Contains some special helpers for machine learning. More...

#include "etl/impl/cce.hpp"
#include "etl/impl/bce.hpp"
#include "etl/impl/mse.hpp"

Include dependency graph for ml_expression_builder.hpp:

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Functions
template<size_t S1 = 1, size_t S2 = 1, size_t P1 = 0, size_t P2 = 0, etl_expr A, etl_expr B>
conv_4d_valid_expr< detail::build_type< A >, detail::build_type< B >, S1, S2, P1, P2, true >	etl::ml::convolution_forward (A &&a, B &&b)
	Forward convolution for a batch of images with a set of kernels. More...

template<etl_expr A, etl_expr B>
dyn_conv_4d_valid_expr< detail::build_type< A >, detail::build_type< B >, true >	etl::ml::convolution_forward (A &&a, B &&b, size_t s1, size_t s2, size_t p1=0, size_t p2=0)
	Forward convolution for a batch of images with a set of kernels. More...

template<size_t S1 = 1, size_t S2 = 1, size_t P1 = 0, size_t P2 = 0, etl_expr A, etl_expr B>
conv_4d_backward_expr< detail::build_type< A >, detail::build_type< B >, S1, S2, P1, P2, true >	etl::ml::convolution_backward (A &&a, B &&b)
	Backward convolution for a batch of images with a set of kernels. More...

template<etl_expr A, etl_expr B>
dyn_conv_4d_backward_expr< detail::build_type< A >, detail::build_type< B >, true >	etl::ml::convolution_backward (A &&a, B &&b, size_t s1, size_t s2, size_t p1=0, size_t p2=0)
	Backward convolution for a batch of images with a set of kernels. More...

template<size_t S1 = 1, size_t S2 = 1, size_t P1 = 0, size_t P2 = 0, etl_expr A, etl_expr B>
conv_4d_backward_filter_expr< detail::build_type< A >, detail::build_type< B >, S1, S2, P1, P2, true >	etl::ml::convolution_backward_filter (A &&a, B &&b)
	Backward convolution for a batch of images with a set of kernels. More...

template<etl_expr A, etl_expr B>
dyn_conv_4d_backward_filter_expr< detail::build_type< A >, detail::build_type< B >, true >	etl::ml::convolution_backward_filter (A &&a, B &&b, size_t s1, size_t s2, size_t p1=0, size_t p2=0)
	Backward convolution for a batch of images with a set of kernels. More...

template<size_t C1, size_t C2, size_t S1 = C1, size_t S2 = C2, size_t P1 = 0, size_t P2 = 0, typename E >
auto	etl::ml::max_pool_forward (E &&value)
	Forward 2D Max Pooling of the given matrix expression. More...

template<typename E >
auto	etl::ml::max_pool_forward (E &&value, size_t c1, size_t c2)
	Forward 2D Max Pooling of the given matrix expression. More...

template<typename E >
auto	etl::ml::max_pool_forward (E &&value, size_t c1, size_t c2, size_t s1, size_t s2, size_t p1=0, size_t p2=0)
	Forward 2D Max Pooling of the given matrix expression. More...

template<size_t C1, size_t C2, size_t C3, typename E >
auto	etl::ml::max_pool_3d_forward (E &&value)
	Forward 3D Max Pooling of the given matrix expression. More...

template<typename E >
auto	etl::ml::max_pool_3d_forward (E &&value, size_t c1, size_t c2, size_t c3)
	Forward 3D Max Pooling of the given matrix expression. More...

template<size_t C1, size_t C2, size_t S1 = C1, size_t S2 = C2, size_t P1 = 0, size_t P2 = 0, typename E >
auto	etl::ml::avg_pool_forward (E &&value)
	Forward Average Pooling of the given matrix expression. More...

template<typename E >
auto	etl::ml::avg_pool_forward (E &&value, size_t c1, size_t c2)
	2D Average Pooling of the given matrix expression More...

template<typename E >
auto	etl::ml::avg_pool_forward (E &&value, size_t c1, size_t c2, size_t s1, size_t s2, size_t p1=0, size_t p2=0)
	2D Average Pooling of the given matrix expression More...

template<size_t C1, size_t C2, size_t C3, typename E >
auto	etl::ml::avg_pool_3d_forward (E &&value)
	Forward 3D Average Pooling of the given matrix expression. More...

template<typename E >
auto	etl::ml::avg_pool_3d_forward (E &&value, size_t c1, size_t c2, size_t c3)
	Forward 3D Average Pooling of the given matrix expression. More...

