Functions¶
All NNabla functions are derived from the nnabla.function.Function
class.
Function¶

class
nnabla.function.
Function
¶ Function interface class.
Instances of
nnabla.function.Function
are not directly created by users. It is indirectly created by the functions available innnabla.functions
. These functions returnnnabla.Variable
(s) holding the created function instance as the parent property.
backward
(self, inputs, outputs, accum=None)¶

forward
(self, inputs, outputs)¶

grad_depends_output_data
(self, int i, int o)¶

info
¶ info – object

inplace_data
(self, int i)¶

inplace_data_with
(self, int i)¶

inplace_grad
(self, int i)¶

inplace_grad_with
(self, int i)¶

min_outputs
(self)¶

setup
(self, inputs, outputs)¶

List of Functions¶
The nnabla.functions
module provides various types of functions listed below.
These functions takes input nnabla.Variable
(s) as its leading argument(s), followed by options
specific to each function.
 Note:
 The functions can also take
NdArray
(s) as output(s) holding output values of the operation. We call this “Imperative Mode” (NdArray + Functions).
Neural Network Layers¶

nnabla.functions.
affine
(x, weight, bias=None, base_axis=1, n_outputs=1, outputs=None)[source]¶ Affine layer, also called as the fully connected layer. It calculates:
\[{\mathbf y} = {\mathbf A} {\mathbf x} + {\mathbf b}.\]where \({\mathbf x}\) is the input and \({\mathbf y}\) is the output.
Parameters:  x (Variable) – Input ND array with shape (\(M_0 \times ... \times M_{B1} \times D_B \times ... \times D_N\)). Dimensions before and after base_axis are flattened as if it is a matrix.
 weight (Variable) – [Parameter] Weight matrix with shape (\((D_B \times ... \times D_N) \times L\))
 bias (Variable) – [Optional Parameter] Bias vector (\(L\))
 base_axis (int) – Base axis of Affine operation. Dimensions up to base_axis is treated as sample dimension.
Returns: \((B + 1)\)D array. (\(M_0 \times ... \times M_{B1} \times L\))
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
convolution
(x, weight, bias=None, base_axis=1, pad=None, stride=None, dilation=None, group=1, n_outputs=1, outputs=None)[source]¶ ND Convolution with bias.
See references for dilated convolution (a.k.a. atrous convolution).
References
 Chen et al., DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs.
 Yu et al., MultiScale Context Aggregation by Dilated Convolutions.
Parameters:  x (Variable) – \((B + 1 + N)\)D array (\(M_1 \times ... \times M_B \times C \times L_1 \times ... \times L_N\)).
 weight (Variable) – [Parameter] \((2 + N)\)D array (\(C' \times C \times K_1 \times ... \times K_N\)).
 bias (Variable) – [Optional Parameter] Bias vector (\(C'\)).
 base_axis (int) – base axis \(B\).
 pad (
tuple
ofint
) – Padding sizes for dimensions.  stride (
tuple
ofint
) – Stride sizes for dimensions.  dilation (
tuple
ofint
) – Dilation sizes for dimensions.  group (int) – Number of groups of channels. This makes the connection across channels sparser, by grouping connections along the mapping direction.
Returns: \((B + 1 + N)\)D array (\(M_1 \times ... \times M_B \times C' \times L'_1 \times ... \times L'_N\)).
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
deconvolution
(x, weight, bias=None, base_axis=1, pad=None, stride=None, dilation=None, group=1, n_outputs=1, outputs=None)[source]¶ ND deconvolution, also known as transposed convolution, with bias operates backward convolution (derivative of the output w.r.t. the input) plus channelwise learned bias.
The weights are specified in the same manner as
convolution()
, as if it was an ordinary convolution function. The forward operation ofdeconvolution()
will then be operationally equivalent to the backward pass ofconvolution()
. Therefore, the number of input channels (can be seen as output channels of forward convolution) is specified in the first dimension, and the number of the output channels divided by the number of groups is specified in the second dimension.Parameters:  x (Variable) – \((B + 1 + N)\)D array (\(M_1 \times ... \times M_B \times C \times L_1 \times ... \times L_N\)).
 weight (Variable) – [Parameter] \((2 + N)\)D array (\(C' \times C \times K_1 \times ... \times K_N\)).
 bias (Variable) – [Optional Parameter] Bias vector (\(C'\)).
 base_axis (int) – base axis \(B\).
 pad (
tuple
ofint
) – Padding sizes for dimensions.  stride (
tuple
ofint
) – Stride sizes for dimensions.  dilation (
tuple
ofint
) – Dilation sizes for dimensions.  group (int) – Number of groups of channels. This makes the connection across channels sparser, by grouping connections along the mapping direction.
Returns: \((B + 1 + N)\)D array (\(M_1 \times ... \times M_B \times C' \times L'_1 \times ... \times L'_N\)).
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
max_pooling
(x, kernel, stride=None, ignore_border=True, pad=None, n_outputs=1, outputs=None)[source]¶ Max pooling. It pools the maximum values inside the scanning kernel:
\[y_{i_1, i_2} = \max_{k_1, k_2 \in K} (x_{i_1 + k_1, i_2 + k_2})\]where \(x_{i_1 + k_1, i_2 + k_2}\) is the input and \(y_{i_1, i_2}\) is the output.
Parameters:  x (Variable) – Input variable.
 kernel (
tuple
ofint
) – Kernel sizes for each spatial axis.  stride (
tuple
ofint
) – Subsampling factors for each spatial axis.  ignore_border (bool) – If false, kernels covering borders are also considered for the output.
 pad (
tuple
ofint
) – Border padding values for each spatial axis. Padding will be added both sides of the dimension.
Returns: Maximum values variable
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
average_pooling
(x, kernel, stride=None, ignore_border=True, pad=None, including_pad=True, n_outputs=1, outputs=None)[source]¶ Average pooling. It pools the averaged values inside the scanning kernel:
\[y_{i_1, i_2} = \frac{1}{K_1 K_2} \sum_{k1} \sum_{k2} x_{i_1 + k_1, i_2 + k_2}\]where \(x_{i_1 + k_1, i_2 + k_2}\) is the input and \(y_{i_1, i_2}\) is the output.
Parameters:  x (Variable) – Input variable.
 kernel (
tuple
ofint
) – Kernel sizes for each spatial axis.  stride (
tuple
ofint
) – Subsampling factors for each spatial axis.  ignore_border (bool) – If false, kernels covering borders are also considered for the output.
 pad (
tuple
ofint
) – Border padding values for each spatial axis. Padding will be added both sides of the dimension.  including_pad (bool) – If true, border padding values are considered for the output.
Returns: Average values variable
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
sum_pooling
(x, kernel, stride=None, ignore_border=True, pad=None, n_outputs=1, outputs=None)[source]¶ Sum pooling. It pools the summed values inside the scanning kernel:
\[y_{i_1, i_2} = \sum_{k1} \sum_{k2} x_{i_1 + k_1, i_2 + k_2}\]where \(x_{i_1 + k_1, i_2 + k_2}\) is the input and \(y_{i_1, i_2}\) is the output.
Parameters:  x (Variable) – Input variable.
 kernel (
tuple
ofint
) – Kernel sizes for each spatial axis.  stride (
tuple
ofint
) – Subsampling factors for each spatial axis.  ignore_border (bool) – If false, kernels covering borders are also considered for the output.
 pad (
tuple
ofint
) – Border padding values for each spatial axis. Padding will be added both sides of the dimension.
Returns: Summed values variable
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
unpooling
(x, kernel, n_outputs=1, outputs=None)[source]¶ Inverse operation of pooling. It spreads the input values:
\[y_{k_1 i_1 + j_1, k_2 i_2 + j_2} = x_{i_1, i_2}\]where \(_{i_1, i_2}\) is the input and \(y_{k_1 i_1 + j_1, k_2 i_2 + j_2}\) is the output.
Parameters: Returns: Spread values variable
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
embed
(x0, x1, n_outputs=1, outputs=None)[source]¶ Embed slices of a matrix/tensor with indexing array/tensor.
Parameters: Returns: Output with shape \((I_0, ..., I_N, W_1, ..., W_M)\)
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.
Neural Network Activation¶

