with backsubstitution (*trsm*). The latter is numerically much safer, and also cheaper. Examples:: Single matrix inverse A = `[ [2.0, 0], [0.5, 2.0] ] potri(A) = `[ [0.26563, -0.0625], [-0.0625, 0.25] ] Batch matrix inverse A = `[ `[ [2.0, 0], [0.5, 2.0] ], `[ [4.0, 0], [1.0, 4.0] ] ] potri(A) = `[ `[ [0.26563, -0.0625], [-0.0625, 0.25] ], `[ [0.06641, -0.01562], [-0.01562, 0,0625] ] ] Defined in src/operator/tensor/la_op.cc:L275
Tensor of lower triangular matrices
org.apache.mxnet.Symbol
Compute the sign and log of the determinant of a matrix. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, *A* is a square matrix. We compute: *sign* = *sign(det(A))* *logabsdet* = *log(abs(det(A)))* If *n>2*, *slogdet* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. .. note:: The gradient is not properly defined on sign, so the gradient of it is not backwarded. .. note:: No gradient is backwarded when A is non-invertible. Please see the docs of operator det for detail. Examples:: Single matrix signed log determinant A = `[ [2., 3.], [1., 4.] ] sign, logabsdet = slogdet(A) sign = [1.] logabsdet = [1.609438] Batch matrix signed log determinant A = `[ `[ [2., 3.], [1., 4.] ], `[ [1., 2.], [2., 4.] ], `[ [1., 2.], [4., 3.] ] ] sign, logabsdet = slogdet(A) sign = [1., 0., -1.] logabsdet = [1.609438, -inf, 1.609438] Defined in src/operator/tensor/la_op.cc:L1031
Tensor of square matrix
org.apache.mxnet.Symbol
Computes the sum of the logarithms of the diagonal elements of a square matrix. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, *A* must be square with positive diagonal entries. We sum the natural logarithms of the diagonal elements, the result has shape (1,). If *n>2*, *sumlogdiag* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: Single matrix reduction A = `[ [1.0, 1.0], [1.0, 7.0] ] sumlogdiag(A) = [1.9459] Batch matrix reduction A = `[ `[ [1.0, 1.0], [1.0, 7.0] ], `[ [3.0, 0], [0, 17.0] ] ] sumlogdiag(A) = [1.9459, 3.9318] Defined in src/operator/tensor/la_op.cc:L445
Tensor of square matrices
org.apache.mxnet.Symbol
Multiplication of matrix with its transpose. Input is a tensor *A* of dimension *n >= 2*. If *n=2*, the operator performs the BLAS3 function *syrk*: *out* = *alpha* \* *A* \* *A*\ :sup:`T` if *transpose=False*, or *out* = *alpha* \* *A*\ :sup:`T` \ \* *A* if *transpose=True*. If *n>2*, *syrk* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: Single matrix multiply A = `[ [1., 2., 3.], [4., 5., 6.] ] syrk(A, alpha=1., transpose=False) = `[ [14., 32.], [32., 77.] ] syrk(A, alpha=1., transpose=True) = `[ [17., 22., 27.], [22., 29., 36.], [27., 36., 45.] ] Batch matrix multiply A = `[ `[ [1., 1.] ], `[ [0.1, 0.1] ] ] syrk(A, alpha=2., transpose=False) = `[ `[ [4.] ], `[ [0.04] ] ] Defined in src/operator/tensor/la_op.cc:L730
Tensor of input matrices
Use transpose of input matrix.
Scalar factor to be applied to the result.
org.apache.mxnet.Symbol
Performs multiplication with a lower triangular matrix. Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape on the leading *n-2* dimensions. If *n=2*, *A* must be triangular. The operator performs the BLAS3 function *trmm*: *out* = *alpha* \* *op*\ (*A*) \* *B* if *rightside=False*, or *out* = *alpha* \* *B* \* *op*\ (*A*) if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the identity or the matrix transposition (depending on *transpose*). If *n>2*, *trmm* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: Single triangular matrix multiply A = `[ [1.0, 0], [1.0, 1.0] ] B = `[ [1.0, 1.0, 1.0], [1.0, 1.0, 1.0] ] trmm(A, B, alpha=2.0) = `[ [2.0, 2.0, 2.0], [4.0, 4.0, 4.0] ] Batch triangular matrix multiply A = `[ `[ [1.0, 0], [1.0, 1.0] ], `[ [1.0, 0], [1.0, 1.0] ] ] B = `[ `[ [1.0, 1.0, 1.0], [1.0, 1.0, 1.0] ], `[ [0.5, 0.5, 0.5], [0.5, 0.5, 0.5] ] ] trmm(A, B, alpha=2.0) = `[ `[ [2.0, 2.0, 2.0], [4.0, 4.0, 4.0] ], `[ [1.0, 1.0, 1.0], [2.0, 2.0, 2.0] ] ] Defined in src/operator/tensor/la_op.cc:L333
Tensor of lower triangular matrices
Tensor of matrices
Use transposed of the triangular matrix
Multiply triangular matrix from the right to non-triangular one.
True if the triangular matrix is lower triangular, false if it is upper triangular.
Scalar factor to be applied to the result.
org.apache.mxnet.Symbol
Solves matrix equation involving a lower triangular matrix. Input are tensors *A*, *B*, each of dimension *n >= 2* and having the same shape on the leading *n-2* dimensions. If *n=2*, *A* must be triangular. The operator performs the BLAS3 function *trsm*, solving for *out* in: *op*\ (*A*) \* *out* = *alpha* \* *B* if *rightside=False*, or *out* \* *op*\ (*A*) = *alpha* \* *B* if *rightside=True*. Here, *alpha* is a scalar parameter, and *op()* is either the identity or the matrix transposition (depending on *transpose*). If *n>2*, *trsm* is performed separately on the trailing two dimensions for all inputs (batch mode). .. note:: The operator supports float32 and float64 data types only. Examples:: Single matrix solve A = `[ [1.0, 0], [1.0, 1.0] ] B = `[ [2.0, 2.0, 2.0], [4.0, 4.0, 4.0] ] trsm(A, B, alpha=0.5) = `[ [1.0, 1.0, 1.0], [1.0, 1.0, 1.0] ] Batch matrix solve A = `[ `[ [1.0, 0], [1.0, 1.0] ], `[ [1.0, 0], [1.0, 1.0] ] ] B = `[ `[ [2.0, 2.0, 2.0], [4.0, 4.0, 4.0] ], `[ [4.0, 4.0, 4.0], [8.0, 8.0, 8.0] ] ] trsm(A, B, alpha=0.5) = `[ `[ [1.0, 1.0, 1.0], [1.0, 1.0, 1.0] ], `[ [2.0, 2.0, 2.0], [2.0, 2.0, 2.0] ] ] Defined in src/operator/tensor/la_op.cc:L396
Tensor of lower triangular matrices
Tensor of matrices
Use transposed of the triangular matrix
Multiply triangular matrix from the right to non-triangular one.
True if the triangular matrix is lower triangular, false if it is upper triangular.
Scalar factor to be applied to the result.
org.apache.mxnet.Symbol
Returns element-wise Natural logarithmic value of the input.