template<size_t C1, size_t C2, size_t S1, size_t S2, size_t P1, size_t P2, etl_expr A, etl_expr B, typename C >
pool_upsample_2d_expr< detail::build_type< A >, detail::build_type< B >, detail::build_type< C >, C1, C2, S1, S2, P1, P2, true >	etl::ml::max_pool_backward (A &&input, B &&output, C &&errors)
	Derivative of the 2D Max Pooling of the given matrix expression and upsampling. More...

template<etl_expr A, etl_expr B, typename C >
dyn_pool_upsample_2d_expr< detail::build_type< A >, detail::build_type< B >, detail::build_type< C >, true >	etl::ml::max_pool_backward (A &&input, B &&output, C &&errors, size_t c1, size_t c2)
	Derivative of the 2D Max Pooling of the given matrix expression and upsampling. More...

template<etl_expr A, etl_expr B, typename C >
dyn_pool_upsample_2d_expr< detail::build_type< A >, detail::build_type< B >, detail::build_type< C >, true >	etl::ml::max_pool_backward (A &&input, B &&output, C &&errors, size_t c1, size_t c2, size_t s1, size_t s2, size_t p1=0, size_t p2=0)
	Derivative of the 2D Max Pooling of the given matrix expression and upsampling. More...

template<size_t C1, size_t C2, size_t C3, etl_expr A, etl_expr B, typename C >
pool_upsample_3d_expr< detail::build_type< A >, detail::build_type< B >, detail::build_type< C >, C1, C2, C3, true >	etl::ml::max_pool_3d_backward (A &&input, B &&output, C &&errors)
	Derivative of the 3D Max Pooling of the given matrix expression and upsampling. More...

template<etl_expr A, etl_expr B, typename C >
dyn_pool_upsample_3d_expr< detail::build_type< A >, detail::build_type< B >, detail::build_type< C >, true >	etl::ml::max_pool_3d_backward (A &&input, B &&output, C &&errors, size_t c1, size_t c2, size_t c3)
	Derivative of the 3D Max Pooling of the given matrix expression and upsampling. More...

template<size_t C1, size_t C2, size_t S1, size_t S2, size_t P1, size_t P2, etl_expr A, etl_expr B, typename C >
pool_upsample_2d_expr< detail::build_type< A >, detail::build_type< B >, detail::build_type< C >, C1, C2, S1, S2, P1, P2, false >	etl::ml::avg_pool_backward (A &&input, B &&output, C &&errors)
	Derivative of the 2D Avg Pooling of the given matrix expression and upsampling. More...

template<etl_expr A, etl_expr B, typename C >
dyn_pool_upsample_2d_expr< detail::build_type< A >, detail::build_type< B >, detail::build_type< C >, false >	etl::ml::avg_pool_backward (A &&input, B &&output, C &&errors, size_t c1, size_t c2)
	Derivative of the 2D Average Pooling of the given matrix expression and upsampling. More...

template<etl_expr A, etl_expr B, typename C >
dyn_pool_upsample_2d_expr< detail::build_type< A >, detail::build_type< B >, detail::build_type< C >, false >	etl::ml::avg_pool_backward (A &&input, B &&output, C &&errors, size_t c1, size_t c2, size_t s1, size_t s2, size_t p1=0, size_t p2=0)
	Derivative of the 2D Average Pooling of the given matrix expression and upsampling. More...

template<size_t C1, size_t C2, size_t C3, etl_expr A, etl_expr B, typename C >
pool_upsample_3d_expr< detail::build_type< A >, detail::build_type< B >, detail::build_type< C >, C1, C2, C3, false >	etl::ml::avg_pool_3d_backward (A &&input, B &&output, C &&errors)
	Derivative of the 2D Avg Pooling of the given matrix expression and upsampling. More...

template<etl_expr A, etl_expr B, typename C >
dyn_pool_upsample_3d_expr< detail::build_type< A >, detail::build_type< B >, detail::build_type< C >, false >	etl::ml::avg_pool_3d_backward (A &&input, B &&output, C &&errors, size_t c1, size_t c2, size_t c3)
	Derivative of the 2D Average Pooling of the given matrix expression and upsampling. More...

template<typename E >
auto	etl::ml::identity_derivative_out ([[maybe_unused]] E &&value)
	Return the derivative of the identiy function for the given output value. More...

