# 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 in nnabla.functions. These functions return nnabla.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 N-D array with shape ($$M_0 \times ... \times M_{B-1} \times D_B \times ... \times D_N$$). Dimensions before and after base_axis are flattened as if it is a matrix. weight (Variable) – Weight matrix with shape ($$(D_B \times ... \times D_N) \times L$$) [parameter] bias (Variable) – Bias vector ($$L$$) [optional][parameter] base_axis (int) – Base axis of Affine operation. Dimensions up to base_axis is treated as sample dimension. [default=1] $$(B + 1)$$-D array. ($$M_0 \times ... \times M_{B-1} \times L$$) Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

N-D Convolution with bias.

See references for dilated convolution (a.k.a. atrous convolution).

References

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) – $$(2 + N)$$-D array ($$C' \times C \times K_1 \times ... \times K_N$$). [parameter] bias (Variable) – Bias vector ($$C'$$). [optional][parameter] base_axis (int) – base axis $$B$$. [default=1] pad (tuple of int) – Padding sizes for dimensions. [default=(0,) * (len(x.shape) - (base_axis+1))] stride (tuple of int) – Stride sizes for dimensions. [default=(1,) * (len(x.shape) - (base_axis+1))] dilation (tuple of int) – Dilation sizes for dimensions. [default=(1,) * (len(x.shape) - (base_axis+1))] group (int) – Number of groups of channels. This makes the connection across channels sparser, by grouping connections along the mapping direction. [default=1] $$(B + 1 + N)$$-D array ($$M_1 \times ... \times M_B \times C' \times L'_1 \times ... \times L'_N$$). Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.depthwise_convolution(x, weight, bias=None, base_axis=1, pad=None, stride=None, dilation=None, multiplier=1, n_outputs=-1, outputs=None)[source]

N-D Depthwise Convolution with bias.

References

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) – $$(1 + N)$$-D array ($$C \times K_1 \times ... \times K_N$$). [parameter] bias (Variable) – Bias vector ($$C$$). [optional][parameter] base_axis (int) – base axis $$B$$. [default=1] pad (tuple of int) – Padding sizes for dimensions. [default=(0,) * (len(x.shape) - (base_axis+1))] stride (tuple of int) – Stride sizes for dimensions. [default=(1,) * (len(x.shape) - (base_axis+1))] dilation (tuple of int) – Dilation sizes for dimensions. [default=(1,) * (len(x.shape) - (base_axis+1))] multiplier (int) – Number of output feature maps per input feature map. [default=1] $$(B + 1 + N)$$-D array ($$M_1 \times ... \times M_B \times C \times L'_1 \times ... \times L'_N$$). Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

N-D deconvolution, also known as transposed convolution, with bias operates backward convolution (derivative of the output w.r.t. the input) plus channel-wise learned bias.

The weights are specified in the same manner as convolution() , as if it was an ordinary convolution function. The forward operation of deconvolution() will then be operationally equivalent to the backward pass of convolution() . 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) – $$(2 + N)$$-D array ($$C' \times C \times K_1 \times ... \times K_N$$). [parameter] bias (Variable) – Bias vector ($$C'$$). [optional][parameter] base_axis (int) – base axis $$B$$. [default=1] pad (tuple of int) – Padding sizes for dimensions. [default=(0,) * (len(x.shape) - (base_axis+1))] stride (tuple of int) – Stride sizes for dimensions. [default=(1,) * (len(x.shape) - (base_axis+1))] dilation (tuple of int) – Dilation sizes for dimensions. [default=(1,) * (len(x.shape) - (base_axis+1))] group (int) – Number of groups of channels. This makes the connection across channels sparser, by grouping connections along the mapping direction. [default=1] $$(B + 1 + N)$$-D array ($$M_1 \times ... \times M_B \times C' \times L'_1 \times ... \times L'_N$$). Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.depthwise_deconvolution(x, weight, bias=None, base_axis=1, pad=None, stride=None, dilation=None, divisor=1, n_outputs=-1, outputs=None)[source]

Depthwise deconvolution computes the transposed depthwise convolution with bias for one-dimensional and two-dimensional input data.

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) – $$(1 + N)$$-D array ($$C \times K_1 \times ... \times K_N$$). [parameter] bias (Variable) – Bias vector ($$C$$). [optional][parameter] base_axis (int) – base axis $$B$$. [default=1] pad (tuple of int) – Padding sizes for dimensions. [default=(0,) * (len(x.shape) - (base_axis+1))] stride (tuple of int) – Stride sizes for dimensions. [default=(1,) * (len(x.shape) - (base_axis+1))] dilation (tuple of int) – Dilation sizes for dimensions. [default=(1,) * (len(x.shape) - (base_axis+1))] divisor (int) – Number of input feature maps per output feature map. [default=1] $$(B + 1 + N)$$-D array ($$M_1 \times ... \times M_B \times C \times L'_1 \times ... \times L'_N$$). Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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 of int) – Kernel sizes for each spatial axis. stride (tuple of int) – Subsampling factors for each spatial axis. [default=kernel] ignore_border (bool) – If false, kernels covering borders are also considered for the output. [default=True] pad (tuple of int) – Border padding values for each spatial axis. Padding will be added both sides of the dimension. [default=(0,) * len(kernel)] Maximum values variable Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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 of int) – Kernel sizes for each spatial axis. stride (tuple of int) – Subsampling factors for each spatial axis. [default=kernel] ignore_border (bool) – If false, kernels covering borders are also considered for the output. [default=True] pad (tuple of int) – Border padding values for each spatial axis. Padding will be added both sides of the dimension. [default=(0,) * len(kernel)] including_pad (bool) – If true, border padding values are considered for the output. [default=True] Average values variable Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.global_average_pooling(x, n_outputs=-1, outputs=None)[source]

Warning

This function is experimental suppport, so please do not actively use it.

Global average pooling. It pools an averaged value from the whole image

Parameters: x (Variable) – Input variable. Average values variable Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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 of int) – Kernel sizes for each spatial axis. stride (tuple of int) – Subsampling factors for each spatial axis. [default=kernel] ignore_border (bool) – If false, kernels covering borders are also considered for the output. [default=True] pad (tuple of int) – Border padding values for each spatial axis. Padding will be added both sides of the dimension. [default=(0,) * len(kernel)] Summed values variable Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x (Variable) – Input variable. kernel (tuple of int) – Kernel sizes for each spatial axis. Spread values variable Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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, w, n_outputs=-1, outputs=None)[source]

Embed slices of a matrix/tensor with indexing array/tensor.

Parameters: x0 (Variable) – Indices with shape $$(I_0, ..., I_N)$$ w (Variable) – Weights with shape $$(W_0, ..., W_M)$$ [parameter] Output with shape $$(I_0, ..., I_N, W_1, ..., W_M)$$ Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise sigmoid function.

$f(x) = \frac{1}{1 + \exp(-x)},$
Parameters: x (Variable) – Input Output Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.swish(x, n_outputs=-1, outputs=None)[source]

Element-wise swish function, by Ramachandran et al. (2017).

$y_i = \frac{x_i}{1 + \exp(-x_i)},$

References

Parameters: x (Variable) – Input Output Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise hyperbolic tangent (tanh) function.