The natural logarithm is logarithm in base *e*, so that ``log(exp(x)) = x``
The storage type of ``log`` output is always dense
Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L76
The input array.
org.apache.mxnet.Symbol
Returns element-wise Base-10 logarithmic value of the input. ``10**log10(x) = x`` The storage type of ``log10`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L93
The input array.
org.apache.mxnet.Symbol
Returns element-wise ``log(1 + x)`` value of the input. This function is more accurate than ``log(1 + x)`` for small ``x`` so that :math:`1+x\approx 1` The storage type of ``log1p`` output depends upon the input storage type: - log1p(default) = default - log1p(row_sparse) = row_sparse - log1p(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L206
The input array.
org.apache.mxnet.Symbol
Returns element-wise Base-2 logarithmic value of the input. ``2**log2(x) = x`` The storage type of ``log2`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_logexp.cc:L105
The input array.
org.apache.mxnet.Symbol
Computes the log softmax of the input. This is equivalent to computing softmax followed by log. Examples:: >>> x = mx.nd.array([1, 2, .1]) >>> mx.nd.log_softmax(x).asnumpy() array([-1.41702998, -0.41702995, -2.31702995], dtype=float32) >>> x = mx.nd.array( `[ [1, 2, .1],[.1, 2, 1] ] ) >>> mx.nd.log_softmax(x, axis=0).asnumpy() array(`[ [-0.34115392, -0.69314718, -1.24115396], [-1.24115396, -0.69314718, -0.34115392] ], dtype=float32)
The input array.
The axis along which to compute softmax.
Temperature parameter in softmax
DType of the output in case this can't be inferred. Defaults to the same as input's dtype if not defined (dtype=None).
Whether to use the length input as a mask over the data input.
org.apache.mxnet.Symbol
Returns the result of logical NOT (!) function Example: logical_not([-2., 0., 1.]) = [0., 1., 0.]
The input array.
org.apache.mxnet.Symbol
Make your own loss function in network construction. This operator accepts a customized loss function symbol as a terminal loss and the symbol should be an operator with no backward dependency. The output of this function is the gradient of loss with respect to the input data. For example, if you are a making a cross entropy loss function. Assume ``out`` is the predicted output and ``label`` is the true label, then the cross entropy can be defined as:: cross_entropy = label * log(out) + (1 - label) * log(1 - out) loss = make_loss(cross_entropy) We will need to use ``make_loss`` when we are creating our own loss function or we want to combine multiple loss functions. Also we may want to stop some variables' gradients from backpropagation. See more detail in ``BlockGrad`` or ``stop_gradient``. The storage type of ``make_loss`` output depends upon the input storage type: - make_loss(default) = default - make_loss(row_sparse) = row_sparse Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L360
The input array.
org.apache.mxnet.Symbol
Computes the max of array elements over given axes. Defined in src/operator/tensor/./broadcast_reduce_op.h:L32
The input
The axis or axes along which to perform the reduction.
The default, axis=()
, will compute over all elements into a
scalar array with shape (1,)
.
If axis
is int, a reduction is performed on a particular axis.
If axis
is a tuple of ints, a reduction is performed on all the axes
specified in the tuple.
If exclude
is true, reduction will be performed on the axes that are
NOT in axis instead.
Negative values means indexing from right to left.
If this is set to True
, the reduced axes are left in the result as dimension with size one.
Whether to perform reduction on axis that are NOT in axis instead.
org.apache.mxnet.Symbol
Computes the max of array elements over given axes. Defined in src/operator/tensor/./broadcast_reduce_op.h:L32
The input
The axis or axes along which to perform the reduction.
The default, axis=()
, will compute over all elements into a
scalar array with shape (1,)
.
If axis
is int, a reduction is performed on a particular axis.
If axis
is a tuple of ints, a reduction is performed on all the axes
specified in the tuple.
If exclude
is true, reduction will be performed on the axes that are
NOT in axis instead.
Negative values means indexing from right to left.
If this is set to True
, the reduced axes are left in the result as dimension with size one.
Whether to perform reduction on axis that are NOT in axis instead.
org.apache.mxnet.Symbol
Computes the mean of array elements over given axes. Defined in src/operator/tensor/./broadcast_reduce_op.h:L84
The input
The axis or axes along which to perform the reduction.
The default, axis=()
, will compute over all elements into a
scalar array with shape (1,)
.
If axis
is int, a reduction is performed on a particular axis.
If axis
is a tuple of ints, a reduction is performed on all the axes
specified in the tuple.
If exclude
is true, reduction will be performed on the axes that are
NOT in axis instead.
Negative values means indexing from right to left.
If this is set to True
, the reduced axes are left in the result as dimension with size one.
Whether to perform reduction on axis that are NOT in axis instead.
org.apache.mxnet.Symbol
Computes the min of array elements over given axes. Defined in src/operator/tensor/./broadcast_reduce_op.h:L47
The input
The axis or axes along which to perform the reduction.
The default, axis=()
, will compute over all elements into a
scalar array with shape (1,)
.
If axis
is int, a reduction is performed on a particular axis.
If axis
is a tuple of ints, a reduction is performed on all the axes
specified in the tuple.
If exclude
is true, reduction will be performed on the axes that are
NOT in axis instead.
Negative values means indexing from right to left.
If this is set to True
, the reduced axes are left in the result as dimension with size one.
Whether to perform reduction on axis that are NOT in axis instead.
org.apache.mxnet.Symbol
Computes the min of array elements over given axes. Defined in src/operator/tensor/./broadcast_reduce_op.h:L47
The input
The axis or axes along which to perform the reduction.
The default, axis=()
, will compute over all elements into a
scalar array with shape (1,)
.
If axis
is int, a reduction is performed on a particular axis.
If axis
is a tuple of ints, a reduction is performed on all the axes
specified in the tuple.
If exclude
is true, reduction will be performed on the axes that are
NOT in axis instead.
Negative values means indexing from right to left.
If this is set to True
, the reduced axes are left in the result as dimension with size one.
Whether to perform reduction on axis that are NOT in axis instead.
org.apache.mxnet.Symbol
Calculate the mean and variance of `data`. The mean and variance are calculated by aggregating the contents of data across axes. If x is 1-D and axes = [0] this is just the mean and variance of a vector. Example: x = `[ [1, 2, 3], [4, 5, 6] ] mean, var = moments(data=x, axes=[0]) mean = [2.5, 3.5, 4.5] var = [2.25, 2.25, 2.25] mean, var = moments(data=x, axes=[1]) mean = [2.0, 5.0] var = [0.66666667, 0.66666667] mean, var = moments(data=x, axis=[0, 1]) mean = [3.5] var = [2.9166667] Defined in src/operator/nn/moments.cc:L54
Input ndarray
Array of ints. Axes along which to compute mean and variance.
produce moments with the same dimensionality as the input.
org.apache.mxnet.Symbol
Mixed Precision version of Phase I of lamb update it performs the following operations and returns g:. Link to paper: https://arxiv.org/pdf/1904.00962.pdf .. math:: \begin{gather*} grad32 = grad(float16) * rescale_grad if (grad < -clip_gradient) then grad = -clip_gradient if (grad > clip_gradient) then grad = clip_gradient mean = beta1 * mean + (1 - beta1) * grad; variance = beta2 * variance + (1. - beta2) * grad ^ 2; if (bias_correction) then mean_hat = mean / (1. - beta1^t); var_hat = var / (1 - beta2^t); g = mean_hat / (var_hat^(1/2) + epsilon) + wd * weight32; else g = mean / (var_data^(1/2) + epsilon) + wd * weight32; \end{gather*} Defined in src/operator/optimizer_op.cc:L1033
Weight
Gradient
Moving mean
Moving variance
Weight32
The decay rate for the 1st moment estimates.
The decay rate for the 2nd moment estimates.
A small constant for numerical stability.
Index update count.
Whether to use bias correction.
Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
org.apache.mxnet.Symbol
Mixed Precision version Phase II of lamb update it performs the following operations and updates grad. Link to paper: https://arxiv.org/pdf/1904.00962.pdf .. math:: \begin{gather*} if (lower_bound >= 0) then r1 = max(r1, lower_bound) if (upper_bound >= 0) then r1 = max(r1, upper_bound) if (r1 == 0 or r2 == 0) then lr = lr else lr = lr * (r1/r2) weight32 = weight32 - lr * g weight(float16) = weight32 \end{gather*} Defined in src/operator/optimizer_op.cc:L1075
Weight
Output of mp_lamb_update_phase 1
r1
r2
Weight32
Learning rate
Lower limit of norm of weight. If lower_bound <= 0, Lower limit is not set
Upper limit of norm of weight. If upper_bound <= 0, Upper limit is not set
org.apache.mxnet.Symbol
Update function for multi-precision Nesterov Accelerated Gradient( NAG) optimizer.
Defined in src/operator/optimizer_op.cc:L745
Weight
Gradient
Momentum
Weight32
Learning rate
The decay rate of momentum estimates at each epoch.
Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
org.apache.mxnet.Symbol
Updater function for multi-precision sgd optimizer
Weight
Gradient
Momentum
Weight32
Learning rate
The decay rate of momentum estimates at each epoch.
Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
If true, lazy updates are applied if gradient's stype is row_sparse and both weight and momentum have the same stype
org.apache.mxnet.Symbol
Updater function for multi-precision sgd optimizer
Weight
gradient
Weight32
Learning rate
Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
If true, lazy updates are applied if gradient's stype is row_sparse.
org.apache.mxnet.Symbol
Check if all the float numbers in all the arrays are finite (used for AMP) Defined in src/operator/contrib/all_finite.cc:L133
Arrays
Number of arrays.
Initialize output to 1.
org.apache.mxnet.Symbol
Compute the LARS coefficients of multiple weights and grads from their sums of square"
Defined in src/operator/contrib/multi_lars.cc:L37
Learning rates to scale by LARS coefficient
sum of square of weights arrays
sum of square of gradients arrays
weight decays
LARS eta
LARS eps
Gradient rescaling factor
org.apache.mxnet.Symbol
Momentum update function for multi-precision Stochastic Gradient Descent (SGD) optimizer. Momentum update has better convergence rates on neural networks. Mathematically it looks like below: .. math:: v_1 = \alpha * \nabla J(W_0)\\ v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\ W_t = W_{t-1} + v_t It updates the weights using:: v = momentum * v - learning_rate * gradient weight += v Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch. Defined in src/operator/optimizer_op.cc:L472
Weights
Learning rates.
Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
The decay rate of momentum estimates at each epoch.
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
Number of updated weights.
org.apache.mxnet.Symbol
Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer.
It updates the weights using::
weight = weight - learning_rate * (gradient + wd * weight)
Defined in src/operator/optimizer_op.cc:L417
Weights
Learning rates.
Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
Number of updated weights.
org.apache.mxnet.Symbol
Momentum update function for Stochastic Gradient Descent (SGD) optimizer. Momentum update has better convergence rates on neural networks. Mathematically it looks like below: .. math:: v_1 = \alpha * \nabla J(W_0)\\ v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\ W_t = W_{t-1} + v_t It updates the weights using:: v = momentum * v - learning_rate * gradient weight += v Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch. Defined in src/operator/optimizer_op.cc:L374
Weights, gradients and momentum
Learning rates.
Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
The decay rate of momentum estimates at each epoch.
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
Number of updated weights.
org.apache.mxnet.Symbol
Update function for Stochastic Gradient Descent (SDG) optimizer.
It updates the weights using::
weight = weight - learning_rate * (gradient + wd * weight)
Defined in src/operator/optimizer_op.cc:L329
Weights
Learning rates.
Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
Number of updated weights.
org.apache.mxnet.Symbol
Compute the sums of squares of multiple arrays Defined in src/operator/contrib/multi_sum_sq.cc:L36
Arrays
number of input arrays.
org.apache.mxnet.Symbol
Update function for Nesterov Accelerated Gradient( NAG) optimizer. It updates the weights using the following formula, .. math:: v_t = \gamma v_{t-1} + \eta * \nabla J(W_{t-1} - \gamma v_{t-1})\\ W_t = W_{t-1} - v_t Where :math:`\eta` is the learning rate of the optimizer :math:`\gamma` is the decay rate of the momentum estimate :math:`\v_t` is the update vector at time step `t` :math:`\W_t` is the weight vector at time step `t` Defined in src/operator/optimizer_op.cc:L726
Weight
Gradient
Momentum
Learning rate
The decay rate of momentum estimates at each epoch.
Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
org.apache.mxnet.Symbol
Computes the product of array elements over given axes treating Not a Numbers (``NaN``) as one. Defined in src/operator/tensor/broadcast_reduce_prod_value.cc:L47
The input
The axis or axes along which to perform the reduction.
The default, axis=()
, will compute over all elements into a
scalar array with shape (1,)
.
If axis
is int, a reduction is performed on a particular axis.
If axis
is a tuple of ints, a reduction is performed on all the axes
specified in the tuple.
If exclude
is true, reduction will be performed on the axes that are
NOT in axis instead.
Negative values means indexing from right to left.
If this is set to True
, the reduced axes are left in the result as dimension with size one.
Whether to perform reduction on axis that are NOT in axis instead.
org.apache.mxnet.Symbol
Computes the sum of array elements over given axes treating Not a Numbers (``NaN``) as zero. Defined in src/operator/tensor/broadcast_reduce_sum_value.cc:L102
The input
The axis or axes along which to perform the reduction.
The default, axis=()
, will compute over all elements into a
scalar array with shape (1,)
.
If axis
is int, a reduction is performed on a particular axis.
If axis
is a tuple of ints, a reduction is performed on all the axes
specified in the tuple.
If exclude
is true, reduction will be performed on the axes that are
NOT in axis instead.
Negative values means indexing from right to left.
If this is set to True
, the reduced axes are left in the result as dimension with size one.
Whether to perform reduction on axis that are NOT in axis instead.
org.apache.mxnet.Symbol
Numerical negative of the argument, element-wise. The storage type of ``negative`` output depends upon the input storage type: - negative(default) = default - negative(row_sparse) = row_sparse - negative(csr) = csr
The input array.
org.apache.mxnet.Symbol
Computes the norm on an NDArray. This operator computes the norm on an NDArray with the specified axis, depending on the value of the ord parameter. By default, it computes the L2 norm on the entire array. Currently only ord=2 supports sparse ndarrays. Examples:: x = `[ `[ [1, 2], [3, 4] ], `[ [2, 2], [5, 6] ] ] norm(x, ord=2, axis=1) = `[ [3.1622777 4.472136 ] [5.3851647 6.3245554] ] norm(x, ord=1, axis=1) = `[ [4., 6.], [7., 8.] ] rsp = x.cast_storage('row_sparse') norm(rsp) = [5.47722578] csr = x.cast_storage('csr') norm(csr) = [5.47722578] Defined in src/operator/tensor/broadcast_reduce_norm_value.cc:L89
The input
Order of the norm. Currently ord=1 and ord=2 is supported.
The axis or axes along which to perform the reduction.
The default, axis=()
, will compute over all elements into a
scalar array with shape (1,)
.
If axis
is int, a reduction is performed on a particular axis.
If axis
is a 2-tuple, it specifies the axes that hold 2-D matrices,
and the matrix norms of these matrices are computed.
The data type of the output.
If this is set to True
, the reduced axis is left in the result as dimension with size one.
org.apache.mxnet.Symbol
Draw random samples from a normal (Gaussian) distribution. .. note:: The existing alias ``normal`` is deprecated. Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale* (standard deviation). Example:: normal(loc=0, scale=1, shape=(2,2)) = `[ [ 1.89171135, -1.16881478], [-1.23474145, 1.55807114] ] Defined in src/operator/random/sample_op.cc:L113
Mean of the distribution.