template<etl_expr E>
auto	etl::ml::sigmoid_derivative_out (E &&value) -> decltype(value >>(1.0 - value))
	Return the derivative of the logistic sigmoid of the given ETL expression, with respect to the output value. More...

template<typename E >
auto	etl::ml::softmax_derivative_out ([[maybe_unused]] E &&e)
	Return the derivative of the softmax function of the given ETL expression, with respect to output values. More...

template<etl_expr E>
auto	etl::ml::tanh_derivative_out (E &&value) -> decltype(1.0 -(value >> value))
	Return the derivative of the tanh function of the given ETL expression, with respect to the output values. More...

template<etl_expr E>
auto	etl::ml::relu_derivative_out (const E &value) -> detail::unary_helper< E, relu_derivative_op >
	Return the derivative of the relu function of the given ETL expression, with respect for the output values. More...

template<typename O , typename E >
decltype(auto)	etl::ml::identity_backward ([[maybe_unused]] O &&output, E &&errors)
	Return the backward activation of the identity function. More...

template<typename O , typename E >
auto	etl::ml::sigmoid_backward (O &&output, E &&errors) -> detail::left_binary_helper< O, E, sigmoid_derivative_binary_op >
	Return the backward activation of the sigmoid function. More...

template<typename O , typename E >
auto	etl::ml::relu_backward (O &&output, E &&errors) -> detail::left_binary_helper< O, E, relu_derivative_binary_op >
	Return the backward activation of the RELU function. More...

template<typename O , typename E >
decltype(auto)	etl::ml::softmax_backward ([[maybe_unused]] O &&output, E &&errors)
	Return the backward activation of the softmax function. More...

template<typename O , etl_expr E>
auto	etl::ml::tanh_backward (O &&output, E &&errors)
	Return the backward activation of the tanh function. More...

template<etl_expr O, etl_expr L>
value_t< O >	etl::ml::cce_loss (O &&output, L &&labels, value_t< O > scale)
	Returns the Categorical Cross Entropy Loss. More...

template<etl_expr O, etl_expr L>
value_t< O >	etl::ml::cce_error (O &&output, L &&labels, value_t< O > scale)
	Returns the Categorical Cross Entropy Error. More...

template<etl_expr O, etl_expr L>
value_t< O >	etl::ml::bce_loss (O &&output, L &&labels, value_t< O > scale)
	Returns the Binary Cross Entropy Loss. More...

template<etl_expr O, etl_expr L>
value_t< O >	etl::ml::bce_error (O &&output, L &&labels, value_t< O > scale)
	Returns the Binary Cross Entropy Error. More...

template<etl_expr O, etl_expr L>
std::pair< value_t< O >, value_t< O > >	etl::ml::bce (O &&output, L &&labels, value_t< O > alpha, value_t< O > beta)
	Returns the Binary Cross Entropy Loss and Error. More...

template<etl_expr O, etl_expr L>
std::pair< value_t< O >, value_t< O > >	etl::ml::cce (O &&output, L &&labels, value_t< O > alpha, value_t< O > beta)
	Returns the Categorical Cross Entropy Loss and Error. More...

template<etl_expr O, etl_expr L>
value_t< O >	etl::ml::mse_loss (O &&output, L &&labels, value_t< O > scale)
	Returns the Binary Cross Entropy Loss. More...

template<etl_expr O, etl_expr L>
value_t< O >	etl::ml::mse_error (O &&output, L &&labels, value_t< O > scale)
	Returns the Binary Cross Entropy Error. More...

template<etl_expr O, etl_expr L>
std::pair< value_t< O >, value_t< O > >	etl::ml::mse (O &&output, L &&labels, value_t< O > alpha, value_t< O > beta)
	Returns the Binary Cross Entropy Loss and Error. More...

Detailed Description

Contains some special helpers for machine learning.

This is mostly a simpler set of names and functions to achieve machine learning features.

Function Documentation

◆ avg_pool_3d_backward() [1/2]

template<size_t C1, size_t C2, size_t C3, etl_expr A, etl_expr B, typename C >

pool_upsample_3d_expr<detail::build_type<A>, detail::build_type<B>, detail::build_type<C>, C1, C2, C3, false> etl::ml::avg_pool_3d_backward	(	A &&	input,
		B &&	output,
		C &&	errors
	)

Derivative of the 2D Avg Pooling of the given matrix expression and upsampling.

Parameters

input	The input
output	The output

Template Parameters

C1	The first pooling ratio
C2	The second pooling ratio

Returns: A expression representing the Derivative of 3D Max Pooling of the input expression.