$y_i = \tanh (x_i)$
Parameters: x (Variable) – N-D array N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise Rectified Linear Unit (ReLU) function.

$y_i = \max (0, x_i)$
Parameters: x (Variable) – N-D array inplace (bool) – The output array is shared with the input array if True. [default=False] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x (Variable) – N-D array. Typically indicates a score. axis (int) – Axis normalization is taken. [default=len(x.shape) - 1] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise 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: x (Variable) – N-D array alpha (float) – Coefficient for negative outputs. $$\alpha$$ in definition [default=1.0] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.selu(x, scale=1.05070098735548, alpha=1.673263242354377, n_outputs=-1, outputs=None)[source]

Element-wise Scaled Exponential Linear Unit (SELU) function by Klambauer et al. (2017).

$\begin{split}y_i= \lambda \left\{ \begin{array}{ll} x_i & (x > 0)\\ \alpha (\exp(x_i) - 1) & (x \leq 0) \end{array} \right..\end{split}$

The coefficients $$\lambda$$ and $$\alpha$$ default to the following values $$\lambda_{01}$$ and $$\alpha_{01}$$, respectively, provided by Klambauer et al. (2017):

$\begin{split}\begin{array}{lll} \lambda_{01} &=& \left( 1 - \operatorname{erfc}\left( \frac{1}{\sqrt{2}} \right) \sqrt{e} \right) \sqrt{2 \pi} \\ && \left( 2 \operatorname{erfc} \left( \sqrt{2} \right) e^2 + \pi \operatorname{erfc}\left( \frac{1}{\sqrt{2}} \right)^2 e \right. \\ && \left. - 2(2 + \pi) \operatorname{erfc} \left( \frac{1}{\sqrt{2}} \right) \sqrt{e} + \pi + 2 \right)^{-1/2} \\ &\approx& 1.0507 \\ \alpha_{01} &=& - \frac {\sqrt {\frac {2}{\pi}}} {\operatorname{erfc} \left( \frac{1}{\sqrt{2}} \right) \exp \left(\frac {1} {2} \right) - 1} \\ &\approx& 1.67326 \end{array}\end{split}$

References

Parameters: x (Variable) – N-D array scale (float) – The coefficient $$\lambda$$ in the definition. [default=1.05070098735548] alpha (float) – The coefficient $$\alpha$$ in the definition. [default=1.673263242354377] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise 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: x (Variable) – N-D array. axis (int) – The ReLU activations of positive inputs and negative inputs are concatenated at axis. [default=1] N-D array where axis dimension is doubled by concatenating. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise Concatenated Exponential Linear Unit (CELU) function. Concatenates ELU outputs of positive and negative inputs together at specified axis.

Parameters: x (Variable) – N-D array. alpha (float) – Coefficient for negative outputs. $$\alpha$$ in definition. [default=1.0] axis (int) – The ELU activations of positive inputs and negative inputs are concatenated at axis. [default=1] N-D array where axis dimension is doubled by concatenating. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise 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: x0 (Variable) – (N-D array) Input x1 (Variable) – (N-D array) Weights base_axis (int) – Dimensions up to base_axis is treated as sample dimension. [default=1] N-D array. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.leaky_relu(x, alpha=0.1, n_outputs=-1, outputs=None)[source]

Element-wise Leaky Rectified Linear Unit (ReLU) function.

It is defined as:

$y_i = \alpha * \min(0, x_i) + \max (0, x_i)$
Parameters: x (Variable) – N-D array alpha (float) – The slope value multiplied to negative numbers. $$\alpha$$ in the definition. [default=0.1] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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=1e-05, 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) – N-D array of input. beta (Variable) – N-D array of beta which is learned. gamma (Variable) – N-D array of gamma which is learned. mean (Variable) – N-D array of running mean (modified during forward execution). variance (Variable) – N-D 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 mini-batch 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. Retruns batch normalization output as Variable. If output_stat=True, it also returns the mean and variance of the mini-batch Variable: Output of the batch normalization Variable: Mean (if output_stat=True) Variable: Variance (if output_stat=True)

nnabla.function_bases.batch_normalization.

nnabla.functions.mean_subtraction(x, mean, t, base_axis=1, update_running_mean=True)[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

$\begin{split}\begin{eqnarray} \mu &=& \frac{1}{M} \sum x_i \\ y_i &=& x_i - \mu \end{eqnarray}\end{split}$

At testing time, the mean values used are those that were computed during training by moving average.

Note

The backward performs an approximated differentiation that takes into account only the latest mini-batch.

Parameters: x (Variable) – N-D array of input. mean (Variable) – N-D 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. [default=1] update_running_mean (bool) – Update running mean during forward execution. [default=True] N-D array. Variable

nnabla.function_bases.mean_subtraction.

nnabla.functions.clip_by_value(x, min, max)[source]

Clip inputs by values.

$\begin{split}y = \begin{cases} max & (x > max) \\ x & (otherwise) \\ min & (x < min) \end{cases}.\end{split}$
Parameters: x (Variable) – An input variable. min (Variable) – A min variable by which x is clipped. Note that the shape of min must be the same as x’s. max (Variable) – A max variable by which x is clipped. Note that the shape of max must be the same as x’s N-D array. Variable
nnabla.functions.clip_grad_by_value(x, min, max, n_outputs=-1, outputs=None)[source]

In forward pass, the function behaves as the identity.

In backward pass,

$\begin{split}g_x = \begin{cases} max & (g_y > max) \\ g_y & (otherwise) \\ min & (g_y < min) \end{cases}.\end{split}$

A typical case for use is to prevent the gradient explosion through a whole computational graph. For example, if you want to clip gradient values for each feature map,

x = nn.Variable([16, 3, 32, 32])
min = F.broadcast(nn.Variable.from_numpy_array(np.asarray([-1.0]).reshape((1, 1, 1, 1))), (16, 3, 32, 32))
max = F.broadcast(nn.Variable.from_numpy_array(np.asarray([1.0]).reshape((1, 1, 1, 1))), (16, 3, 32, 32))
h = PF.convolution(c, 64, (3, 3), pad=(1, 1))

Parameters: x (Variable) – N-D array of input. min (Variable) – N-D array of minimum input value by which the gradients of the y are clipped. Note that the shape of min must be the same as x’s and the backward to min is not performed. max (Variable) – N-D array of maximum input value by which the gradients of the y are clipped. Note that the shape of max must be the same as x’s and the backward to max is not performed. N-D array. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.clip_by_norm(x, clip_norm, axis=None)[source]

ClipByNorm

$y = N \times \frac{x}{\|x\|_2}.$

where $$x$$ the input, $$y$$ is the output, and $$N$$ is clip_norm where the norm of $$x$$ becomes. this is the case that axes is not set. When axes is set, the norm is computed over axes.

Parameters: x (Variable) – An input variable. clip_norm (Variable or float) – An input scalar variable or float value. axis (None, int or tuple of ints) – Axis or axes along which the is performed. Passing the default value None will reduce all dimensions. (reduction) – N-D array. Variable
nnabla.functions.clip_grad_by_norm(x, clip_norm=None, axes=None, n_outputs=-1, outputs=None)[source]

In the forward pass, the function behaves like the identity.