nnabla.functions.
sigmoid
(x, n_outputs=1, outputs=None)[source]¶ Elementwise sigmoid function.
\[f(x) = \frac{1}{1 + \exp(x)},\]Parameters: x (Variable) – Input Returns: Output Return type: Variable Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
tanh
(x, n_outputs=1, outputs=None)[source]¶ Elementwise hyperbolic tangent (tanh) function.
\[y_i = \tanh (x_i)\]Parameters: x (Variable) – ND array Returns: ND array with the same shape as x Return type: Variable Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
relu
(x, inplace=False, n_outputs=1, outputs=None)[source]¶ Elementwise Rectified Linear Unit (ReLU) function.
\[y_i = \max (0, x_i)\]Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
softmax
(x, axis=None, n_outputs=1, outputs=None)[source]¶ Softmax normalization. Calculates
\[y_i = \frac{\exp(x_i)}{\sum_j exp(x_j)}\]along the dimension specified by axis, where \(y_i\) is the input and \(x_i\) is the output.
Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
elu
(x, alpha=1.0, n_outputs=1, outputs=None)[source]¶ Elementwise Exponential Linear Unit (ELU) function.
\[\begin{split}y_i= \left\{ \begin{array}{ll} x_i & (x > 0)\\ \alpha (\exp(x_i)  1) & (x \leq 0) \end{array} \right..\end{split}\]References
Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
crelu
(x, axis=1, n_outputs=1, outputs=None)[source]¶ Elementwise Concatenated Rectified Linear Unit (CReLU) function. This function calculates the ReLU of \(x\) and \(x\) , then concatenates the results together at a specified axis, and returns the resulting array.
References
Parameters: Returns: ND array where axis dimension is doubled by concatenating.
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
celu
(x, alpha=1.0, axis=1, n_outputs=1, outputs=None)[source]¶ Elementwise Concatenated Exponential Linear Unit (CELU) function. Concatenates ELU outputs of positive and negative inputs together at specified axis.
Parameters: Returns: ND array where axis dimension is doubled by concatenating.
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
prelu
(x0, x1, base_axis=1, n_outputs=1, outputs=None)[source]¶ Elementwise Parametrized Rectified Linear Unit function. Calculates:
\[y_i = \max(0, x_i) + w_i \min(0, x_i)\]where negative slope \(w\) is learned and can vary across channels (an axis specified with base_axis).
Parameters: Returns: ND array.
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.
Normalization¶

nnabla.functions.
batch_normalization
(x, beta, gamma, mean, variance, axes=[1], decay_rate=0.9, eps=1e05, batch_stat=True, output_stat=False, n_outputs=None)[source]¶ Batch normalization.
\[\begin{split}\begin{eqnarray} \mu &=& \frac{1}{M} \sum x_i \\ \sigma^2 &=& \frac{1}{M} \left(\sum x_i  \mu\right)^2 \\ \hat{x}_i &=& \frac{x_i  \mu}{\sqrt{\sigma^2 + \epsilon}} \\ y_i &=& \hat{x}_i \gamma + \beta. \end{eqnarray}\end{split}\]At testing time, the mean and variance values used are those that were computed during training by moving average.
References
Parameters:  x (Variable) – ND array of input.
 beta (Variable) – ND array of beta which is learned.
 gamma (Variable) – ND array of gamma which is learned.
 mean (Variable) – ND array of running mean (modified during forward execution).
 variance (Variable) – ND array of running variance (modified during forward execution).
 axes (repeated int64) – Axes mean and variance are taken.
 decay_rate (float) – Decay rate of running mean and variance.
 eps (float) – Tiny value to avoid zero division by std.
 batch_stat (bool) – Use minibatch statistics rather than running ones.
 output_stat (bool) – It true, the batch statistics of mean and variance, will be returned as Variables. They are also differentiable.
Returns: Retruns batch normalization output as
Variable
. Ifoutput_stat=True
, it also returns the mean and variance of the minibatchSee also
nnabla.function_bases.batch_normalization
.