◆ avg_pool_3d_backward() [2/2]

template<etl_expr A, etl_expr B, typename C >

dyn_pool_upsample_3d_expr<detail::build_type<A>, detail::build_type<B>, detail::build_type<C>, false> etl::ml::avg_pool_3d_backward	(	A &&	input,
		B &&	output,
		C &&	errors,
		size_t	c1,
		size_t	c2,
		size_t	c3
	)

Derivative of the 2D Average Pooling of the given matrix expression and upsampling.

Parameters

input	The input
output	The output
c1	The first pooling ratio
c2	The second pooling ratio

Returns: A expression representing the Derivative of 3D Average Pooling of the input expression.

◆ avg_pool_3d_forward() [1/2]

template<size_t C1, size_t C2, size_t C3, typename E >

auto etl::ml::avg_pool_3d_forward ( E && value )

Forward 3D Average Pooling of the given matrix expression.

Parameters

value The matrix expression

Template Parameters

C1	The first pooling ratio
C2	The second pooling ratio
C3	The third pooling ratio

Returns: A expression representing the 2D Forward Average Pooling of the input expression.

◆ avg_pool_3d_forward() [2/2]

template<typename E >

auto etl::ml::avg_pool_3d_forward	(	E &&	value,
		size_t	c1,
		size_t	c2,
		size_t	c3
	)

Forward 3D Average Pooling of the given matrix expression.

Parameters

value	The matrix expression
c1	The first pooling ratio
c2	The second pooling ratio
c3	The third pooling ratio

Returns: A expression representing the 2D Average Pooling of the input expression.

◆ avg_pool_backward() [1/3]

template<size_t C1, size_t C2, size_t S1, size_t S2, size_t P1, size_t P2, etl_expr A, etl_expr B, typename C >

pool_upsample_2d_expr<detail::build_type<A>, detail::build_type<B>, detail::build_type<C>, C1, C2, S1, S2, P1, P2, false> etl::ml::avg_pool_backward	(	A &&	input,
		B &&	output,
		C &&	errors
	)

Derivative of the 2D Avg Pooling of the given matrix expression and upsampling.

Parameters

input	The input
output	The output

Template Parameters

C1	The first pooling ratio
C2	The second pooling ratio

Returns: A expression representing the Derivative of 3D Max Pooling of the input expression.

◆ avg_pool_backward() [2/3]

template<etl_expr A, etl_expr B, typename C >

dyn_pool_upsample_2d_expr<detail::build_type<A>, detail::build_type<B>, detail::build_type<C>, false> etl::ml::avg_pool_backward	(	A &&	input,
		B &&	output,
		C &&	errors,
		size_t	c1,
		size_t	c2
	)

Derivative of the 2D Average Pooling of the given matrix expression and upsampling.

Parameters

input	The input
output	The output
c1	The first pooling ratio
c2	The second pooling ratio

Returns: A expression representing the Derivative of 3D Average Pooling of the input expression.

◆ avg_pool_backward() [3/3]

template<etl_expr A, etl_expr B, typename C >

dyn_pool_upsample_2d_expr<detail::build_type<A>, detail::build_type<B>, detail::build_type<C>, false> etl::ml::avg_pool_backward	(	A &&	input,
		B &&	output,
		C &&	errors,
		size_t	c1,
		size_t	c2,
		size_t	s1,
		size_t	s2,
		size_t	p1 = `0`,
		size_t	p2 = `0`
	)

Derivative of the 2D Average Pooling of the given matrix expression and upsampling.

Parameters

input	The input
output	The output
c1	The first pooling ratio
c2	The second pooling ratio

Returns: A expression representing the Derivative of 3D Average Pooling of the input expression.

◆ avg_pool_forward() [1/3]

template<size_t C1, size_t C2, size_t S1 = C1, size_t S2 = C2, size_t P1 = 0, size_t P2 = 0, typename E >

auto etl::ml::avg_pool_forward ( E && value )

Forward Average Pooling of the given matrix expression.

Parameters

value The matrix expression

Template Parameters

C1	The first pooling ratio
C2	The second pooling ratio

Returns: A expression representing the 2D Forward Average Pooling of the input expression.

◆ avg_pool_forward() [2/3]

template<typename E >

auto etl::ml::avg_pool_forward	(	E &&	value,
		size_t	c1,
		size_t	c2
	)

2D Average Pooling of the given matrix expression

Parameters

value	The matrix expression
c1	The first pooling ratio
c2	The second pooling ratio

Returns: A expression representing the 2D Average Pooling of the input expression.