In the backward pass,

$g_x = N \times \frac{g_y}{\|g_y\|_2}.$

where $$g_x$$ is the gradient w.r.t the input, $$g_y$$ is the gradient w.r.t. the output, and $$N$$ is clip_norm where the norm of $$g_y$$ becomes. this is the case that axes is not set. When axes is set, the norm is computed over axes.

A typical case for use is to prevent the gradient explosion through a whole computational graph. For example, if you want to normalize gradient values over feature axis,

x = nn.Variable([16, 3, 32, 32])
h = PF.convolution(c, 64, (3, 3), pad=(1, 1))

Parameters: x (Variable) – N-D array of input. clip_norm (float) – Clip to the norm of input to clip_norm in the backward pass. [default=1.0] axes (repeated int64) – Axes to be reduced. If empty list is given, all dimensions are reduced to scalar. This is used in the forward pass. [default=range(x.ndim)] N-D array. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x (Variable) – An input variable. axis (None, int or tuple of ints) – Axis or axes along which the sum is calculated. Passing the default value None will reduce all dimensions. keepdims (bool) – Flag whether the reduced axes are kept as a dimension with 1 element. N-D array. Variable
nnabla.functions.mean(x, axis=None, keepdims=False)[source]

Reduction along axes with mean operation.

Parameters: x (Variable) – An input variable. axis (None, int or tuple of ints) – Axis or axes along which mean is calculated. Passing the default value None will reduce all dimensions. keepdims (bool) – Flag whether the reduced axes are kept as a dimension with 1 element. N-D array. Variable
nnabla.functions.max(x, axis=None, keepdims=False)[source]

Reduction along axes with max operation.

Parameters: x (Variable) – An input variable. axis (None, int or tuple of ints) – Axis or axes along which max is calculated. Passing the default value None will reduce all dimensions. keepdims (bool) – Flag whether the reduced axes are kept as a dimension with 1 element. N-D array. Variable
nnabla.functions.min(x, axis=None, keepdims=False)[source]

Reduction along axes with min operation.

Parameters: x (Variable) – An input variable. axis (None, int or tuple of ints) – Axis or axes along which min is calculated. Passing the default value None will reduce all dimensions. keepdims (bool) – Flag whether the reduced axes are kept as a dimension with 1 element. N-D array. Variable
nnabla.functions.prod(x, axis=None, keepdims=False)[source]

Reduction along axes with product operation.

Parameters: x (Variable) – An input variable. axis (None, int or tuple of ints) – Axis or axes along which product is calculated. Passing the default value None will reduce all dimensions. keepdims (bool) – Flag whether the reduced axes are kept as a dimension with 1 element. N-D array. Variable

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) – N-D array. N-D array Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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) – N-D array N-D array Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

$y_i = x^{(0)}_i + x^{(1)}_i$
Parameters: x0 (Variable) – N-D array x1 (Variable) – N-D array inplace (bool) – The output array is shared with the 1st input array if True. [default=False] N-D array Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise subtraction.

$y_i = x^{(0)}_i - x^{(1)}_i$
Parameters: x0 (Variable) – N-D array x1 (Variable) – N-D array N-D array Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise multiplication.

$y_i = x^{(0)}_i x^{(1)}_i$
Parameters: x0 (Variable) – N-D array x1 (Variable) – N-D array N-D array Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise division.

$y_i = \frac{x^{(0)}_i} {x^{(1)}_i}$
Parameters: x0 (Variable) – N-D array x1 (Variable) – N-D array N-D array Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise power function.

$y_i = {(x^{(0)}_i)} ^ {x^{(1)}_i}$
Parameters: x0 (Variable) – N-D array x1 (Variable) – N-D array N-D array Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

$y_i = x_i + v$
Parameters: x (Variable) – Input variable val (float) – Value of the scalar [default=1] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise scalar multiplication.

$y_i = v x_i$
Parameters: x (Variable) – Input variable val (float) – Value of the scalar [default=1] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise scalar power function.

$y_i = (x_i) ^ v$
Parameters: x (Variable) – Input variable val (float) – Value of the scalar [default=1] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise scalar subtraction.

$y_i = v - x_i$
Parameters: x (Variable) – Input variable val (float) – Value of the scalar [default=1] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise scalar division.

$y_i = \frac{v}{x_i}$
Parameters: x (Variable) – Input variable val (float) – Value of the scalar [default=1] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise scalar power function.

$y_i = v ^ {x_i}$
Parameters: x (Variable) – Input variable val (float) – Value of the scalar [default=1] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x0 (Variable) – N-D array x1 (Variable) – N-D array No Description Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x0 (Variable) – Input variable val (float) – Value of the scalar [default=1] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x0 (Variable) – N-D array x1 (Variable) – N-D array No Description Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x0 (Variable) – N-D array x1 (Variable) – N-D array No Description Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x0 (Variable) – Input variable val (float) – Value of the scalar [default=1] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x0 (Variable) – Input variable val (float) – Value of the scalar [default=1] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x0 (Variable) – N-D array x1 (Variable) – N-D array No Description Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x0 (Variable) – N-D array x1 (Variable) – N-D array No Description Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x0 (Variable) – Input variable val (float) – Value of the scalar [default=1] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x0 (Variable) – Input variable val (float) – Value of the scalar [default=1] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x0 (Variable) – N-D array x1 (Variable) – N-D array No Description Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x0 (Variable) – Input variable val (bool) – No Description N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise 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 N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x0 (Variable) – N-D array x1 (Variable) – N-D array No Description Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x0 (Variable) – Input variable val (bool) – No Description N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x0 (Variable) – N-D array x1 (Variable) – N-D array No Description Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x0 (Variable) – Input variable val (bool) – No Description N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x0 (Variable) – N-D array x1 (Variable) – N-D array No Description Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x0 (Variable) – Input variable val (float) – Value of the scalar [default=1] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise 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: x (Variable) – Input alpha (float) – Value in case of $$x = 0$$. [default=0.0] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise minimum.

$y_i = \min(x^{(0)}_i, x^{(1)}_i)$
Parameters: x0 (Variable) – N-D array x1 (Variable) – N-D array N-D array of min value Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise maximum.

$y_i = \max(x^{(0)}_i, x^{(1)}_i)$
Parameters: x0 (Variable) – N-D array x1 (Variable) – N-D array N-D array of max value Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise scalar minimum.

$y_i = \min(x_i, v)$
Parameters: x (Variable) – Input variable val (float) – Value of the scalar [default=1.0] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise scalar maximum.

$y_i = \max (x_i, v)$
Parameters: x (Variable) – Input variable val (float) – Value of the scalar [default=1.0] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.constant(val=0, shape=[], n_outputs=-1, outputs=None)[source]

Generate a constant-valued array.

Parameters: val (float) – Constant value. [default=0] shape (tuple of int) – Shape of the output array. [default=[]] N-D array where all values are the specified constant. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.abs(x, n_outputs=-1, outputs=None)[source]

Element-wise absolute value function.

$y_i = |x_i|$
Parameters: x (Variable) – Input variable Element-wise absolute variable Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise natural exponential function.

$y_i = \exp(x_i).$
Parameters: x (Variable) – Input variable Element-wise exp variable Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise natural logarithm function.