nnabla.functions.
mean_subtraction
(x, rmean, t, base_axis=1, update_running_mean=True, n_outputs=1, outputs=None)[source]¶ It subtracts the mean of the elements of the input array, and normalizes it to \(0\). Preprocessing arrays with this function has the effect of improving accuracy in various tasks such as image classification.
At training time, this function is defined as
\[\begin{split}\begin{eqnarray} \mu &=& \frac{1}{M} \sum x_i \\ rm &=& ({\rm decay\_rate}) rm + (1  {\rm decay\_rate}) \mu \\ y_i &=& x_i  rm \end{eqnarray}\end{split}\]At validation time, it is defined as
\[y_i = x_i  rm\]Note
The backward performs an approximated differentiation that takes into account only the latest minibatch.
Parameters:  x (Variable) – ND array of input.
 rmean (Variable) – ND array of running mean (modified during forward execution).
 t (Variable) – Scalar of num of iteration of running mean (modified during forward execution).
 base_axis (int) – Base axis of Mean Subtraction operation. Dimensions up to base_axis is treated as sample dimension.
 update_running_mean (bool) – Update running mean during forward execution.
Returns: ND array.
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.
Reduction¶

nnabla.functions.
sum
(x, axis=None, keepdims=False)[source]¶ Reduction along axes with sum operation.
Parameters: Returns: ND array.
Return type:

nnabla.functions.
mean
(x, axis=None, keepdims=False)[source]¶ Reduction along axes with mean operation.
Parameters: Returns: ND array.
Return type:

nnabla.functions.
max
(x, axis=None, keepdims=False)[source]¶ Reduction along axes with max operation.
Parameters: Returns: ND array.
Return type:

nnabla.functions.
min
(x, axis=None, keepdims=False)[source]¶ Reduction along axes with min operation.
Parameters: Returns: ND array.
Return type:

nnabla.functions.
prod
(x, axis=None, keepdims=False)[source]¶ Reduction along axes with product operation.
Parameters: Returns: ND array.
Return type: Note
Backward computation is not accurate in a zero value input.

nnabla.functions.
reduce_sum
(x, n_outputs=1, outputs=None)[source]¶ Reduction along an axis with sum operation.
Note
This is deprecated. Use
sum
instead.Parameters: x (Variable) – ND array. Returns: ND array Return type: Variable Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
reduce_mean
(x, n_outputs=1, outputs=None)[source]¶ Reduction by mean along an axis.
Note
This is deprecated. Use
mean
instead.Parameters: x (Variable) – ND array Returns: ND array Return type: Variable Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.
Arithmetic¶

nnabla.functions.
add2
(x0, x1, inplace=False, n_outputs=1, outputs=None)[source]¶ Elementwise addition.
\[y_i = x^{(0)}_i + x^{(1)}_i\]Parameters: Returns: ND array
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
sub2
(x0, x1, n_outputs=1, outputs=None)[source]¶ Elementwise subtraction.
\[y_i = x^{(0)}_i  x^{(1)}_i\]Parameters: Returns: ND array
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
mul2
(x0, x1, n_outputs=1, outputs=None)[source]¶ Elementwise multiplication.
\[y_i = x^{(0)}_i x^{(1)}_i\]Parameters: Returns: ND array
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
div2
(x0, x1, n_outputs=1, outputs=None)[source]¶ Elementwise division.
\[y_i = \frac{x^{(0)}_i} {x^{(1)}_i}\]Parameters: Returns: ND array
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
pow2
(x0, x1, n_outputs=1, outputs=None)[source]¶ Elementwise power funtion.
\[y_i = {(x^{(0)}_i)} ^ {x^{(1)}_i}\]Parameters: Returns: ND array
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
add_scalar
(x, val=1, n_outputs=1, outputs=None)[source]¶ Elementwise scalar addition.
\[y_i = x_i + v\]Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
mul_scalar
(x, val=1, n_outputs=1, outputs=None)[source]¶ Elementwise scalar multiplication.
\[y_i = v x_i\]Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
pow_scalar
(x, val=1, n_outputs=1, outputs=None)[source]¶ Elementwise scalar power function.
\[y_i = (x_i) ^ v\]Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
r_sub_scalar
(x, val=1, n_outputs=1, outputs=None)[source]¶ Elementwise scalar subtraction.
\[y_i = v  x_i\]Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
r_div_scalar
(x, val=1, n_outputs=1, outputs=None)[source]¶ Elementwise scalar division.
\[y_i = \frac{v}{x_i}\]Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
r_pow_scalar
(x, val=1, n_outputs=1, outputs=None)[source]¶ Elementwise scalar power function.
\[y_i = v ^ {x_i}\]Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.
Logical¶