◆ avg_pool_forward() [3/3]

template<typename E >

auto etl::ml::avg_pool_forward	(	E &&	value,
		size_t	c1,
		size_t	c2,
		size_t	s1,
		size_t	s2,
		size_t	p1 = `0`,
		size_t	p2 = `0`
	)

2D Average Pooling of the given matrix expression

Parameters

value	The matrix expression
c1	The first pooling ratio
c2	The second pooling ratio

Returns: A expression representing the 2D Average Pooling of the input expression.

◆ bce()

template<etl_expr O, etl_expr L>

std::pair<value_t<O>, value_t<O> > etl::ml::bce	(	O &&	output,
		L &&	labels,
		value_t< O >	alpha,
		value_t< O >	beta
	)

Returns the Binary Cross Entropy Loss and Error.

Parameters

output	The outputs
labels	The labels

Returns: The BCE Loss and Error of the output and labels

◆ bce_error()

template<etl_expr O, etl_expr L>

value_t<O> etl::ml::bce_error	(	O &&	output,
		L &&	labels,
		value_t< O >	scale
	)

Returns the Binary Cross Entropy Error.

Parameters

output	The outputs
labels	The labels

Returns: The BCE Error of the output and labels

◆ bce_loss()

template<etl_expr O, etl_expr L>

value_t<O> etl::ml::bce_loss	(	O &&	output,
		L &&	labels,
		value_t< O >	scale
	)

Returns the Binary Cross Entropy Loss.

Parameters

output	The outputs
labels	The labels

Returns: The BCE Loss of the output and labels

◆ cce()

template<etl_expr O, etl_expr L>

std::pair<value_t<O>, value_t<O> > etl::ml::cce	(	O &&	output,
		L &&	labels,
		value_t< O >	alpha,
		value_t< O >	beta
	)

Returns the Categorical Cross Entropy Loss and Error.

Parameters

output	The outputs
labels	The labels

Returns: The BCE Loss and Error of the output and labels

◆ cce_error()

template<etl_expr O, etl_expr L>

value_t<O> etl::ml::cce_error	(	O &&	output,
		L &&	labels,
		value_t< O >	scale
	)

Returns the Categorical Cross Entropy Error.

Parameters

output	The outputs
labels	The labels

Returns: The CCE Error of the output and labels

◆ cce_loss()

template<etl_expr O, etl_expr L>

value_t<O> etl::ml::cce_loss	(	O &&	output,
		L &&	labels,
		value_t< O >	scale
	)

Returns the Categorical Cross Entropy Loss.

Parameters

output	The outputs
labels	The labels

Returns: The CCE Loss of the output and labels

◆ convolution_backward() [1/2]

template<size_t S1 = 1, size_t S2 = 1, size_t P1 = 0, size_t P2 = 0, etl_expr A, etl_expr B>

conv_4d_backward_expr<detail::build_type<A>, detail::build_type<B>, S1, S2, P1, P2, true> etl::ml::convolution_backward	(	A &&	a,
		B &&	b
	)

Backward convolution for a batch of images with a set of kernels.

This will compute the 2D backward convolutions of each image with each given kernels. The results accross channels will be accumulated together.

The 4D matrix a is assumed to be of [N, K, Hi, Wi] dimensions. The 4D matrix b is assumed to be of [K, C, Hj, Wj] dimensions. The 4D matrix c is assumed to be of [N, C, (Hi - Hj + 2 * P1) / S1 + 1, (Wi - Hj + 2 * P2) / S2 + 1] dimensions.

Parameters

a	An expression containing the batch of images
b	An expression containing the set of kernels

Template Parameters

S1	The stride in the first dimension
S2	The stride in the second dimension
P1	The padding of the first dimension
P2	The padding of the second dimension

Returns: an expression representing the result of the forward convolution

◆ convolution_backward() [2/2]

template<etl_expr A, etl_expr B>

dyn_conv_4d_backward_expr<detail::build_type<A>, detail::build_type<B>, true> etl::ml::convolution_backward	(	A &&	a,
		B &&	b,
		size_t	s1,
		size_t	s2,
		size_t	p1 = `0`,
		size_t	p2 = `0`
	)

Backward convolution for a batch of images with a set of kernels.

This will compute the 2D convolutions of each image with each given kernels. The results accross channels will be accumulated together.