$y_i = \ln(x_i).$
Parameters: x (Variable) – Input variable Element-wise log variable Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.round(x, n_outputs=-1, outputs=None)[source]

Element-wise round function.

In the forward pass, this function simply computes round to the nearest integer value.

$y_i = round(x_i).$

In the backward pass, the simple Straight-Through Estimator (STE) is applied,

$\frac{\partial y_i}{\partial x_i} = 1.$
Parameters: x (Variable) – Input variable N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.ceil(x, n_outputs=-1, outputs=None)[source]

Element-wise ceil function.

In the forward pass, this function simply returns the smallest integer which is not less than the input.

$y_i = ceil(x_i).$

In the backward pass, the simple Straight-Through Estimator (STE) is applied,

$\frac{\partial y_i}{\partial x_i} = 1.$
Parameters: x (Variable) – Input variable N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.floor(x, n_outputs=-1, outputs=None)[source]

Element-wise floor function.

In the forward pass, this function simply returns the largest integer which is not greater than the input.

$y_i = floor(x_i).$

In the backward pass, the simple Straight-Through Estimator (STE) is applied,

$\frac{\partial y_i}{\partial x_i} = 1.$
Parameters: x (Variable) – Input variable N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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) – N-D array. N-D array Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.matrix_diag(x, n_outputs=-1, outputs=None)[source]

Returns an array where the last two dimensions consist of the diagonal matrix.

Parameters: x (Variable) – N-D array with shape ($$M_0 \times \ldots \times M_N$$). N-D array with shape ($$M_0 \times \ldots \times M_N \times M_N$$). Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.matrix_diag_part(x, n_outputs=-1, outputs=None)[source]

Returns an array in which the values of the last dimension consist of the diagonal elements of the last two dimensions of an input array.

Parameters: x (Variable) – N-D array with shape ($$M_0 \times \ldots \times M_N \times M_N$$). N-D array with shape ($$M_0 \times \ldots \times M_N$$). Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.batch_matmul(a, b, transpose_a=False, transpose_b=False, n_outputs=-1, outputs=None)[source]

Batch matrix multiplication.

Two of batchs of matrices are multiplied for each sample in a batch. A batch of matrices is composed as […, P, Q] where the last two dimensions compose matrix dimensions, and the first dimensions up to the third last dimension are considered as batch samples.

Parameters: a (Variable) – N-D array with >= 2-dim. The last two dimensions will be treated as a matrix. b (Variable) – N-D array with >= 2-dim. The last two dimensions will be treated as a matrix. The product of the size of 0-th dimension through the size of the third last dimension must be same as that of the input a. transpose_a (bool) – Transpose the last two axes of a in matrix multiplication. [default=False] transpose_b (bool) – Transpose the last two axes of b in matrix multiplication. [default=False] Output of sample-wise matrix multiplication in a batch. When a is of a shape of [N, P, Q], b is of a shape of [N, Q, R], and transpose options are all False, the output will be a shape of [N, P, R]. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.sin(x, n_outputs=-1, outputs=None)[source]

Element-wise sine (sin) function.

$y_i = \sin (x_i)$
Parameters: x (Variable) – N-D array N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.cos(x, n_outputs=-1, outputs=None)[source]

Element-wise cosine (cos) function.

$y_i = \cos (x_i)$
Parameters: x (Variable) – N-D array N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.tan(x, n_outputs=-1, outputs=None)[source]

Element-wise tangent (tan) function.

$y_i = \tan (x_i)$
Parameters: x (Variable) – N-D array N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.sinh(x, n_outputs=-1, outputs=None)[source]

Element-wise hyperbolic sine (sinh) function.

$y_i = \sinh (x_i)$
Parameters: x (Variable) – N-D array N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.cosh(x, n_outputs=-1, outputs=None)[source]

Element-wise hyperbolic cosine (cosh) function.

$y_i = \cosh (x_i)$
Parameters: x (Variable) – N-D array N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise hyperbolic tangent (tanh) function.

$y_i = \tanh (x_i)$
Parameters: x (Variable) – N-D array N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.asin(x, n_outputs=-1, outputs=None)[source]

Element-wise arcsine (asin) function.

$y_i = \arcsin (x_i)$
Parameters: x (Variable) – N-D array N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.acos(x, n_outputs=-1, outputs=None)[source]

Element-wise arccosine (acos) function.

$y_i = \arccos (x_i)$
Parameters: x (Variable) – N-D array N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.atan(x, n_outputs=-1, outputs=None)[source]

Element-wise arctangent (atan) function.

$y_i = \arctan (x_i)$
Parameters: x (Variable) – N-D array N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.asinh(x, n_outputs=-1, outputs=None)[source]

Element-wise hyperbolic arcsine (asinh) function.

$y_i = \text{arcsinh} (x_i)$
Parameters: x (Variable) – N-D array N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.acosh(x, n_outputs=-1, outputs=None)[source]

Element-wise hyperbolic arccosine (acosh) function.

$y_i = \text{arccosh} (x_i)$
Parameters: x (Variable) – N-D array N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.atanh(x, n_outputs=-1, outputs=None)[source]

Element-wise hyperbolic arctangent (atanh) function.

$y_i = \text{arctanh} (x_i)$
Parameters: x (Variable) – N-D array N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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(*x, **kw)[source]

Concatenate a variable number of input arrays along the specified axis.

Parameters: *x (Variable) – N-D arrays. [variadic][parameter] axis (int) – Axis [default=len(x[0].shape) - 1] Concatenate variable Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]) of Variable s.

Parameters: x (Variable) – N-D array axis (int) – Axis

Returns: A tuple of Variable s

nnabla.function_bases.split().

nnabla.functions.stack(*x, **kw)[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: *x (Variable) – N-D arrays. The sizes of all the arrays to be stacked must be the same. [variadic][parameter] axis (int) – 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). [default=0] Output Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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) – N-D array start (repeated int64) – Start indices for each axis [default=(0,) * len(x.shape)] stop (repeated int64) – Stop indices for each axis [default=tuple(x.shape)] step (repeated int64) – Step indices for each axis [default=(1,) * len(x.shape)] Sliced N-D array Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.pad(x, pad_width=None, mode='constant', constant_value=None, n_outputs=-1, outputs=None)[source]

Pads given N-D array with specified sizes of dimensions. Padding begins at the last dimension of input x and continues for the specified padding dimension.

Parameters: x (Variable) – N-D array pad_width (repeated int64) – n-elem tuple, where n/2 <= input dimensions and n is even. len(pad_width)/2 represents the padding dimension(e.g. 1D, 2D, 3D etc.). (Currently padding upto 3D is supported) [default=(0,) * len(x.shape)] mode (string) – Padding mode is one of the following. constant : Elements in pad region are filled with constant_value. replicate : Padded elements are filled with the values in nearest edges. reflect : Padded with the reflection of the vector mirrored on the first and last values of the vector along each axis. (Currently only constant mode is supported) [default=’constant’] constant_value (float) – Constant values filled in padded regions if mode is constant. [default=0] Padded N-D array (e.g. (B, C, H, W) shape) where dimension depends on pad_width. ndim() of output N-D array will be same as ndim() of input N-D array. -for 1D padding : N-D input array with padding of the form (padLeft, padRight). The output N-D array dimension (B, C, H, padLeft + W + padRight). -for 2D padding : N-D input array with padding of the form (padTop, padBottom, padLeft, padRight). The output N-D array dimension (B, C, padTop + H + padBottom, padLeft + W + padRight). -for 3D padding : N-D input array with padding of the form (pasFront, padBack, padTop, padBottom, padLeft, padRight). The output N-D array dimension (B, padFront + C + padBack, padTop + H + padBottom, padLeft + W + padRight). Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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) – N-D array axes (repeated int64) – Source axis indices for each axis. Transposed N-D array. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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 ND-array to the specified shape.