Standard deviation of the distribution.
Shape of the output.
Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.
DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).
org.apache.mxnet.Symbol
Returns a one-hot array. The locations represented by `indices` take value `on_value`, while all other locations take value `off_value`. `one_hot` operation with `indices` of shape ``(i0, i1)`` and `depth` of ``d`` would result in an output array of shape ``(i0, i1, d)`` with:: output[i,j,:] = off_value output[i,j,indices[i,j] ] = on_value Examples:: one_hot([1,0,2,0], 3) = `[ [ 0. 1. 0.] [ 1. 0. 0.] [ 0. 0. 1.] [ 1. 0. 0.] ] one_hot([1,0,2,0], 3, on_value=8, off_value=1, dtype='int32') = `[ [1 8 1] [8 1 1] [1 1 8] [8 1 1] ] one_hot(`[ [1,0],[1,0],[2,0] ], 3) = `[ `[ [ 0. 1. 0.] [ 1. 0. 0.] ] `[ [ 0. 1. 0.] [ 1. 0. 0.] ] `[ [ 0. 0. 1.] [ 1. 0. 0.] ] ] Defined in src/operator/tensor/indexing_op.cc:L824
array of locations where to set on_value
Depth of the one hot dimension.
The value assigned to the locations represented by indices.
The value assigned to the locations not represented by indices.
DType of the output
org.apache.mxnet.Symbol
Return an array of ones with the same shape and type as the input array. Examples:: x = `[ [ 0., 0., 0.], [ 0., 0., 0.] ] ones_like(x) = `[ [ 1., 1., 1.], [ 1., 1., 1.] ]
The input
org.apache.mxnet.Symbol
Pads an input array with a constant or edge values of the array. .. note:: `Pad` is deprecated. Use `pad` instead. .. note:: Current implementation only supports 4D and 5D input arrays with padding applied only on axes 1, 2 and 3. Expects axes 4 and 5 in `pad_width` to be zero. This operation pads an input array with either a `constant_value` or edge values along each axis of the input array. The amount of padding is specified by `pad_width`. `pad_width` is a tuple of integer padding widths for each axis of the format ``(before_1, after_1, ... , before_N, after_N)``. The `pad_width` should be of length ``2*N`` where ``N`` is the number of dimensions of the array. For dimension ``N`` of the input array, ``before_N`` and ``after_N`` indicates how many values to add before and after the elements of the array along dimension ``N``. The widths of the higher two dimensions ``before_1``, ``after_1``, ``before_2``, ``after_2`` must be 0. Example:: x = `[ [`[ [ 1. 2. 3.] [ 4. 5. 6.] ] `[ [ 7. 8. 9.] [ 10. 11. 12.] ] ] `[ `[ [ 11. 12. 13.] [ 14. 15. 16.] ] `[ [ 17. 18. 19.] [ 20. 21. 22.] ] ] ] pad(x,mode="edge", pad_width=(0,0,0,0,1,1,1,1)) = `[ [`[ [ 1. 1. 2. 3. 3.] [ 1. 1. 2. 3. 3.] [ 4. 4. 5. 6. 6.] [ 4. 4. 5. 6. 6.] ] `[ [ 7. 7. 8. 9. 9.] [ 7. 7. 8. 9. 9.] [ 10. 10. 11. 12. 12.] [ 10. 10. 11. 12. 12.] ] ] `[ `[ [ 11. 11. 12. 13. 13.] [ 11. 11. 12. 13. 13.] [ 14. 14. 15. 16. 16.] [ 14. 14. 15. 16. 16.] ] `[ [ 17. 17. 18. 19. 19.] [ 17. 17. 18. 19. 19.] [ 20. 20. 21. 22. 22.] [ 20. 20. 21. 22. 22.] ] ] ] pad(x, mode="constant", constant_value=0, pad_width=(0,0,0,0,1,1,1,1)) = `[ [`[ [ 0. 0. 0. 0. 0.] [ 0. 1. 2. 3. 0.] [ 0. 4. 5. 6. 0.] [ 0. 0. 0. 0. 0.] ] `[ [ 0. 0. 0. 0. 0.] [ 0. 7. 8. 9. 0.] [ 0. 10. 11. 12. 0.] [ 0. 0. 0. 0. 0.] ] ] `[ `[ [ 0. 0. 0. 0. 0.] [ 0. 11. 12. 13. 0.] [ 0. 14. 15. 16. 0.] [ 0. 0. 0. 0. 0.] ] `[ [ 0. 0. 0. 0. 0.] [ 0. 17. 18. 19. 0.] [ 0. 20. 21. 22. 0.] [ 0. 0. 0. 0. 0.] ] ] ] Defined in src/operator/pad.cc:L766
An n-dimensional input array.
Padding type to use. "constant" pads with constant_value
"edge" pads using the edge values of the input array "reflect" pads by reflecting values with respect to the edges.
Widths of the padding regions applied to the edges of each axis. It is a tuple of integer padding widths for each axis of the format
. It should be of length (before_1, after_1, ... , before_N, after_N)
where 2*N
is the number of dimensions of the array.This is equivalent to pad_width in numpy.pad, but flattened.N
The value used for padding when mode
is "constant".
org.apache.mxnet.Symbol
Picks elements from an input array according to the input indices along the given axis. Given an input array of shape ``(d0, d1)`` and indices of shape ``(i0,)``, the result will be an output array of shape ``(i0,)`` with:: output[i] = input[i, indices[i] ] By default, if any index mentioned is too large, it is replaced by the index that addresses the last element along an axis (the `clip` mode). This function supports n-dimensional input and (n-1)-dimensional indices arrays. Examples:: x = `[ [ 1., 2.], [ 3., 4.], [ 5., 6.] ] // picks elements with specified indices along axis 0 pick(x, y=[0,1], 0) = [ 1., 4.] // picks elements with specified indices along axis 1 pick(x, y=[0,1,0], 1) = [ 1., 4., 5.] y = `[ [ 1.], [ 0.], [ 2.] ] // picks elements with specified indices along axis 1 using 'wrap' mode // to place indicies that would normally be out of bounds pick(x, y=[2,-1,-2], 1, mode='wrap') = [ 1., 4., 5.] y = `[ [ 1.], [ 0.], [ 2.] ] // picks elements with specified indices along axis 1 and dims are maintained pick(x,y, 1, keepdims=True) = `[ [ 2.], [ 3.], [ 6.] ] Defined in src/operator/tensor/broadcast_reduce_op_index.cc:L155
The input array
The index array
int or None. The axis to picking the elements. Negative values means indexing from right to left. If is None
, the elements in the index w.r.t the flattened input will be picked.
If true, the axis where we pick the elements is left in the result as dimension with size one.
Specify how out-of-bound indices behave. Default is "clip". "clip" means clip to the range. So, if all indices mentioned are too large, they are replaced by the index that addresses the last element along an axis. "wrap" means to wrap around.
org.apache.mxnet.Symbol
Momentum update function for multi-precision Stochastic Gradient Descent (SGD) optimizer. Momentum update has better convergence rates on neural networks. Mathematically it looks like below: .. math:: v_1 = \alpha * \nabla J(W_0)\\ v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\ W_t = W_{t-1} + v_t It updates the weights using:: v = momentum * v - learning_rate * gradient weight += v Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch. Defined in src/operator/contrib/preloaded_multi_sgd.cc:L200
Weights, gradients, momentums, learning rates and weight decays
The decay rate of momentum estimates at each epoch.
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
Number of updated weights.
org.apache.mxnet.Symbol
Update function for multi-precision Stochastic Gradient Descent (SDG) optimizer.