The 4D matrix a is assumed to be of [N, K, Hi, Wi] dimensions. The 4D matrix b is assumed to be of [K, C, Hj, Wj] dimensions. The 4D matrix c is assumed to be of [N, C, (Hi - Hj + 2 * P1) / S1 + 1, (Wi - Hj + 2 * P2) / S2 + 1] dimensions.

Parameters

a	An expression containing the batch of images
b	An expression containing the set of kernels
s1	The stride in the first dimension
s2	The stride in the second dimension
p1	The padding of the first dimension
p2	The padding of the second dimension

Returns: an expression representing the result of the forward convolution

◆ convolution_backward_filter() [1/2]

template<size_t S1 = 1, size_t S2 = 1, size_t P1 = 0, size_t P2 = 0, etl_expr A, etl_expr B>

conv_4d_backward_filter_expr<detail::build_type<A>, detail::build_type<B>, S1, S2, P1, P2, true> etl::ml::convolution_backward_filter	(	A &&	a,
		B &&	b
	)

Backward convolution for a batch of images with a set of kernels.

This will compute the 2D backward convolutions of each image with each given kernels. The results accross channels will be accumulated together.

The 4D matrix a is assumed to be of [N, K, Hi, Wi] dimensions. The 4D matrix b is assumed to be of [K, C, Hj, Wj] dimensions. The 4D matrix c is assumed to be of [N, C, (Hi - Hj + 2 * P1) / S1 + 1, (Wi - Hj + 2 * P2) / S2 + 1] dimensions.

Parameters

a	An expression containing the batch of images
b	An expression containing the set of kernels

Template Parameters

S1	The stride in the first dimension
S2	The stride in the second dimension
P1	The padding of the first dimension
P2	The padding of the second dimension

Returns: an expression representing the result of the forward convolution

◆ convolution_backward_filter() [2/2]

template<etl_expr A, etl_expr B>

dyn_conv_4d_backward_filter_expr<detail::build_type<A>, detail::build_type<B>, true> etl::ml::convolution_backward_filter	(	A &&	a,
		B &&	b,
		size_t	s1,
		size_t	s2,
		size_t	p1 = `0`,
		size_t	p2 = `0`
	)

Backward convolution for a batch of images with a set of kernels.

This will compute the 2D convolutions of each image with each given kernels. The results accross channels will be accumulated together.

The 4D matrix a is assumed to be of [N, K, Hi, Wi] dimensions. The 4D matrix b is assumed to be of [K, C, Hj, Wj] dimensions. The 4D matrix c is assumed to be of [N, C, (Hi - Hj + 2 * P1) / S1 + 1, (Wi - Hj + 2 * P2) / S2 + 1] dimensions.

Parameters

a	An expression containing the batch of images
b	An expression containing the set of kernels
s1	The stride in the first dimension
s2	The stride in the second dimension
p1	The padding of the first dimension
p2	The padding of the second dimension

Returns: an expression representing the result of the forward convolution

◆ convolution_forward() [1/2]

template<size_t S1 = 1, size_t S2 = 1, size_t P1 = 0, size_t P2 = 0, etl_expr A, etl_expr B>

conv_4d_valid_expr<detail::build_type<A>, detail::build_type<B>, S1, S2, P1, P2, true> etl::ml::convolution_forward	(	A &&	a,
		B &&	b
	)

Forward convolution for a batch of images with a set of kernels.

This will compute the 2D convolutions of each image with each given kernels. The results accross channels will be accumulated together.

The 4D matrix a is assumed to be of [N, C, Hi, Wi] dimensions. The 4D matrix b is assumed to be of [K, C, Hj, Wj] dimensions. The 4D matrix c is assumed to be of [N, K, (Hi - Hj + 2 * P1) / S1 + 1, (Wi - Hj + 2 * P2) / S2 + 1] dimensions.

Parameters

a	An expression containing the batch of images
b	An expression containing the set of kernels

Template Parameters

S1	The stride in the first dimension
S2	The stride in the second dimension
P1	The padding of the first dimension
P2	The padding of the second dimension

Returns: an expression representing the result of the forward convolution

◆ convolution_forward() [2/2]

template<etl_expr A, etl_expr B>

dyn_conv_4d_valid_expr<detail::build_type<A>, detail::build_type<B>, true> etl::ml::convolution_forward	(	A &&	a,
		B &&	b,
		size_t	s1,
		size_t	s2,
		size_t	p1 = `0`,
		size_t	p2 = `0`
	)

Forward convolution for a batch of images with a set of kernels.