Parameters: x (Variable) – N-D array shape (tuple of int) – Shape broadcasted to. The size must be the same in axis where x’s shape is not 1. Broadcasted N-D array Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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_to(x, y, axis=None, n_outputs=-1, outputs=None)[source]

Warning

This function is experimental suppport, so please do not actively use it.

Broadcasting ND-array to the specified buffer.

Parameters: x (Variable) – N-D array y (Variable) – N-D array axis (int) – Target axis to start broadcasting. If this is not set, broadcast will try to fit y to x starting from the last dimension [default=-1] Broadcasted N-D array Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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) – N-D 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). [default=[len(x.shape) - 1]] N-D array Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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) – N-D 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). [default=(0,) * len(x.shape)] 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. [default=’nearest’] N-D array. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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, inplace=True, n_outputs=-1, outputs=None)[source]

Reshapes the input variable in-place. It does not create a copy of the variable. The output variable (y) has a new shape but points to the same data as the input variable (x). This means that if the data in the output variable (y) is modified, the data in the input variable (x) also gets modified since the reshape was done in-place.

Note

This function has the same behavior as the nnabla.Variable.reshape() method.

Parameters: x (Variable) – N-D array. shape (tuple of int) – Dimensions for each axis. -1 can be specified only in one shape dimension. The value is calculated from the size of the array and remaining dimensions. inplace (bool) – The output array is shared with the input array if True. [default=True] Reshaped N-D array Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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 one-hot vector based on input indices.

Parameters: x (Variable) – N-D array shape (tuple of int) – No Description N-D array Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.rand(low=0, high=1, shape=[], seed=-1, n_outputs=-1, outputs=None)[source]

Samples numbers from a uniform distribution $$x \sim U(low, high)$$ given lowest value $$low$$, upper bound $$high$$, and shape of the returned Variable.

Parameters: low (float) – $$low$$ in definition. [default=0] high (float) – $$high$$ in definition. [default=1] shape (tuple of int) – Shape of returned variable. [default=[]] seed (int) – Random seed. When -1, seed is sampled from global random number generator. [default=-1] Variable with the shape specified in the argument. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.randint(low=0, high=1, shape=[], seed=-1, n_outputs=-1, outputs=None)[source]

Samples integer numbers from a uniform distribution $$x \sim U(low, high)$$ given lowest value $$low$$, upper bound $$high$$, and shape of the returned Variable.

Parameters: low (int) – $$low$$ in definition. [default=0] high (int) – $$high$$ in definition. [default=1] shape (tuple of int) – Shape of returned variable. [default=[]] seed (int) – Random seed. When -1, seed is sampled from global random number generator. [default=-1] Variable with the shape specified in the argument. The dtype is int32. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.randn(mu=0, sigma=1, shape=[], seed=-1, n_outputs=-1, outputs=None)[source]

Samples numbers from a normal distribution $$x \sim N(\mu, \sigma)$$ given mean $$\mu$$, standard deviation $$\sigma$$, and shape of the returned Variable.

Parameters: mu (float) – $$\mu$$ in definition. [default=0] sigma (float) – $$\sigma$$ in definition. [default=1] shape (tuple of int) – Shape of returned variable. [default=[]] seed (int) – Random seed. When -1, seed is sampled from global random number generator. [default=-1] Variable with the shape specified in the argument. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.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 $$u \leq p$$.

$\begin{split}y = \left\{ \begin{array}{ll} \frac{x}{1 - p} & (u > p) \\ 0 & ({\rm otherwise}) \end{array} \right.\end{split}$

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: x (Variable) – N-D array p (float) – $$p$$ in definition. [default=0.5] seed (int) – Random seed. When -1, seed is sampled from global random number generator. [default=-1] N-D array with the same shape as x Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.top_k_data(x, k, abs=False, reduce=True, base_axis=1, n_outputs=-1, outputs=None)[source]

Select the k largest values from each sample in x to propagate unmodified and set all other values to 0. If abs is True, the k largest values are selected by magnitude. If reduce is True (the default), all feature dimensions are reduced to a single dimension of size k that propagates only the k largest values. Otherwise, if reduce is False, input and output dimensions are identical. Dimensions before base_axis are treated as number of sample dimensions and k values get selected from all elements of a sample (dimensions from base_axis) regardless of shape.

>>> import nnabla as nn, nnabla.functions as F
>>> x = nn.Variable((4, 5, 6))
>>> F.top_k_data(x, 3, reduce=False).shape
(4, 5, 6)
>>> F.top_k_data(x, 3, reduce=True).shape
(4, 3)
>>> F.top_k_data(x, 3, reduce=True, base_axis=2).shape
(4, 5, 3)

Parameters: x (Variable) – N-D array k (int) – Number of largest data values to propagate. abs (bool) – Determine largest data values by magnitude. [default=False] reduce (bool) – Reduce feature size to one dimension of size k. [default=True] base_axis (int) – First dimension of the sample shape. [default=1] N-D array. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.top_k_grad(x, k, abs=False, base_axis=1, n_outputs=-1, outputs=None)[source]

Select the k largest gradients for each sample in x to back-propagate unmodified and set all other gradients to 0. If abs is True, the k largest gradients are selected by magnitude. Dimensions before base_axis are treated as number of sample dimensions and k gradients get selected from all gradients of a sample (dimensions from base_axis) regardless of shape.

Parameters: x (Variable) – N-D array k (int) – Number of largest gradients to propagate. abs (bool) – Determine largest gradients by magnitude. [default=False] base_axis (int) – First dimension of the sample shape. [default=1] N-D array with same shape and data as x. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: x (Variable) – N-D array shape (tuple of int) – The data size to extract. For example, to randomly extract a portion of the image (3,48,48) from a 3,64,64 image, specify (3,48,48). [default=x.shape] base_axis (int) – No Description [default=1] seed (int) – Random seed. When -1, seed is sampled from global random number generator. [default=-1] N-D array Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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) – N-D 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). [default=[len(x.shape) - 1]] base_axis (int) – No Description [default=1] seed (int) – Random seed. When -1, seed is sampled from global random number generator. [default=-1] N-D array Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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) – N-D 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). [default=(0,) * len(x.shape)] 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. [default=’nearest’] base_axis (int) – No Description [default=1] seed (int) – Random seed. When -1, seed is sampled from global random number generator. [default=-1] N-D array. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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) – N-D array. shape (tuple of int) – The output image data size. [default=x.shape] pad (tuple of int) – Border padding values for each spatial axis. Padding will be added both sides of the dimension. [default=(0, 0)] 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”. [default=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”. [default=1.0] 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”. [default=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”. [default=1.0] distortion (float) – The distortion range when randomly distorting the image. To not apply distortion, specify “0.0”. [default=0.0] flip_lr (bool) – Whether to randomly flip the image horizontally at 50% probability. [default=False] flip_ud (bool) – Whether to randomly flip the image vertically at 50% probability. [default=False] 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”. [default=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. [default=False] 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”. [default=1.0] contrast_center (float) – Intensity center used for applying contrast. [default=0.0] 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. [default=False] noise (float) – Sigma of normal random number to be added. [default=0.0] seed (int) – Random seed. When -1, seed is sampled from global random number generator. [default=-1] N-D array. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise 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: x (Variable) – N-D array. Typically indicates a score. The value lies in $$[-\infty, \infty]$$ [parameter] target (Variable) – N-D array of labels. Only 0 or 1 value is allowed. [parameter] N-D array of element-wise losses. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise 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: x (Variable) – Probabilities N-D array. $$-\infty$$ to $$\infty$$. target (Variable) – N-D array of labels. Usually set as 0 or 1, but, unlike SigmoidCrossEntropy, it allows probability (0 to 1) as inputs and backpropagation can be done. N-D array of element-wise losses. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise cross entropy between the variables and the variables of a label given by a category index with Softmax normalization.