It updates the weights using::
weight = weight - learning_rate * (gradient + wd * weight)
Defined in src/operator/contrib/preloaded_multi_sgd.cc:L140
Weights, gradients, learning rates and weight decays
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
Number of updated weights.
org.apache.mxnet.Symbol
Momentum update function for Stochastic Gradient Descent (SGD) optimizer. Momentum update has better convergence rates on neural networks. Mathematically it looks like below: .. math:: v_1 = \alpha * \nabla J(W_0)\\ v_t = \gamma v_{t-1} - \alpha * \nabla J(W_{t-1})\\ W_t = W_{t-1} + v_t It updates the weights using:: v = momentum * v - learning_rate * gradient weight += v Where the parameter ``momentum`` is the decay rate of momentum estimates at each epoch. Defined in src/operator/contrib/preloaded_multi_sgd.cc:L91
Weights, gradients, momentum, learning rates and weight decays
The decay rate of momentum estimates at each epoch.
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
Number of updated weights.
org.apache.mxnet.Symbol
Update function for Stochastic Gradient Descent (SDG) optimizer.
It updates the weights using::
weight = weight - learning_rate * (gradient + wd * weight)
Defined in src/operator/contrib/preloaded_multi_sgd.cc:L42
Weights, gradients, learning rates and weight decays
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
Number of updated weights.
org.apache.mxnet.Symbol
Computes the product of array elements over given axes. Defined in src/operator/tensor/./broadcast_reduce_op.h:L31
The input
The axis or axes along which to perform the reduction.
The default, axis=()
, will compute over all elements into a
scalar array with shape (1,)
.
If axis
is int, a reduction is performed on a particular axis.
If axis
is a tuple of ints, a reduction is performed on all the axes
specified in the tuple.
If exclude
is true, reduction will be performed on the axes that are
NOT in axis instead.
Negative values means indexing from right to left.
If this is set to True
, the reduced axes are left in the result as dimension with size one.
Whether to perform reduction on axis that are NOT in axis instead.
org.apache.mxnet.Symbol
Converts each element of the input array from degrees to radians. .. math:: radians([0, 90, 180, 270, 360]) = [0, \pi/2, \pi, 3\pi/2, 2\pi] The storage type of ``radians`` output depends upon the input storage type: - radians(default) = default - radians(row_sparse) = row_sparse - radians(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_trig.cc:L293
The input array.
org.apache.mxnet.Symbol
Draw random samples from an exponential distribution. Samples are distributed according to an exponential distribution parametrized by *lambda* (rate). Example:: exponential(lam=4, shape=(2,2)) = `[ [ 0.0097189 , 0.08999364], [ 0.04146638, 0.31715935] ] Defined in src/operator/random/sample_op.cc:L137
Lambda parameter (rate) of the exponential distribution.
Shape of the output.
Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.
DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).
org.apache.mxnet.Symbol
Draw random samples from a gamma distribution. Samples are distributed according to a gamma distribution parametrized by *alpha* (shape) and *beta* (scale). Example:: gamma(alpha=9, beta=0.5, shape=(2,2)) = `[ [ 7.10486984, 3.37695289], [ 3.91697288, 3.65933681] ] Defined in src/operator/random/sample_op.cc:L125
Alpha parameter (shape) of the gamma distribution.
Beta parameter (scale) of the gamma distribution.
Shape of the output.
Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.
DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).
org.apache.mxnet.Symbol
Draw random samples from a generalized negative binomial distribution. Samples are distributed according to a generalized negative binomial distribution parametrized by *mu* (mean) and *alpha* (dispersion). *alpha* is defined as *1/k* where *k* is the failure limit of the number of unsuccessful experiments (generalized to real numbers). Samples will always be returned as a floating point data type. Example:: generalized_negative_binomial(mu=2.0, alpha=0.3, shape=(2,2)) = `[ [ 2., 1.], [ 6., 4.] ] Defined in src/operator/random/sample_op.cc:L179
Mean of the negative binomial distribution.
Alpha (dispersion) parameter of the negative binomial distribution.
Shape of the output.
Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.
DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).
org.apache.mxnet.Symbol
Draw random samples from a negative binomial distribution. Samples are distributed according to a negative binomial distribution parametrized by *k* (limit of unsuccessful experiments) and *p* (failure probability in each experiment). Samples will always be returned as a floating point data type. Example:: negative_binomial(k=3, p=0.4, shape=(2,2)) = `[ [ 4., 7.], [ 2., 5.] ] Defined in src/operator/random/sample_op.cc:L164
Limit of unsuccessful experiments.
Failure probability in each experiment.
Shape of the output.
Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.
DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).
org.apache.mxnet.Symbol
Draw random samples from a normal (Gaussian) distribution. .. note:: The existing alias ``normal`` is deprecated. Samples are distributed according to a normal distribution parametrized by *loc* (mean) and *scale* (standard deviation). Example:: normal(loc=0, scale=1, shape=(2,2)) = `[ [ 1.89171135, -1.16881478], [-1.23474145, 1.55807114] ] Defined in src/operator/random/sample_op.cc:L113
Mean of the distribution.
Standard deviation of the distribution.
Shape of the output.
Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.
DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).
org.apache.mxnet.Symbol
Computes the value of the PDF of *sample* of Dirichlet distributions with parameter *alpha*. The shape of *alpha* must match the leftmost subshape of *sample*. That is, *sample* can have the same shape as *alpha*, in which case the output contains one density per distribution, or *sample* can be a tensor of tensors with that shape, in which case the output is a tensor of densities such that the densities at index *i* in the output are given by the samples at index *i* in *sample* parameterized by the value of *alpha* at index *i*. Examples:: random_pdf_dirichlet(sample=`[ [1,2],[2,3],[3,4] ], alpha=[2.5, 2.5]) = [38.413498, 199.60245, 564.56085] sample = `[ `[ [1, 2, 3], [10, 20, 30], [100, 200, 300] ], `[ [0.1, 0.2, 0.3], [0.01, 0.02, 0.03], [0.001, 0.002, 0.003] ] ] random_pdf_dirichlet(sample=sample, alpha=[0.1, 0.4, 0.9]) = `[ [2.3257459e-02, 5.8420084e-04, 1.4674458e-05], [9.2589635e-01, 3.6860607e+01, 1.4674468e+03] ] Defined in src/operator/random/pdf_op.cc:L316
Samples from the distributions.
Concentration parameters of the distributions.
If set, compute the density of the log-probability instead of the probability.
org.apache.mxnet.Symbol
Computes the value of the PDF of *sample* of exponential distributions with parameters *lam* (rate). The shape of *lam* must match the leftmost subshape of *sample*. That is, *sample* can have the same shape as *lam*, in which case the output contains one density per distribution, or *sample* can be a tensor of tensors with that shape, in which case the output is a tensor of densities such that the densities at index *i* in the output are given by the samples at index *i* in *sample* parameterized by the value of *lam* at index *i*. Examples:: random_pdf_exponential(sample=`[ [1, 2, 3] ], lam=[1]) = `[ [0.36787945, 0.13533528, 0.04978707] ] sample = `[ [1,2,3], [1,2,3], [1,2,3] ] random_pdf_exponential(sample=sample, lam=[1,0.5,0.25]) = `[ [0.36787945, 0.13533528, 0.04978707], [0.30326533, 0.18393973, 0.11156508], [0.1947002, 0.15163267, 0.11809164] ] Defined in src/operator/random/pdf_op.cc:L305
Samples from the distributions.
Lambda (rate) parameters of the distributions.