nnabla.functions.
equal
(x0, x1, n_outputs=1, outputs=None)[source]¶ Element wise ‘equal’
\[\begin{split}f(x^{(0)}_i,x^{(1)}_i) = \begin{cases} 1 & (x^{(0)}_i = x^{(1)}_i) \\ 0 & otherwise \end{cases}.\end{split}\]Parameters: Returns: No Description
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
equal_scalar
(x0, val=1, n_outputs=1, outputs=None)[source]¶ Element wise ‘equal’ with a scalar
\[\begin{split}f(x_i,v) = \begin{cases} 1 & (x_i = v) \\ 0 & otherwise \end{cases}.\end{split}\]Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
greater
(x0, x1, n_outputs=1, outputs=None)[source]¶ Element wise comparison. The \(i^{th}\) element of the output is:
\[\begin{split}f(x^{(0)}_i,x^{(1)}_i) = \begin{cases} 1 & (x^{(0)}_i > x^{(1)}_i) \\ 0 & (x^{(0)}_i \leq x^{(1)}_i) \end{cases}.\end{split}\]Parameters: Returns: No Description
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
greater_equal
(x0, x1, n_outputs=1, outputs=None)[source]¶ Element wise comparison. The \(i^{th}\) element of the output is:
\[\begin{split}f(x^{(0)}_i,x^{(1)}_i) = \begin{cases} 1 & (x^{(0)}_i \geq x^{(1)}_i) \\ 0 & (x^{(0)}_i < x^{(1)}_i) \end{cases}.\end{split}\]Parameters: Returns: No Description
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
greater_equal_scalar
(x0, val=1, n_outputs=1, outputs=None)[source]¶ Element wise comparison with a scalar. The \(i^{th}\) element of the output is:
\[\begin{split}f(x^{(0)}_i,v) = \begin{cases} 1 & (x^{(0)}_i \geq v \\ 0 & (x^{(0)}_i < v \end{cases}.\end{split}\]Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
greater_scalar
(x0, val=1, n_outputs=1, outputs=None)[source]¶ Element wise comparison with a scalar. The \(i^{th}\) element of the output is:
\[\begin{split}f(x^{(0)}_i,v) = \begin{cases} 1 & (x^{(0)}_i > v \\ 0 & (x^{(0)}_i \leq v \end{cases}.\end{split}\]Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
less
(x0, x1, n_outputs=1, outputs=None)[source]¶ Element wise comparison. The \(i^{th}\) element of the output is:
\[\begin{split}f(x^{(0)}_i,x^{(1)}_i) = \begin{cases} 1 & (x^{(0)}_i < x^{(1)}_i) \\ 0 & (x^{(0)}_i \geq x^{(1)}_i) \end{cases}.\end{split}\]Parameters: Returns: No Description
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
less_equal
(x0, x1, n_outputs=1, outputs=None)[source]¶ Element wise comparison. The \(i^{th}\) element of the output is:
\[\begin{split}f(x^{(0)}_i,x^{(1)}_i) = \begin{cases} 1 & (x^{(0)}_i \leq x^{(1)}_i) \\ 0 & (x^{(0)}_i > x^{(1)}_i) \end{cases}.\end{split}\]Parameters: Returns: No Description
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
less_equal_scalar
(x0, val=1, n_outputs=1, outputs=None)[source]¶ Element wise comparison with a scalar. The \(i^{th}\) element of the output is:
\[\begin{split}f(x^{(0)}_i,v) = \begin{cases} 1 & (x^{(0)}_i \leq v) \\ 0 & (x^{(0)}_i > v) \end{cases}.\end{split}\]Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
less_scalar
(x0, val=1, n_outputs=1, outputs=None)[source]¶ Element wise comparison with a scalar. The \(i^{th}\) element of the output is:
\[\begin{split}f(x^{(0)}_i,v) = \begin{cases} 1 & (x^{(0)}_i < v) \\ 0 & (x^{(0)}_i \geq v) \end{cases}.\end{split}\]Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
logical_and
(x0, x1, n_outputs=1, outputs=None)[source]¶ Elementwise logical AND.
\[\begin{split}f(x^{(0)}_i,x^{(1)}_i) = \begin{cases} 1 & (x^{(0)}_i \neq 0 \;\&\; x^{(1)}_i \neq 0) \\ 0 & otherwise \end{cases}.\end{split}\]Parameters: Returns: No Description
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
logical_and_scalar
(x0, val, n_outputs=1, outputs=None)[source]¶ Elementwise logical AND with scalar.
\[\begin{split}f(x_i,v) = \begin{cases} 1 & (x_i \neq 0 \;\&\; v \neq 0) \\ 0 & otherwise \end{cases}.\end{split}\]Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
logical_not
(x0, n_outputs=1, outputs=None)[source]¶ Elementwise logical NOT operation
\[\begin{split}f(x_i) = \begin{cases} 1 & (x_i = 0) \\ 0 & otherwise \end{cases}.\end{split}\]Parameters: x0 (Variable) – Input variable Returns: ND array with the same shape as x Return type: Variable Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
logical_or
(x0, x1, n_outputs=1, outputs=None)[source]¶ Elementwise logical OR.
\[\begin{split}f(x^{(0)}_i,x^{(1)}_i) = \begin{cases} 0 & (x^{(0)}_i = 0 \;\&\; x^{(1)}_i = 0) \\ 1 & otherwise \end{cases}.\end{split}\]Parameters: Returns: No Description
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
logical_or_scalar
(x0, val, n_outputs=1, outputs=None)[source]¶ Elementwise logical OR with scalar.
\[\begin{split}f(x_i,v) = \begin{cases} 0 & (x_i = 0 \;\&\; v = 0) \\ 1 & otherwise \end{cases}.\end{split}\]Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
logical_xor
(x0, x1, n_outputs=1, outputs=None)[source]¶ Elementwise logical XOR.
\[\begin{split}f(x^{(0)}_i,x^{(1)}_i) = \begin{cases} 1 & (x^{(0)}_i = 0 \;\&\; x^{(1)}_i = 0) \\ 1 & (x^{(0)}_i \neq 0 \;\&\; x^{(1)}_i \neq 0) \\ 0 & otherwise \end{cases}.\end{split}\]Parameters: Returns: No Description
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
logical_xor_scalar
(x0, val, n_outputs=1, outputs=None)[source]¶ Elementwise logical XOR with scalar.
\[\begin{split}f(x_i,v) = \begin{cases} 1 & (x_i = 0 \;\&\; v = 0) \\ 1 & (x_i \neq 0 \;\&\; v \neq 0) \\ 0 & otherwise \end{cases}.\end{split}\]Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
not_equal
(x0, x1, n_outputs=1, outputs=None)[source]¶ Element wise ‘not equal’
\[\begin{split}f(x^{(0)}_i,x^{(1)}_i) = \begin{cases} 0 & (x^{(0)}_i = x^{(1)}_i) \\ 1 & otherwise \end{cases}.\end{split}\]Parameters: Returns: No Description
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
not_equal_scalar
(x0, val=1, n_outputs=1, outputs=None)[source]¶ Element wise ‘not equal’ with a scalar
\[\begin{split}f(x_i,v) = \begin{cases} 0 & (x_i = v) \\ 1 & otherwise \end{cases}.\end{split}\]Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
sign
(x, alpha=0.0, n_outputs=1, outputs=None)[source]¶ Elementwise sign function.
In the forward pass, it is defined as
\[\begin{split}f(x) = \begin{cases} 1 & (x > 0) \\ 1 & (x < 0) \\ \alpha & (x = 0) \end{cases}.\end{split}\]In the backward pass, it is defined as
\[\frac{\partial f(x)}{\partial x} = 1,\]or in other words, it behaves as the identity function for the gradient in the backward pass.
Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
minimum2
(x0, x1, n_outputs=1, outputs=None)[source]¶ Elementwise minimum.
\[y_i = \min(x^{(0)}_i, x^{(1)}_i)\]Parameters: Returns: ND array of min value
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
maximum2
(x0, x1, n_outputs=1, outputs=None)[source]¶ Elementwise maximum.
\[y_i = \max(x^{(0)}_i, x^{(1)}_i)\]Parameters: Returns: ND array of max value
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
minimum_scalar
(x, val=1.0, n_outputs=1, outputs=None)[source]¶ Elementwise scalar minimum.
\[y_i = \min(x_i, v)\]Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
maximum_scalar
(x, val=1.0, n_outputs=1, outputs=None)[source]¶ Elementwise scalar maximum.
\[y_i = \max (x_i, v)\]Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.
Math¶