$y_{j} = -\ln \left(\frac{\exp(x_{j,t_j})}{\sum_{i'} \exp(x_{j,i'})}\right)$

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: x (Variable) – N-D array. Typically indicates a score. $$(D_1 \times ... \times D_i \times ... \times D_N)$$ [parameter] target (Variable) – N-D array of labels. $$(D_1 \times ... \times 1 \times ... \times D_N)$$ [parameter] axis (int) – Axis normalization is taken. [default=len(x.shape) - 1] N-D array of element-wise losses. $$(D_1 \times ... \times 1 \times ... \times D_N)$$ Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise cross entropy between x and the target t where targets are given by a category index.

$y_{j} = -\ln \left( x_{j, t_j} \right)$

along dimension specified by axis ($$i$$ is the axis where normalization is performed on).

Parameters: x (Variable) – N-D array. Typically indicates a score. $$(D_1 \times ... \times D_i \times ... \times D_N)$$ [parameter] target (Variable) – N-D array of labels. $$(D_1 \times ... \times 1 \times ... \times D_N)$$ [parameter] axis (int) – Axis normalization is taken. [default=len(x.shape) - 1] N-D array of element-wise losses. $$(D_1 \times ... \times 1 \times ... \times D_N)$$ Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise squared error

$y_i = \left(x^{(0)}_i - x^{(1)}_i\right)^2.$
Parameters: x0 (Variable) – N-D array. x1 (Variable) – N-D array. N-D array. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.absolute_error(x0, x1, n_outputs=-1, outputs=None)[source]

Element-wise absolute error

$y_i = | x^{(0)}_i - x^{(1)}_i |.$
Parameters: x0 (Variable) – N-D array. x1 (Variable) – N-D array. N-D array. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise 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: x0 (Variable) – N-D array. x1 (Variable) – N-D array. delta (float) – Delta [default=1.0] N-D array of element-wise losses. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.epsilon_insensitive_loss(x0, x1, epsilon, n_outputs=-1, outputs=None)[source]

Element-wise Epsilon Insensitive Loss

$\begin{split}y_i= \left\{ \begin{array}{ll} | x^{(0)}_i - x^{(1)}_i | - \epsilon & if \ \ | x^{(0)}_i - x^{(1)}_i | > \epsilon \\ 0 & otherwise \end{array} \right.\end{split}$
Parameters: x0 (Variable) – N-D array. x1 (Variable) – N-D array. epsilon (float) – Insensitive parameter. N-D array of element-wise losses. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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: p (Variable) – N-D array of the source categorical probabilities q (Variable) – N-D array of the target categorical probabilities base_axis (int) – Dimensions up to base_axis is treated as sample dimension. [default=1] Kullback Leibler divergence $$KL(p \parallel q)$$. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.

### Quantized Neural Network Layers¶

nnabla.functions.binary_sigmoid(x, n_outputs=-1, outputs=None)[source]

Element-wise binary sigmoid function. In the forward pass, it computes

$\begin{split}f(x) = \begin{cases} 1 & (x > 0) \\ 0 & ({\rm otherwise})\end{cases},\end{split}$

but in the backward pass, a straight-through approximation of the gradient is used, i.e.,

$\begin{split}\frac{\partial f(x)}{\partial x} = \begin{cases} 0 & (|x| \geq 1) \\ \frac{1}{2} & ({\rm otherwise}) \end{cases}.\end{split}$

References

Parameters: x (Variable) – Input . Output. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

Element-wise binary tanh function. In the forward pass, it computes

$\begin{split}f(x) = \begin{cases} 1 & (x > 0) \\ -1 & ({\rm otherwise}) \end{cases},\end{split}$

but in the backward pass, a straight-through approximation of the gradient is used, i.e.,

$\begin{split}\frac{\partial f(x)}{\partial x} = \begin{cases} 0 & (|x| \geq 1) \\ 1 & ({\rm otherwise}) \end{cases}.\end{split}$

References

Parameters: x (Variable) – Input . Output. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

This function provides a BinaryConnect affine layer. It computes in the forward pass

$y_j = \sum_{i} sign(w_{j,i}) x_i,$

i.e., the weights $$w_{j,i}$$ are binarized to $$sign(w_{j,i})$$ and, hence, each weight is in $$\{-1,\,1\}$$. By this weight binarization, the inner product computations do not require any multiplications anymore as they turn into additions/subtractions.

This function should be used together with batch_normalization().

Note

1) If you would like to share the binary weights between other 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 to backward(). If you wish to store the parameters of the network, remember to call forward(), 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: x (Variable) – Input . weight (Variable) – Weight . [parameter] binary_weight (Variable) – Binarized weight . [parameter] bias (Variable) – Bias. [optional][parameter] base_axis (int) – Dimensions up to base_axis is treated as sample dimension. [default=1] Output. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

This function provides a BinaryConnect convolution layer. It computes in the forward pass

$y_{n, a, b} = \sum_{m} \sum_{i} \sum_{j} sign(w_{n, m, i, j}) x_{m, a + i, b + j},$

i.e., the weights $$w_{n, m, i, j}$$ are binarized to $$sign(w_{n, m, i, j})$$ and, hence, each weight is in $$\{-1,\,1\}$$. By this weight binarization, the inner product computations do not require any multiplications anymore as they turn into additions/subtractions.

This function should be used together with batch_normalization().