If set, compute the density of the log-probability instead of the probability.
org.apache.mxnet.Symbol
Computes the value of the PDF of *sample* of gamma distributions with parameters *alpha* (shape) and *beta* (rate). *alpha* and *beta* must have the same shape, which must match the leftmost subshape of *sample*. That is, *sample* can have the same shape as *alpha* and *beta*, in which case the output contains one density per distribution, or *sample* can be a tensor of tensors with that shape, in which case the output is a tensor of densities such that the densities at index *i* in the output are given by the samples at index *i* in *sample* parameterized by the values of *alpha* and *beta* at index *i*. Examples:: random_pdf_gamma(sample=`[ [1,2,3,4,5] ], alpha=[5], beta=[1]) = `[ [0.01532831, 0.09022352, 0.16803136, 0.19536681, 0.17546739] ] sample = `[ [1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7] ] random_pdf_gamma(sample=sample, alpha=[5,6,7], beta=[1,1,1]) = `[ [0.01532831, 0.09022352, 0.16803136, 0.19536681, 0.17546739], [0.03608941, 0.10081882, 0.15629345, 0.17546739, 0.16062315], [0.05040941, 0.10419563, 0.14622283, 0.16062315, 0.14900276] ] Defined in src/operator/random/pdf_op.cc:L303
Samples from the distributions.
Alpha (shape) parameters of the distributions.
If set, compute the density of the log-probability instead of the probability.
Beta (scale) parameters of the distributions.
org.apache.mxnet.Symbol
Computes the value of the PDF of *sample* of generalized negative binomial distributions with parameters *mu* (mean) and *alpha* (dispersion). This can be understood as a reparameterization of the negative binomial, where *k* = *1 / alpha* and *p* = *1 / (mu \* alpha + 1)*. *mu* and *alpha* must have the same shape, which must match the leftmost subshape of *sample*. That is, *sample* can have the same shape as *mu* and *alpha*, in which case the output contains one density per distribution, or *sample* can be a tensor of tensors with that shape, in which case the output is a tensor of densities such that the densities at index *i* in the output are given by the samples at index *i* in *sample* parameterized by the values of *mu* and *alpha* at index *i*. Examples:: random_pdf_generalized_negative_binomial(sample=`[ [1, 2, 3, 4] ], alpha=[1], mu=[1]) = `[ [0.25, 0.125, 0.0625, 0.03125] ] sample = `[ [1,2,3,4], [1,2,3,4] ] random_pdf_generalized_negative_binomial(sample=sample, alpha=[1, 0.6666], mu=[1, 1.5]) = `[ [0.25, 0.125, 0.0625, 0.03125 ], [0.26517063, 0.16573331, 0.09667706, 0.05437994] ] Defined in src/operator/random/pdf_op.cc:L314
Samples from the distributions.
Means of the distributions.
If set, compute the density of the log-probability instead of the probability.
Alpha (dispersion) parameters of the distributions.
org.apache.mxnet.Symbol
Computes the value of the PDF of samples of negative binomial distributions with parameters *k* (failure limit) and *p* (failure probability). *k* and *p* must have the same shape, which must match the leftmost subshape of *sample*. That is, *sample* can have the same shape as *k* and *p*, in which case the output contains one density per distribution, or *sample* can be a tensor of tensors with that shape, in which case the output is a tensor of densities such that the densities at index *i* in the output are given by the samples at index *i* in *sample* parameterized by the values of *k* and *p* at index *i*. Examples:: random_pdf_negative_binomial(sample=`[ [1,2,3,4] ], k=[1], p=a[0.5]) = `[ [0.25, 0.125, 0.0625, 0.03125] ] # Note that k may be real-valued sample = `[ [1,2,3,4], [1,2,3,4] ] random_pdf_negative_binomial(sample=sample, k=[1, 1.5], p=[0.5, 0.5]) = `[ [0.25, 0.125, 0.0625, 0.03125 ], [0.26516506, 0.16572815, 0.09667476, 0.05437956] ] Defined in src/operator/random/pdf_op.cc:L310
Samples from the distributions.
Limits of unsuccessful experiments.
If set, compute the density of the log-probability instead of the probability.
Failure probabilities in each experiment.
org.apache.mxnet.Symbol
Computes the value of the PDF of *sample* of normal distributions with parameters *mu* (mean) and *sigma* (standard deviation). *mu* and *sigma* must have the same shape, which must match the leftmost subshape of *sample*. That is, *sample* can have the same shape as *mu* and *sigma*, in which case the output contains one density per distribution, or *sample* can be a tensor of tensors with that shape, in which case the output is a tensor of densities such that the densities at index *i* in the output are given by the samples at index *i* in *sample* parameterized by the values of *mu* and *sigma* at index *i*. Examples:: sample = `[ [-2, -1, 0, 1, 2] ] random_pdf_normal(sample=sample, mu=[0], sigma=[1]) = `[ [0.05399097, 0.24197073, 0.3989423, 0.24197073, 0.05399097] ] random_pdf_normal(sample=sample*2, mu=[0,0], sigma=[1,2]) = `[ [0.05399097, 0.24197073, 0.3989423, 0.24197073, 0.05399097], [0.12098537, 0.17603266, 0.19947115, 0.17603266, 0.12098537] ] Defined in src/operator/random/pdf_op.cc:L300
Samples from the distributions.
Means of the distributions.
If set, compute the density of the log-probability instead of the probability.
Standard deviations of the distributions.
org.apache.mxnet.Symbol
Computes the value of the PDF of *sample* of Poisson distributions with parameters *lam* (rate). The shape of *lam* must match the leftmost subshape of *sample*. That is, *sample* can have the same shape as *lam*, in which case the output contains one density per distribution, or *sample* can be a tensor of tensors with that shape, in which case the output is a tensor of densities such that the densities at index *i* in the output are given by the samples at index *i* in *sample* parameterized by the value of *lam* at index *i*. Examples:: random_pdf_poisson(sample=`[ [0,1,2,3] ], lam=[1]) = `[ [0.36787945, 0.36787945, 0.18393973, 0.06131324] ] sample = `[ [0,1,2,3], [0,1,2,3], [0,1,2,3] ] random_pdf_poisson(sample=sample, lam=[1,2,3]) = `[ [0.36787945, 0.36787945, 0.18393973, 0.06131324], [0.13533528, 0.27067056, 0.27067056, 0.18044704], [0.04978707, 0.14936121, 0.22404182, 0.22404182] ] Defined in src/operator/random/pdf_op.cc:L307
Samples from the distributions.
Lambda (rate) parameters of the distributions.
If set, compute the density of the log-probability instead of the probability.
org.apache.mxnet.Symbol
Computes the value of the PDF of *sample* of uniform distributions on the intervals given by *[low,high)*. *low* and *high* must have the same shape, which must match the leftmost subshape of *sample*. That is, *sample* can have the same shape as *low* and *high*, in which case the output contains one density per distribution, or *sample* can be a tensor of tensors with that shape, in which case the output is a tensor of densities such that the densities at index *i* in the output are given by the samples at index *i* in *sample* parameterized by the values of *low* and *high* at index *i*. Examples:: random_pdf_uniform(sample=`[ [1,2,3,4] ], low=[0], high=[10]) = [0.1, 0.1, 0.1, 0.1] sample = `[ `[ [1, 2, 3], [1, 2, 3] ], `[ [1, 2, 3], [1, 2, 3] ] ] low = `[ [0, 0], [0, 0] ] high = `[ [ 5, 10], [15, 20] ] random_pdf_uniform(sample=sample, low=low, high=high) = `[ `[ [0.2, 0.2, 0.2 ], [0.1, 0.1, 0.1 ] ], `[ [0.06667, 0.06667, 0.06667], [0.05, 0.05, 0.05 ] ] ] Defined in src/operator/random/pdf_op.cc:L298
Samples from the distributions.
Lower bounds of the distributions.