nnabla.functions.
abs
(x, n_outputs=1, outputs=None)[source]¶ Elementwise absolute value function.
\[y_i = x_i\]Parameters: x (Variable) – Input variable Returns: Elementwise absolute variable Return type: Variable Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
exp
(x, n_outputs=1, outputs=None)[source]¶ Elementwise natural exponential function.
\[y_i = \exp(x_i).\]Parameters: x (Variable) – Input variable Returns: Elementwise exp variable Return type: Variable Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
log
(x, n_outputs=1, outputs=None)[source]¶ Elementwise natural logarithm function.
\[y_i = \ln(x_i).\]Parameters: x (Variable) – Input variable Returns: Elementwise log variable Return type: Variable Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
identity
(x, n_outputs=1, outputs=None)[source]¶ Identity function.
\[y = x\]Parameters: x (Variable) – ND array. Returns: ND array Return type: Variable Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.
Array Manipulation¶

nnabla.functions.
concatenate
(*inputs, **args)[source]¶ Concatenate two arrays along the specified axis.
Parameters: Returns: Concatenate variable
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
split
(x, axis=0)[source]¶ Split arrays at the specified axis.
It returns a number corresponding the size of the given axis (i.e
x.shape[axis]
) ofVariable
s.Parameters: Returns: A
tuple
ofVariable
sSee also
nnabla.function_bases.split()
.

nnabla.functions.
stack
(*inputs, **args)[source]¶ Joins two or more arrays on a new axis.
Note
Unlike
nnabla.functions.concatenate()
, which joins arrays on an existing axis, Stack joins arrays on a new axis.Parameters:  *inputs (Variable) – [Variadic Parameter] ND arrays. The sizes of all the arrays to be stacked must be the same.
 **param (int) – [name=axis] The axis on which to concatenate arrays. Axis indices take on values 0, 1, 2, and so on from the left. For example, to stack four (3,28,28) inputs on the second axis, specify 1. In this case, the output size will be (3,4,28,28).
Returns: Output
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
slice
(x, start=None, stop=None, step=None, n_outputs=1, outputs=None)[source]¶ Slice arrays along specified axis.
Parameters:  x (Variable) – ND array
 start (repeated int64) – Start indices for each axis
 stop (repeated int64) – Stop indices for each axis
 step (repeated int64) – Step indices for each axis
Returns: Sliced ND array
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
transpose
(x, axes, n_outputs=1, outputs=None)[source]¶ Transposes tensor dimensions.
Parameters:  x (Variable) – ND array
 axes (repeated int64) – Source axis indices for each axis.
Returns: Transposed ND array.
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
broadcast
(x, shape, n_outputs=1, outputs=None)[source]¶ Broadcasting NDarray to the specified shape.
Parameters: Returns: Broadcasted ND array
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
flip
(x, axes=None, n_outputs=1, outputs=None)[source]¶ Reverses the order of elements of the specified dimension of an array.
Parameters:  x (Variable) – ND array
 axes (repeated int64) – The index of the dimension to reverse the order of the elements. Axis indices take on values 0, 1, 2, and so on from the left. For example, to flip a 32 (W) by 24 (H) 100 RGB image (100,3,24,32) vertically and horizontally, specify (2,3).
Returns: ND array
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
shift
(x, shifts=None, border_mode='nearest', n_outputs=1, outputs=None)[source]¶ Shifts the array elements by the specified amount.
Parameters:  x (Variable) – ND array.
 shifts (repeated int64) – The amount to shift elements. For example, to shift image data to the right by 2 pixels and up 3 pixels, specify (3,2).
 border_mode (string) – Specify how to process the ends of arrays whose values will be undetermined as a result of shifting. nearest: The data at the ends of the original array is copied and used. reflect: Original data reflected at the ends of the original array is used.
Returns: ND array.
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
reshape
(x, shape, n_outputs=1, outputs=None)[source]¶ Returns a copy of the reshaped input variable.
Note
If you do not need a copy, you should use the
nnabla.Variable.reshape()
method instead.Parameters: Returns: Reshaped ND array
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
one_hot
(x, shape, n_outputs=1, outputs=None)[source]¶ OneHot creates onehot vector based on input indices.
Parameters: Returns: ND array
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.
Stochasticity¶