Reference

Note

1) If you would like to share the binary weights between other 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 to backward(). If you wish to store the parameters of the network, remember to call forward(), 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) – Weight. [parameter] binary_weight (Variable) – Binarized weight. [parameter] bias (Variable) – Bias. [optional][parameter] base_axis (int) – Dimensions up to base_axis is treated as sample dimension. [default=1] pad (tuple of int) – Padding sizes for dimensions. [default=(0,) * (len(x.shape) - (base_axis+1))] stride (tuple of int) – Stride sizes for dimensions. [default=(1,) * (len(x.shape) - (base_axis+1))] dilation (tuple of int) – Dilation sizes for dimensions. [default=(1,) * (len(x.shape) - (base_axis+1))] group (int) – Number of groups of channels. This makes the connection across channels sparser, by grouping connections along the mapping direction. [default=1] Output Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

This function provides a Binary Weight Network affine layer. It computes in the forward pass

$y_j = \frac{1}{\|\mathbf{w}_j\|_{\ell_1}} \sum_{i} sign(w_{j,i}) x_i$

i.e., the weights $$w_{j,i}$$ are binarized to $$sign(w_{j,i})$$ and, hence, each weight is in $$\{-1,\,1\}$$. By this weight binarization, the inner product computations turn into additions/subtractions which are followed by multiplication with the scaling factor $$\alpha_j = \frac{1}{\|\mathbf{w}_j\|_{\ell_1}}$$.

Reference

Note

1) If you would like to share the binary weights with other 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 to backward(). If you wish to store the parameters of the network, remember to call forward(), 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) – Weight. [parameter] binary_weight (Variable) – Binarized weight. [parameter] alpha (Variable) – Alpha. [parameter] bias (Variable) – Bias. [optional][parameter] base_axis (int) – Dimensions up to base_axis is treated as sample dimension. [default=1] Output. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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]

This function provides a Binary Weight Network convolution layer. It computes in the forward pass

$y_{n, a, b} = \frac{1}{\|\mathbf{w}_n\|_{\ell_1}} \sum_{m} \sum_{i} \sum_{j} sign(w_{n, m, i, j}) x_{m, a + i, b + j}.$

i.e., the weights $$w_{n, m, i, j}$$ are binarized to $$sign(w_{n, m, i, j})$$ and, hence, each weight is in $$\{-1,\,1\}$$. By this weight binarization, the inner product computations turn into additions/subtractions which are followed by multiplication with the scaling factor $$\alpha_n = \frac{1}{\|\mathbf{w}_n\|_{\ell_1}}$$.

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 to backward(). If you wish to store the parameters of the network, remember to call forward(), 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) – Weight. [parameter] binary_weight (Variable) – Binarized weight. [parameter] alpha (Variable) – Alpha. [parameter] bias (Variable) – Bias. [optional][parameter] base_axis (int) – Dimensions up to base_axis is treated as sample dimension. [default=1] pad (tuple of int) – Padding sizes for dimensions. [default=(0,) * (len(x.shape) - (base_axis+1))] stride (tuple of int) – Stride sizes for dimensions. [default=(1,) * (len(x.shape) - (base_axis+1))] dilation (tuple of int) – Dilation sizes for dimensions. [default=(1,) * (len(x.shape) - (base_axis+1))] group (int) – Number of groups of channels. This makes the connection across channels sparser, by grouping connections along the mapping direction. [default=1] Output Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.fixed_point_quantize(x, sign=True, n=8, delta=0.0625, quantize=True, ste_fine_grained=True, outputs=None)[source]

Fixed Point Quantize

Parameters: x (Variable) – An input variable. sign (bool) – Indicate the signed number or the unsigned number. Default is true. n (int) – Bit width used. Note that sign consumes one bit. $$n-1$$ is used for number representation in signed case. delta (float) – Step size. quantize (bool) – If true, quantize input, otherwise not. ste_fine_grained (bool) – If true, STE is not 1. N-D array. Variable

nnabla.function_bases.fixed_point_quantize.

In the forward pass,

$\begin{split}$$q_i= \left\{ \begin{array}{ll} max & if \ \ \ x_i > max \\ sign(x_i) \times floor(|x_i| \delta^{-1} + 2^{-1}) \times \delta & if \ \ min \le x_i \le max \\ min & if \ \ x_i < min \\ \end{array} \right.,$$\end{split}$

where $$\delta$$ is the step size, $$(min, max) :=(- (2^{n-1} - 1)\delta, (2^{n-1} - 1)\delta)$$ if $$sign$$ is true, $$(min, max) := (0, (2^n - 1) \delta)$$ otherwise, and $$n$$ is the total bit-width used.

In the backward pass when using ste_fine_grained as false,

$$$\frac{\partial q_i}{\partial x_i} = 1.$$$

In the backward pass when using ste_fine_grained as true,

$\begin{split}$$\frac{\partial q_i}{\partial x_i}= \left\{ \begin{array}{ll} 0 & if \ \ \ x_i > max \\ 1 & if \ \ min \le x_i \le max \\ 0 & if \ \ x_i < min \\ \end{array} \right..$$\end{split}$

Note

Quantized values are stored as floating point number, since this function is for simulation purposes.

nnabla.functions.pow2_quantize(x, sign=True, with_zero=True, n=8, m=1, quantize=True, ste_fine_grained=True, outputs=None)[source]

Pow2 Quantize

Parameters: x (Variable) – An input variable. sign (bool) – Indicate the signed number or the unsigned number. Default is true. with_zero (bool) – Indicate using zero as a quantized value. Default is true. Note that zero consumes one bit. n (int) – Bit width used. Note that sign consumes one bit. $$n-1$$ is used for number representation in signed case. Default is 8. m (int) – $$2^m$$ is the upper bound of the dynamic range and $$-2^m$$ is the lower bound, $$m \in \mathcal{Z}$$. Default is 1. quantize (bool) – If true, quantize input, otherwise not. ste_fine_grained (bool) – If true, STE is not 1. N-D array. Variable

nnabla.function_bases.pow2_quantize.

In the forward pass of signed case,

$\begin{split}q_i= \left\{ \begin{array}{ll} max_{+} & if \ \ \overline{q_i} > max_{+} \\ \overline{q_i} & if \ \ min_{+} \le \overline{q_i} \le max_{+} \\ min_{+} & if \ \ 0 \le \overline{q_i} < min_{+} \\ min_{-} & if \ \ min_{-} < \overline{q_i} < 0 \\ \overline{q_i} & if \ \ max_{-} \le \overline{q_i} \le min_{-}\\ max_{-} & if \ \ \overline{q_i} < max_{-} \\ \end{array} \right.,\end{split}$

where

$\begin{split}&& max_{+} = 2^{m}, min_{+} = 2^{m - (2^{n-1} - 1)},\\ && max_{-} = -2^{m}, min_{-} = -2^{m - (2^{n-1} - 1)},\\ && \overline{q_i} = sign(x_i) \times 2^{round(\log_2 |x_i|)}.\end{split}$

This quantization uses the geometric mean between two power-of-two numbers as quantization threshold.

In the forward pass of unsigned case,

$\begin{split}q_i= \left\{ \begin{array}{ll} max & if \ \ \overline{q_i} > max \\ \overline{q_i} & if \ \ min \le \overline{q_i} \le max \\ min & if \ \ 0 < \overline{q_i} < min \\ \end{array} \right.,\end{split}$

where

$\begin{split}&& max = 2^{m}, min = 2^{m - (2^{n} - 1)},\\ && \overline{q_i} = 2^{int(\log_2 |x_i|)}.\end{split}$

When using with_zero as true, a pruning threshold is used to round an input to 0 or $$min$$. The pruning threshold is defined in this function as the following,

$pruning\ threshold = min \times 2^{-\frac{1}{2}}.$

If an absolute value of the input is lesser than this value, the input is rounded to 0, otherwise $$min$$.