This will compute the 2D convolutions of each image with each given kernels. The results accross channels will be accumulated together.

The 4D matrix a is assumed to be of [N, C, Hi, Wi] dimensions. The 4D matrix b is assumed to be of [K, C, Hj, Wj] dimensions. The 4D matrix c is assumed to be of [N, K, (Hi - Hj + 2 * P1) / S1 + 1, (Wi - Hj + 2 * P2) / S2 + 1] dimensions.

Parameters

a	An expression containing the batch of images
b	An expression containing the set of kernels
s1	The stride in the first dimension
s2	The stride in the second dimension
p1	The padding of the first dimension
p2	The padding of the second dimension

Returns: an expression representing the result of the forward convolution

◆ identity_backward()

template<typename O , typename E >

decltype(auto) etl::ml::identity_backward	(	[[maybe_unused] ] O &&	output,
		E &&	errors
	)

Return the backward activation of the identity function.

Parameters

output	The output of the forward activation function
errors	The errors at output of this activation function

Returns: the backward activation of the activation function

◆ identity_derivative_out()

template<typename E >

auto etl::ml::identity_derivative_out ( [[maybe_unused] ] E && value )

Return the derivative of the identiy function for the given output value.

Parameters

value The ETL expression

Returns: 1.0

◆ max_pool_3d_backward() [1/2]

template<size_t C1, size_t C2, size_t C3, etl_expr A, etl_expr B, typename C >

pool_upsample_3d_expr<detail::build_type<A>, detail::build_type<B>, detail::build_type<C>, C1, C2, C3, true> etl::ml::max_pool_3d_backward	(	A &&	input,
		B &&	output,
		C &&	errors
	)

Derivative of the 3D Max Pooling of the given matrix expression and upsampling.

Parameters

input	The input
output	The output

Template Parameters

C1	The first pooling ratio
C2	The second pooling ratio

Returns: A expression representing the Derivative of 3D Max Pooling of the input expression.

◆ max_pool_3d_backward() [2/2]

template<etl_expr A, etl_expr B, typename C >

dyn_pool_upsample_3d_expr<detail::build_type<A>, detail::build_type<B>, detail::build_type<C>, true> etl::ml::max_pool_3d_backward	(	A &&	input,
		B &&	output,
		C &&	errors,
		size_t	c1,
		size_t	c2,
		size_t	c3
	)

Derivative of the 3D Max Pooling of the given matrix expression and upsampling.

Parameters

input	The input
output	The output
c1	The first pooling ratio
c2	The second pooling ratio

Returns: A expression representing the Derivative of 3D Max Pooling of the input expression.

◆ max_pool_3d_forward() [1/2]

template<size_t C1, size_t C2, size_t C3, typename E >

auto etl::ml::max_pool_3d_forward ( E && value )

Forward 3D Max Pooling of the given matrix expression.

Parameters

value The matrix expression

Template Parameters

C1	The first pooling ratio
C2	The second pooling ratio
C3	The third pooling ratio

Returns: A expression representing the 2D Forward Max Pooling of the input expression.

◆ max_pool_3d_forward() [2/2]

template<typename E >

auto etl::ml::max_pool_3d_forward	(	E &&	value,
		size_t	c1,
		size_t	c2,
		size_t	c3
	)

Forward 3D Max Pooling of the given matrix expression.

Parameters

value	The matrix expression
c1	The first pooling ratio
c2	The second pooling ratio
c3	The second pooling ratio

Returns: A expression representing the 2D Max Pooling of the input expression.

◆ max_pool_backward() [1/3]

template<size_t C1, size_t C2, size_t S1, size_t S2, size_t P1, size_t P2, etl_expr A, etl_expr B, typename C >

pool_upsample_2d_expr<detail::build_type<A>, detail::build_type<B>, detail::build_type<C>, C1, C2, S1, S2, P1, P2, true> etl::ml::max_pool_backward	(	A &&	input,
		B &&	output,
		C &&	errors
	)

Derivative of the 2D Max Pooling of the given matrix expression and upsampling.

Parameters

input	The input
output	The output

Template Parameters

C1	The first pooling ratio
C2	The second pooling ratio

Returns: A expression representing the Derivative of 3D Max Pooling of the input expression.