nnabla.functions.
dropout
(x, p=0.5, seed=1, n_outputs=1, outputs=None)[source]¶ Dropout. Samples a number \(u\) from a uniform distribution in \([0, 1]\) , and ignores the input if \(u > p\).
\[\begin{split}y = \left\{ \begin{array}{ll} \frac{x}{1  p} & (u > p) \\ 0 & ({\rm otherwise}) \end{array} \right.\end{split}\]Note
Usually dropout only applied during training as below (except Bayesian dropout).
h = PF.affine(x, num_hidden) if train: h = F.dropout(h, 0.5)
Parameters: Returns: ND array with the same shape as x
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
random_crop
(x, shape=None, base_axis=1, seed=1, n_outputs=1, outputs=None)[source]¶ RandomCrop randomly extracts a portion of an array.
Parameters: Returns: ND array
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
random_flip
(x, axes=None, base_axis=1, seed=1, n_outputs=1, outputs=None)[source]¶ Reverses the order of elements of the specified dimension of an array at 50% probability.
Parameters:  x (Variable) – ND array
 axes (repeated int64) – The index of the axis to reverse the order of the elements. Axis indices take on values 0, 1, 2, and so on from the left. For example, to flip a 32 (W) by 24 (H) 100 RGB images (100, 3,24,32) vertically and horizontally at random, specify (2,3).
 base_axis (int) – No Description
 seed (int) – Random seed
Returns: ND array
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
random_shift
(x, shifts=None, border_mode='nearest', base_axis=1, seed=1, n_outputs=1, outputs=None)[source]¶ Randomly shifts the array elements within the specified range.
Parameters:  x (Variable) – ND array.
 shifts (repeated int64) – Max absolute amount to shift elements. For example, to shift image data horizontally by \(\pm 2\) pixels and vertically by \(\pm 3\) pixels, specify (3,2).
 border_mode (string) – Specify how to process the ends of arrays whose values will be undetermined as a result of shifting. nearest: The data at the ends of the original array is copied and used. reflect: Original data reflected at the ends of the original array is used.
 base_axis (int) – No Description
 seed (int) – Random seed
Returns: ND array.
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
image_augmentation
(x, shape=None, pad=(0, 0), min_scale=1.0, max_scale=1.0, angle=0.0, aspect_ratio=1.0, distortion=0.0, flip_lr=False, flip_ud=False, brightness=0.0, brightness_each=False, contrast=1.0, contrast_center=0.0, contrast_each=False, noise=0.0, seed=1, n_outputs=1, outputs=None)[source]¶ ImageAugmentation randomly alters the input image.
Parameters:  x (Variable) – ND array.
 shape (
tuple
ofint
) – The output image data size.  pad (
tuple
ofint
) – Border padding values for each spatial axis. Padding will be added both sides of the dimension.  min_scale (float) – The minimum scale ratio when randomly scaling the image. For example, to scale down to 0.8 times the size of the original image, specify “0.8”. To not apply random scaling, set both min_scale and max_scale to “1.0”.
 max_scale (float) – The maximum scale ratio when randomly scaling the image. For example, to scale down to 2 times the size of the original image, specify “2.0”.
 angle (float) – The rotation angle range in radians when randomly rotating the image. The image is randomly rotated in the Angle to +Angle range. For example, to rotate in a +15 degree range, specify “0.26” (15 degrees/360 degrees * 2PI). To not apply random rotation, specify “0.0”.
 aspect_ratio (float) – The aspect ratio range when randomly deforming the image. For example, to deform aspect ratio of image from 1:1.3 to 1.3:1, specify “1.3”. To not apply random deforming, specify “1.0”.
 distortion (float) – The distortion range when randomly distorting the image. To not apply distortion, specify “0.0”.
 flip_lr (bool) – Whether to randomly flip the image horizontally at 50% probability.
 flip_ud (bool) – Whether to randomly flip the image vertically at 50% probability.
 brightness (float) – The absolute range of values to randomly add to the brightness. A random value in the Brightness to +Brightness range is added to the brightness. For example, to vary the brightness in the 0.05 to +0.05 range, specify “0.05”. To not apply random addition to brightness, specify “0.0”.
 brightness_each (bool) – Whether to apply the random addition to brightness (as specified by brightness) to each color channel. True: brightness is added based on a different random number for each channel. False: brightness is added based on a random number common to all channels.
 contrast (float) – The range in which to randomly vary the image contrast. The contrast is varied in the 1/Contrast times to Contrast times range. The output brightness is equal to (input  contrast_center) * contrast + contrast_center. For example, to vary the contrast in the 0.91 times to 1.1 times range, specify “1.1”. To not apply random contrast variation, specify “1.0”.
 contrast_center (float) – Intensity center used for applying contrast.
 contrast_each (bool) – Whether to apply the random contrast variation (as specified by contrast) to each color channel. True: contrast is varied based on a different random number for each channel. False: contrast is varied based on a random number common to all channels.
 noise (float) – Sigma of normal random number to be added.
 seed (int) – Random seed.
Returns: ND array.
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.
Loss Functions¶