In the backward pass when using ste_fine_grained as false,

$\frac{\partial q_i}{\partial x_i} = 1.$

In the backward pass when using ste_fine_grained as true,

$\begin{split}\frac{\partial q_i}{\partial x_i}= \left\{ \begin{array}{ll} 0 & if \ \ \overline{q_i} > max_{+} \\ 1 & if \ \ otherwise \\ 0 & if \ \ \overline{q_i} < max_{-} \\ \end{array} \right..\end{split}$

### Unsupported, Special Use¶

nnabla.functions.vat_noise(x, w, base_axis=1, eps=1.0, n_outputs=-1, outputs=None)[source]

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: x (Variable) – N-D array of noise input. Noise is standard Gaussian noise initially, but the next step, fed back gradient variable. w (Variable) – N-D array for keep gradient values. base_axis (int) – Dimensions up to base_axis is treated as sample dimension. [default=1] eps (float) – Noise norm (l2) factor. [default=1.0] N-D array Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.

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) – N-D array. N-D array. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.sink(*x, **kw)[source]

Creates a dummy variable used to call forward or backward function of multiple variables at one place.

This takes any numbers of input variables with any shape, and creates a single 0-shape outputs. The forward pass does nothing. The backward pass set ones to the input grads if one_input_grad is set as true.

Note

sink can only be called at the very end of the graph, and grad of input variables are cleared

when y.backward(clear_buffer=True) is called.
Parameters: *x (Variable) – Any number of inputs with any shape. [variadic] one_input_grad (bool) – Set grads of inputs as one during backward. It is useful to set false if you want to set external gradients to the input variables. [default=True] Dummy variable. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.

### Image Object Detection¶

nnabla.functions.nms_detection2d(x, thresh=None, nms=None, nms_per_class=None, n_outputs=-1, outputs=None)[source]

Non-Maximum Suppression (NMS) to 2D Object detector output. The input is a 3-dimensional tensor with shape of (B, N, 5 + C) where B denotes batch size, N denotes the number of detection box candidates, and C denotes the number of classes of object detection. 5 + C consists of the box coordinates x, y, w, h in normalized coordinates (size of each x and y are 1.0), objectness (learned to predict IoU value to ground truth box), and the class

probabilities of C classes.

It outputs a tensor with the same dimensions as the input, where all values are copied from the input to the output, except the class probabilities are multiplied by objectness, and possibly suppressed to 0 by NMS. During NMS, all of combination of pairs of bounding boxes is compared. For each pair, the bounding box with a lower detection score (described below) is suppressed if the overlap ratio (the IoU) is greater than the value of nms.

There are two suppression modes for NMS.

1. Suppress by class probability (nms_per_class is True): For each bounding box, the detection score is calculated by objectness * probability[class_id] for each class. The suppression is done for each class independently.

2. Suppress by objectness (nms_per_class is False): The suppression is done for each bounding box using objectness as a detection score. All class probabilities becomes 0 for every suppressed boxes.

References

Parameters: x (Variable) – A 3-dimensional array. thresh (float) – Detection score threshold. [default=0.5] nms (float) – IoU threshold for Non-maximum suppression (NMS). [default=0.45] nms_per_class (bool) – If true, NMS is applied for each class. [default=True] A 3-dim array with the same dimensions with the input. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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 the dimension specified by the axis, the element of outputs is

$\begin{split}y_i = \left \{ \begin{array}{l} 1 \ (x_i \ is \ not \ within \ N-th \ place) \\ 0 \ (x_i \ is \ within \ N-th \ place) \end{array} \right.\end{split}$
Parameters: x (Variable) – Probabilities N-D array. $$D_1 \times ... \times D_i \times ... \times D_N$$ target (Variable) – N-D array of labels. $$D_1 \times ... \times 1 \times ... \times D_N$$ axis (int) – Axis on which the top N error is calculated. [default=len(x.shape) - 1] n (int) – top N [default=1] Element-wise error N-D array. ($$D_1 \times ... \times 1 \times ... \times D_N$$) Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.

### Spectral Operation¶

nnabla.functions.fft(x, signal_ndim, normalized=False, n_outputs=-1, outputs=None)[source]

Complex-to-complex Descrete Fourier Transform,

$X_{k_1, \ldots, k_d} = \sum_{n_1=0}^{N_1-1} \dots \sum_{n_d=0}^{N_d-1} x_{n_1, \ldots, n_d} \exp\left(-2 \pi j \left( \sum_{i=0}^{d} \frac{k_i n_i}{N_i} \right) \right),$

where

$k_i = 0, \ldots, N_i - 1.$

This function now supports 1-D, 2-D, and 3-D DFT with or without the leading batch dimentsion(s).

The input is expected to be complex-valued with at least signal_ndim + 1 dimensions. The last dimension has a shape of two where x[…, 0] is the real part and x[…, 1] the imaginary part.

Example:

import numpy as np
import nnabla as nn
import nnabla.functions as F
from nnabla.ext_utils import get_extension_context

ctx = get_extension_context("cudnn")
nn.set_default_context(ctx)

# Example for a batched 2D-FFT and 2D-IFFT (batch-size: 2, data-size: 4x3)
x_data = np.random.rand(2, 4, 3) + 1j * np.random.rand(2, 4, 3)
x = nn.Variable.from_numpy_array(np.stack([np.real(x_data), np.imag(x_data)], axis=3))
y = F.fft(x, signal_ndim=2, normalized=True)
z = F.ifft(y, signal_ndim=2, normalized=True)
z.forward()

np.allclose(z.d[..., 0] + 1j*z.d[...,1], x_data)

Parameters: x (Variable) – Input. signal_ndim (int) – The number of dimentsions for each signal. It must be 1, 2, or 3. normalized (bool) – Use unitary normalization. If True, the normalization constant $$\sqrt{\frac{1}{\prod_{i=1}^{d} N_i}}$$ is multiplied. [default=False] FFT transformed signal. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.ifft(x, signal_ndim, normalized=False, n_outputs=-1, outputs=None)[source]

Complex-to-complex inverse Descrete Fourier Transform,

$X_{k_1, \ldots, k_d} = \frac{1}{\prod_{i=1}^{d} N_i} \sum_{n_1=0}^{N_1-1} \dots \sum_{n_d=0}^{N_d-1} x_{n_1, \ldots, n_d} \exp\left(2 \pi j \left( \sum_{i=0}^{d} \frac{k_i n_i}{N_i} \right) \right),$

where

$k_i = 0, \ldots, N_i - 1.$

This function now supports 1-D, 2-D, and 3-D DFT with or without the leading batch dimentsion(s).

The input is expected to be complex-valued with at least signal_ndim + 1 dimensions. The last dimension has a shape of two where x[…, 0] is the real part and x[…, 1] the imaginary part.

Parameters: x (Variable) – Input. signal_ndim (int) – The number of dimentsions for each signal. It must be 1, 2, or 3. normalized (bool) – Use unitary normalization. If True, the normalization constant $$\frac{1}{\prod_{i=1}^{d} N_i}$$ becomes $$\sqrt{\frac{1}{\prod_{i=1}^{d} N_i}}$$. [default=False] IFFT transformed signal. Variable

Note

All nnabla functions in nnabla.functions are decorated with the nnabla.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.