If set, compute the density of the log-probability instead of the probability.
Upper bounds of the distributions.
org.apache.mxnet.Symbol
Draw random samples from a Poisson distribution. Samples are distributed according to a Poisson distribution parametrized by *lambda* (rate). Samples will always be returned as a floating point data type. Example:: poisson(lam=4, shape=(2,2)) = `[ [ 5., 2.], [ 4., 6.] ] Defined in src/operator/random/sample_op.cc:L150
Lambda parameter (rate) of the Poisson distribution.
Shape of the output.
Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.
DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).
org.apache.mxnet.Symbol
Draw random samples from a discrete uniform distribution. Samples are uniformly distributed over the half-open interval *[low, high)* (includes *low*, but excludes *high*). Example:: randint(low=0, high=5, shape=(2,2)) = `[ [ 0, 2], [ 3, 1] ] Defined in src/operator/random/sample_op.cc:L194
Lower bound of the distribution.
Upper bound of the distribution.
Shape of the output.
Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.
DType of the output in case this can't be inferred. Defaults to int32 if not defined (dtype=None).
org.apache.mxnet.Symbol
Draw random samples from a uniform distribution. .. note:: The existing alias ``uniform`` is deprecated. Samples are uniformly distributed over the half-open interval *[low, high)* (includes *low*, but excludes *high*). Example:: uniform(low=0, high=1, shape=(2,2)) = `[ [ 0.60276335, 0.85794562], [ 0.54488319, 0.84725171] ] Defined in src/operator/random/sample_op.cc:L96
Lower bound of the distribution.
Upper bound of the distribution.
Shape of the output.
Context of output, in format [cpu|gpu|cpu_pinned](n). Only used for imperative calls.
DType of the output in case this can't be inferred. Defaults to float32 if not defined (dtype=None).
org.apache.mxnet.Symbol
Converts a batch of index arrays into an array of flat indices. The operator follows numpy conventions so a single multi index is given by a column of the input matrix. The leading dimension may be left unspecified by using -1 as placeholder. Examples:: A = `[ [3,6,6],[4,5,1] ] ravel(A, shape=(7,6)) = [22,41,37] ravel(A, shape=(-1,6)) = [22,41,37] Defined in src/operator/tensor/ravel.cc:L42
Batch of multi-indices
Shape of the array into which the multi-indices apply.
org.apache.mxnet.Symbol
Returns element-wise inverse cube-root value of the input. .. math:: rcbrt(x) = 1/\sqrt[3]{x} Example:: rcbrt([1,8,-125]) = [1.0, 0.5, -0.2] Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L269
The input array.
org.apache.mxnet.Symbol
Returns the reciprocal of the argument, element-wise. Calculates 1/x. Example:: reciprocal([-2, 1, 3, 1.6, 0.2]) = [-0.5, 1.0, 0.33333334, 0.625, 5.0] Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L42
The input array.
org.apache.mxnet.Symbol
Computes rectified linear activation. .. math:: max(features, 0) The storage type of ``relu`` output depends upon the input storage type: - relu(default) = default - relu(row_sparse) = row_sparse - relu(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L85
The input array.
org.apache.mxnet.Symbol
Repeats elements of an array. By default, ``repeat`` flattens the input array into 1-D and then repeats the elements:: x = `[ [ 1, 2], [ 3, 4] ] repeat(x, repeats=2) = [ 1., 1., 2., 2., 3., 3., 4., 4.] The parameter ``axis`` specifies the axis along which to perform repeat:: repeat(x, repeats=2, axis=1) = `[ [ 1., 1., 2., 2.], [ 3., 3., 4., 4.] ] repeat(x, repeats=2, axis=0) = `[ [ 1., 2.], [ 1., 2.], [ 3., 4.], [ 3., 4.] ] repeat(x, repeats=2, axis=-1) = `[ [ 1., 1., 2., 2.], [ 3., 3., 4., 4.] ] Defined in src/operator/tensor/matrix_op.cc:L744
Input data array
The number of repetitions for each element.
The axis along which to repeat values. The negative numbers are interpreted counting from the backward. By default, use the flattened input array, and return a flat output array.
org.apache.mxnet.Symbol
Set to zero multiple arrays
Defined in src/operator/contrib/reset_arrays.cc:L36
Arrays
number of input arrays.
org.apache.mxnet.Symbol
Reshapes the input array. .. note:: ``Reshape`` is deprecated, use ``reshape`` Given an array and a shape, this function returns a copy of the array in the new shape. The shape is a tuple of integers such as (2,3,4). The size of the new shape should be same as the size of the input array. Example:: reshape([1,2,3,4], shape=(2,2)) = `[ [1,2], [3,4] ] Some dimensions of the shape can take special values from the set {0, -1, -2, -3, -4}. The significance of each is explained below: - ``0`` copy this dimension from the input to the output shape. Example:: - input shape = (2,3,4), shape = (4,0,2), output shape = (4,3,2) - input shape = (2,3,4), shape = (2,0,0), output shape = (2,3,4) - ``-1`` infers the dimension of the output shape by using the remainder of the input dimensions keeping the size of the new array same as that of the input array. At most one dimension of shape can be -1. Example:: - input shape = (2,3,4), shape = (6,1,-1), output shape = (6,1,4) - input shape = (2,3,4), shape = (3,-1,8), output shape = (3,1,8) - input shape = (2,3,4), shape=(-1,), output shape = (24,) - ``-2`` copy all/remainder of the input dimensions to the output shape. Example:: - input shape = (2,3,4), shape = (-2,), output shape = (2,3,4) - input shape = (2,3,4), shape = (2,-2), output shape = (2,3,4) - input shape = (2,3,4), shape = (-2,1,1), output shape = (2,3,4,1,1) - ``-3`` use the product of two consecutive dimensions of the input shape as the output dimension. Example:: - input shape = (2,3,4), shape = (-3,4), output shape = (6,4) - input shape = (2,3,4,5), shape = (-3,-3), output shape = (6,20) - input shape = (2,3,4), shape = (0,-3), output shape = (2,12) - input shape = (2,3,4), shape = (-3,-2), output shape = (6,4) - ``-4`` split one dimension of the input into two dimensions passed subsequent to -4 in shape (can contain -1). Example:: - input shape = (2,3,4), shape = (-4,1,2,-2), output shape =(1,2,3,4) - input shape = (2,3,4), shape = (2,-4,-1,3,-2), output shape = (2,1,3,4) If the argument `reverse` is set to 1, then the special values are inferred from right to left. Example:: - without reverse=1, for input shape = (10,5,4), shape = (-1,0), output shape would be (40,5) - with reverse=1, output shape will be (50,4). Defined in src/operator/tensor/matrix_op.cc:L175
Input data to reshape.
The target shape
If true then the special values are inferred from right to left
(Deprecated! Use
instead.) Target new shape. One and only one dim can be 0, in which case it will be inferred from the rest of dimsshape
(Deprecated! Use
instead.) Whether keep the highest dim unchanged.If set to true, then the first dim in target_shape is ignored,and always fixed as inputshape
org.apache.mxnet.Symbol
Reshape some or all dimensions of `lhs` to have the same shape as some or all dimensions of `rhs`. Returns a **view** of the `lhs` array with a new shape without altering any data. Example:: x = [1, 2, 3, 4, 5, 6] y = `[ [0, -4], [3, 2], [2, 2] ] reshape_like(x, y) = `[ [1, 2], [3, 4], [5, 6] ] More precise control over how dimensions are inherited is achieved by specifying \ slices over the `lhs` and `rhs` array dimensions. Only the sliced `lhs` dimensions \ are reshaped to the `rhs` sliced dimensions, with the non-sliced `lhs` dimensions staying the same. Examples:: - lhs shape = (30,7), rhs shape = (15,2,4), lhs_begin=0, lhs_end=1, rhs_begin=0, rhs_end=2, output shape = (15,2,7) - lhs shape = (3, 5), rhs shape = (1,15,4), lhs_begin=0, lhs_end=2, rhs_begin=1, rhs_end=2, output shape = (15) Negative indices are supported, and `None` can be used for either `lhs_end` or `rhs_end` to indicate the end of the range. Example:: - lhs shape = (30, 12), rhs shape = (4, 2, 2, 3), lhs_begin=-1, lhs_end=None, rhs_begin=1, rhs_end=None, output shape = (30, 2, 2, 3) Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L513
First input.