nnabla.functions.
sigmoid_cross_entropy
(x, target, n_outputs=1, outputs=None)[source]¶ Elementwise cross entropy between x and the target variables, passed to a sigmoid function.
\[y_i =  \left(x^{(1)}_i \ln \left(\sigma \left(x^{(0)}_i \right)\right) + \ \left(1  x^{(1)}_i\right) \ln \left(1  \sigma \left(x^{(0)}_i \ \right)\right)\right)\]where \(\sigma(s)=\frac{1}{1+\exp(s)}\).
Note
SigmoidCrossEntropy is equivalent to Sigmoid+BinaryCrossEntropy, but computing them at once has the effect of reducing computational error.
Parameters: Returns: ND array of elementwise losses.
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
binary_cross_entropy
(x, target, n_outputs=1, outputs=None)[source]¶ Elementwise cross entropy between x and the target variables.
\[y_i =  \left(x^{(1)}_i * \ln \left(x^{(0)}_i\right) + \left(1  \ x^{(1)}_i\right) * \ln \left(1  x^{(0)}_i\right)\right).\]Parameters: Returns: ND array of elementwise losses.
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
softmax_cross_entropy
(x, target, axis=None, n_outputs=1, outputs=None)[source]¶ Elementwise cross entropy between the variables and the variables of a label given by a category index with Softmax normalization.
\[y_{j} = \ln \left(\frac{\exp(x_{t_j,j})}{\sum_{i'} exp(x_{i'j})}\right)\]along dimension specified by axis (\(i\) is the axis where normalization is performed on).
Note
SoftmaxCrossEntropy is equivalent to Softmax+CategoricalCrossEntropy, but computing them at once has the effect of reducing computational error.
Parameters: Returns: ND array of elementwise losses. \((D_1 \times ... \times 1 \times ... \times D_N)\)
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
categorical_cross_entropy
(x, target, axis=None, n_outputs=1, outputs=None)[source]¶ Elementwise cross entropy between x and the target, given by a category index.
\[y_{j} = \ln \left(\frac{\exp(x_{t_j,j})}{\sum_{i'} exp(x_{i'j})}\right)\]along dimension specified by axis (\(i\) is the axis where normalization is performed on).
Parameters: Returns: ND array of elementwise losses. \((D_1 \times ... \times 1 \times ... \times D_N)\)
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
squared_error
(x0, x1, n_outputs=1, outputs=None)[source]¶ Elementwise squared error
\[y_i = \left(x^{(0)}_i  x^{(1)}_i\right)^2.\]Parameters: Returns: ND array.
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
huber_loss
(x0, x1, delta=1.0, n_outputs=1, outputs=None)[source]¶ Elementwise Huber loss
\[\begin{split}y_i= \left\{ \begin{array}{ll} d^2 & (d < \delta)\\ \delta (2 d  \delta) & ({\rm otherwise}) \end{array} \right.\end{split}\]where \(d = x^{(0)}_i  x^{(1)}_i\)
Parameters: Returns: ND array of elementwise losses.
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
kl_multinomial
(p, q, base_axis=1, n_outputs=1, outputs=None)[source]¶ The Kullback Leibler Divergence for multinomial distributions.
\[D = \sum_i p_i \log \left( \frac{p_i}{q_i} \right)\]Parameters: Returns: Kullback Leibler divergence \(KL(p \parallel q)\).
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.
Quantization Neural Network Layers¶

nnabla.functions.
binary_sigmoid
(x, n_outputs=1, outputs=None)[source]¶ Elementwise binary sigmoid function.
In the forward pass,
\[\begin{split}f(x) = \begin{cases} 1 & (x > 0) \\ 0 & ({\rm otherwise})\end{cases},\end{split}\]but in the backward pass,
\[\begin{split}\frac{\partial f(x)}{\partial x} = \begin{cases} 0 & (x \geq 1) \\ \frac{1}{2} & ({\rm otherwise}) \end{cases}.\end{split}\]References
Parameters: x (Variable) – Input . Returns: Output. Return type: Variable Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
binary_tanh
(x, n_outputs=1, outputs=None)[source]¶ Elementwise Binary Tanh function.
In the forward pass,
\[\begin{split}f(x) = \begin{cases} 1 & (x > 0) \\ 1 & ({\rm otherwise}) \end{cases},\end{split}\]but in the backward pass,
\[\begin{split}\frac{\partial f(x)}{\partial x} = \begin{cases} 0 & (x \geq 1) \\ 1 & ({\rm otherwise}) \end{cases}.\end{split}\]References
Parameters: x (Variable) – Input . Returns: Output. Return type: Variable Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
binary_connect_affine
(x, weight, binary_weight, bias=None, base_axis=1, n_outputs=1, outputs=None)[source]¶ Binary Connect Affine, multiplierless innerproduct.
Binary Connect Affine is the affine function, but the innerproduct in this function is the following,
\[y_i = \sum_{i} sign(w_i) x_i.\]Therefore, \(sign(w_i)\) becomes a discrete parameter belonging to \(\{0,\,1\}\), thus the inner product simplifies to addition.
This function should be used together with
batch_normalization()
.Note
1) If you would like to share the binary weights between other standard layers, please use the standard, floating value weights (weight) and not the binary weights (binary_weight).
2) The weights and the binary weights become in sync only after a call to
forward()
, and not after a call tobackward()
. If you wish to store the parameters of the network, remember to callforward()
, once before doing so, otherwise the weights and the binary weights will not be in sync.3) CPU and GPU implementations now use floating values for binary_weight , since this function is for simulation purposes.
References
Parameters: Returns: Output.
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
binary_connect_convolution
(x, weight, binary_weight, bias=None, base_axis=1, pad=None, stride=None, dilation=None, group=1, n_outputs=1, outputs=None)[source]¶ Binary Connect Convolution, multiplierless innerproduct.
Binary Connect Convolution is the convolution function, but the innerproduct in this function is the following,
\[y_{n, a, b} = \sum_{m} \sum_{i} \sum_{j} sign(w_{n, m, i, j}) x_{m, a + i, b + j}.\]Therefore, \(sign(w_{n, m, i, j})\) becomes a discrete parameter belonging to \(\{0,\,1\}\), thus the inner product simplifies to addition.
This function should be used together with
batch_normalization()
.Reference
Note
1) If you would like to share the binary weights between other standard layers, please use the standard, floating value weights (weight) and not the binary weights (binary_weight).
2) The weights and the binary weights become in sync only after a call to
forward()
, and not after a call tobackward()
. If you wish to store the parameters of the network, remember to callforward()
, once before doing so, otherwise the weights and the binary weights will not be in sync.3) CPU and GPU implementations now use floating values for binary_weight , since this function is for simulation purposes.
Parameters:  x (Variable) – Input.
 weight (Variable) – [Parameter] Weight.
 binary_weight (Variable) – [Parameter] Binarized weight.
 bias (Variable) – [Optional Parameter] Bias.
 base_axis (int) – Dimensions up to base_axis is treated as sample dimension.
 pad (
tuple
ofint
) – Padding sizes for dimensions.  stride (
tuple
ofint
) – Stride sizes for dimensions.  dilation (
tuple
ofint
) – Dilation sizes for dimensions.  group (int) – Number of groups of channels. This makes the connection across channels sparser, by grouping connections along the mapping direction.
Returns: Output
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
binary_weight_affine
(x, weight, binary_weight, alpha, bias=None, base_axis=1, n_outputs=1, outputs=None)[source]¶ Binary Weight Affine, multiplierless innerproduct with a scale factor.
Binary Weight Affine is the affine function, but the innerproduct in this function is the following,
\[y_j = \frac{1}{\\mathbf{w}_j\_{\ell_1}} \sum_{i} sign(w_{ji}) x_i\]Therefore, \(sign(w_{ji})\) becomes a discrete parameter belonging to \(\{0,\,1\}\), thus the inner product simplifies to addition followed by a scaling factor \(\alpha_n = \frac{1}{\\mathbf{w}_n\_{\ell_1}} \, (n = 1, \ldots, N)\) , where \(N\) is the number of outmaps of this function.
Reference
Note
1) If you would like to share the binary weights between other standard layers, please use the standard, floating value weights (weight) and not the binary weights (binary_weight).
2) The weights and the binary weights become in sync only after a call to
forward()
, and not after a call tobackward()
. If you wish to store the parameters of the network, remember to callforward()
, once before doing so, otherwise the weights and the binary weights will not be in sync.3) CPU and GPU implementations now use floating values for binary_weight , since this function is for simulation purposes.
Parameters: Returns: Output.
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
binary_weight_convolution
(x, weight, binary_weight, alpha, bias=None, base_axis=1, pad=None, stride=None, dilation=None, group=1, n_outputs=1, outputs=None)[source]¶ Binary Weight Convolution, multiplierless innerproduct with a scale factor.
Binary Weight Convolution is the convolution function, but the innerproduct in this function is the following,
\[y_{n, a, b} = \frac{1}{\\mathbf{w}_n\_{\ell_1}} \sum_{m} \sum_{i} \sum_{j} sign(w_{n, m, i, j}) x_{m, a + i, b + j}.\]Therefore, \(sign(w_{n, m, i, j})\) becomes a discrete parameter belonging to \(\{0,\,1\}\), thus the inner product simplifies to addition followed by a scaling factor \(\alpha_n = \frac{1}{\\mathbf{w}_n\_{\ell_1}} \, (n = 1, \ldots, N)\) , where \(N\) is the number of outmaps of this function.
Reference
Note
1) If you would like to share the binary weights between other standard layers, please use the standard, floating value weights (weight) and not the binary weights (binary_weight).
2) The weights and the binary weights become in sync only after a call to
forward()
, and not after a call tobackward()
. If you wish to store the parameters of the network, remember to callforward()
, once before doing so, otherwise the weights and the binary weights will not be in sync.3) CPU and GPU implementations now use floating values for binary_weight , since this function is for simulation purposes.
Parameters:  x (Variable) – Input.
 weight (Variable) – [Parameter] Weight.
 binary_weight (Variable) – [Parameter] Binarized weight.
 alpha (Variable) – [Parameter] Alpha.
 bias (Variable) – [Optional Parameter] Bias.
 base_axis (int) – Dimensions up to base_axis is treated as sample dimension.
 pad (
tuple
ofint
) – Padding sizes for dimensions.  stride (
tuple
ofint
) – Stride sizes for dimensions.  dilation (
tuple
ofint
) – Dilation sizes for dimensions.  group (int) – Number of groups of channels. This makes the connection across channels sparser, by grouping connections along the mapping direction.
Returns: Output
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.
Unsupported, Special Use¶

nnabla.functions.
vat_noise
(x, w, base_axis=1, eps=1.0, n_outputs=1, outputs=None)[source]¶ Noise for virtual adversarial training.
This layer is a special layer for GUI network designing, specialized for getting the noise of virtual adversarial training.
In the backward process, the weight parameter will be replaced with the gradient.
Forward
\[y_i = \frac{\epsilon x_i}{\sqrt{\sum_k x_k^2 + c}}\]Backward
\[\delta x_i = 0\]\[w_i = \epsilon \delta y_i\]Note
This layer is a special layer for GUI network designing.
References
Parameters: Returns: ND array
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.

nnabla.functions.
unlink
(x, n_outputs=1, outputs=None)[source]¶ This function behaves as an identity function on the forward pass, and deletes the gradient for the background pass.
This layer is a special layer for GUI network designing, used for getting zero backward operation by adding this layer.
Forward
\[y_i = x_i\]Backward
\[\delta x_i = 0\]Note
This layer is a special layer for GUI network designing.
Parameters: x (Variable) – ND array. Returns: ND array. Return type: Variable Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.
Validation¶

nnabla.functions.
top_n_error
(x, target, axis=None, n=1, n_outputs=1, outputs=None)[source]¶ Top N error along dimension specified by axis.
\[\begin{split}y_i = \left \{ \begin{array}{l} 1 (x_i is not within Nth place) \\ 0 (x_i is within Nth place) \end{array} \right.\end{split}\]Parameters: Returns: Elementwise error ND array. (f$D_1 times ... times 1 times ... times D_Nf$)
Return type: Note
All nnabla functions in
nnabla.functions
are decorated with thennabla.function_bases.function_api
decorator, which queries the current context and passes it into the first argument of the original function. The original function always takes a context as the first argument.