Second input.
Defaults to 0. The beginning index along which the lhs dimensions are to be reshaped. Supports negative indices.
Defaults to None. The ending index along which the lhs dimensions are to be used for reshaping. Supports negative indices.
Defaults to 0. The beginning index along which the rhs dimensions are to be used for reshaping. Supports negative indices.
Defaults to None. The ending index along which the rhs dimensions are to be used for reshaping. Supports negative indices.
org.apache.mxnet.Symbol
Reverses the order of elements along given axis while preserving array shape. Note: reverse and flip are equivalent. We use reverse in the following examples. Examples:: x = `[ [ 0., 1., 2., 3., 4.], [ 5., 6., 7., 8., 9.] ] reverse(x, axis=0) = `[ [ 5., 6., 7., 8., 9.], [ 0., 1., 2., 3., 4.] ] reverse(x, axis=1) = `[ [ 4., 3., 2., 1., 0.], [ 9., 8., 7., 6., 5.] ] Defined in src/operator/tensor/matrix_op.cc:L832
Input data array
The axis which to reverse elements.
org.apache.mxnet.Symbol
Returns element-wise rounded value to the nearest integer of the input. .. note:: - For input ``n.5`` ``rint`` returns ``n`` while ``round`` returns ``n+1``. - For input ``-n.5`` both ``rint`` and ``round`` returns ``-n-1``. Example:: rint([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2., 1., -2., 2., 2.] The storage type of ``rint`` output depends upon the input storage type: - rint(default) = default - rint(row_sparse) = row_sparse - rint(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L799
The input array.
org.apache.mxnet.Symbol
Update function for `RMSProp` optimizer. `RMSprop` is a variant of stochastic gradient descent where the gradients are divided by a cache which grows with the sum of squares of recent gradients? `RMSProp` is similar to `AdaGrad`, a popular variant of `SGD` which adaptively tunes the learning rate of each parameter. `AdaGrad` lowers the learning rate for each parameter monotonically over the course of training. While this is analytically motivated for convex optimizations, it may not be ideal for non-convex problems. `RMSProp` deals with this heuristically by allowing the learning rates to rebound as the denominator decays over time. Define the Root Mean Square (RMS) error criterion of the gradient as :math:`RMS[g]_t = \sqrt{E[g^2]_t + \epsilon}`, where :math:`g` represents gradient and :math:`E[g^2]_t` is the decaying average over past squared gradient. The :math:`E[g^2]_t` is given by: .. math:: E[g^2]_t = \gamma * E[g^2]_{t-1} + (1-\gamma) * g_t^2 The update step is .. math:: \theta_{t+1} = \theta_t - \frac{\eta}{RMS[g]_t} g_t The RMSProp code follows the version in http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf Tieleman & Hinton, 2012. Hinton suggests the momentum term :math:`\gamma` to be 0.9 and the learning rate :math:`\eta` to be 0.001. Defined in src/operator/optimizer_op.cc:L797
Weight
Gradient
n
Learning rate
The decay rate of momentum estimates.
A small constant for numerical stability.
Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
Clip weights to the range of [-clip_weights, clip_weights] If clip_weights <= 0, weight clipping is turned off. weights = max(min(weights, clip_weights), -clip_weights).
org.apache.mxnet.Symbol
Update function for RMSPropAlex optimizer. `RMSPropAlex` is non-centered version of `RMSProp`. Define :math:`E[g^2]_t` is the decaying average over past squared gradient and :math:`E[g]_t` is the decaying average over past gradient. .. math:: E[g^2]_t = \gamma_1 * E[g^2]_{t-1} + (1 - \gamma_1) * g_t^2\\ E[g]_t = \gamma_1 * E[g]_{t-1} + (1 - \gamma_1) * g_t\\ \Delta_t = \gamma_2 * \Delta_{t-1} - \frac{\eta}{\sqrt{E[g^2]_t - E[g]_t^2 + \epsilon}} g_t\\ The update step is .. math:: \theta_{t+1} = \theta_t + \Delta_t The RMSPropAlex code follows the version in http://arxiv.org/pdf/1308.0850v5.pdf Eq(38) - Eq(45) by Alex Graves, 2013. Graves suggests the momentum term :math:`\gamma_1` to be 0.95, :math:`\gamma_2` to be 0.9 and the learning rate :math:`\eta` to be 0.0001. Defined in src/operator/optimizer_op.cc:L836
Weight
Gradient
n
g
delta
Learning rate
Decay rate.
Decay rate.
A small constant for numerical stability.
Weight decay augments the objective function with a regularization term that penalizes large weights. The penalty scales with the square of the magnitude of each weight.
Rescale gradient to grad = rescale_grad*grad.
Clip gradient to the range of [-clip_gradient, clip_gradient] If clip_gradient <= 0, gradient clipping is turned off. grad = max(min(grad, clip_gradient), -clip_gradient).
Clip weights to the range of [-clip_weights, clip_weights] If clip_weights <= 0, weight clipping is turned off. weights = max(min(weights, clip_weights), -clip_weights).
org.apache.mxnet.Symbol
Returns element-wise rounded value to the nearest integer of the input. Example:: round([-1.5, 1.5, -1.9, 1.9, 2.1]) = [-2., 2., -2., 2., 2.] The storage type of ``round`` output depends upon the input storage type: - round(default) = default - round(row_sparse) = row_sparse - round(csr) = csr Defined in src/operator/tensor/elemwise_unary_op_basic.cc:L778
The input array.
org.apache.mxnet.Symbol
Returns element-wise inverse square-root value of the input. .. math:: rsqrt(x) = 1/\sqrt{x} Example:: rsqrt([4,9,16]) = [0.5, 0.33333334, 0.25] The storage type of ``rsqrt`` output is always dense Defined in src/operator/tensor/elemwise_unary_op_pow.cc:L193
The input array.
org.apache.mxnet.Symbol
Concurrent sampling from multiple exponential distributions with parameters lambda (rate). The parameters of the distributions are provided as an input array. Let *[s]* be the shape of the input array, *n* be the dimension of *[s]*, *[t]* be the shape specified as the parameter of the operator, and *m* be the dimension of *[t]*. Then the output will be a *(n+m)*-dimensional array with shape *[s]x[t]*. For any valid *n*-dimensional index *i* with respect to the input array, *output[i]* will be an *m*-dimensional array that holds randomly drawn samples from the distribution which is parameterized by the input value at index *i*. If the shape parameter of the operator is not set, then one sample will be drawn per distribution and the output array has the same shape as the input array. Examples:: lam = [ 1.0, 8.5 ] // Draw a single sample for each distribution sample_exponential(lam) = [ 0.51837951, 0.09994757] // Draw a vector containing two samples for each distribution sample_exponential(lam, shape=(2)) = `[ [ 0.51837951, 0.19866663], [ 0.09994757, 0.50447971] ] Defined in src/operator/random/multisample_op.cc:L284
typesafe Symbol API: Symbol.api._ Main code will be generated during compile time through Macros