◆ max_pool_backward() [2/3]

template<etl_expr A, etl_expr B, typename C >

dyn_pool_upsample_2d_expr<detail::build_type<A>, detail::build_type<B>, detail::build_type<C>, true> etl::ml::max_pool_backward	(	A &&	input,
		B &&	output,
		C &&	errors,
		size_t	c1,
		size_t	c2
	)

Derivative of the 2D Max Pooling of the given matrix expression and upsampling.

Parameters

input	The input
output	The output
c1	The first pooling ratio
c2	The second pooling ratio

Returns: A expression representing the Derivative of 3D Max Pooling of the input expression.

◆ max_pool_backward() [3/3]

template<etl_expr A, etl_expr B, typename C >

dyn_pool_upsample_2d_expr<detail::build_type<A>, detail::build_type<B>, detail::build_type<C>, true> etl::ml::max_pool_backward	(	A &&	input,
		B &&	output,
		C &&	errors,
		size_t	c1,
		size_t	c2,
		size_t	s1,
		size_t	s2,
		size_t	p1 = `0`,
		size_t	p2 = `0`
	)

Derivative of the 2D Max Pooling of the given matrix expression and upsampling.

Parameters

input	The input
output	The output
c1	The first pooling ratio
c2	The second pooling ratio

Returns: A expression representing the Derivative of 3D Max Pooling of the input expression.

◆ max_pool_forward() [1/3]

template<size_t C1, size_t C2, size_t S1 = C1, size_t S2 = C2, size_t P1 = 0, size_t P2 = 0, typename E >

auto etl::ml::max_pool_forward ( E && value )

Forward 2D Max Pooling of the given matrix expression.

Parameters

value The matrix expression

Template Parameters

C1	The first pooling ratio
C2	The second pooling ratio

Returns: A expression representing the 2D Forward Max Pooling of the input expression.

◆ max_pool_forward() [2/3]

template<typename E >

auto etl::ml::max_pool_forward	(	E &&	value,
		size_t	c1,
		size_t	c2
	)

Forward 2D Max Pooling of the given matrix expression.

Parameters

value	The matrix expression
c1	The first pooling ratio
c2	The second pooling ratio

Returns: A expression representing the 2D Max Pooling of the input expression.

◆ max_pool_forward() [3/3]

template<typename E >

auto etl::ml::max_pool_forward	(	E &&	value,
		size_t	c1,
		size_t	c2,
		size_t	s1,
		size_t	s2,
		size_t	p1 = `0`,
		size_t	p2 = `0`
	)

Forward 2D Max Pooling of the given matrix expression.

Parameters

value	The matrix expression
c1	The first pooling ratio
c2	The second pooling ratio

Returns: A expression representing the 2D Max Pooling of the input expression.

◆ mse()

template<etl_expr O, etl_expr L>

std::pair<value_t<O>, value_t<O> > etl::ml::mse	(	O &&	output,
		L &&	labels,
		value_t< O >	alpha,
		value_t< O >	beta
	)

Returns the Binary Cross Entropy Loss and Error.

Parameters

output	The outputs
labels	The labels

Returns: The MSE Loss and Error of the output and labels

◆ mse_error()

template<etl_expr O, etl_expr L>

value_t<O> etl::ml::mse_error	(	O &&	output,
		L &&	labels,
		value_t< O >	scale
	)

Returns the Binary Cross Entropy Error.

Parameters

output	The outputs
labels	The labels

Returns: The MSE Error of the output and labels

◆ mse_loss()

template<etl_expr O, etl_expr L>

value_t<O> etl::ml::mse_loss	(	O &&	output,
		L &&	labels,
		value_t< O >	scale
	)

Returns the Binary Cross Entropy Loss.

Parameters

output	The outputs
labels	The labels

Returns: The MSE Loss of the output and labels

◆ relu_backward()

template<typename O , typename E >

auto etl::ml::relu_backward	(	O &&	output,
		E &&	errors
	)		-> detail::left_binary_helper<O, E, relu_derivative_binary_op>

Return the backward activation of the RELU function.

Parameters

output	The output of the forward activation function
errors	The errors at output of this activation function

Returns: the backward activation of the activation function

◆ relu_derivative_out()

template<etl_expr E>

auto etl::ml::relu_derivative_out ( const E & value ) -> detail::unary_helper<E, relu_derivative_op>

Return the derivative of the relu function of the given ETL expression, with respect for the output values.

Parameters

value The ETL expression

Returns: An ETL expression representing the derivative of the relu function of the input.

◆ sigmoid_backward()

template<typename O , typename E >

auto etl::ml::sigmoid_backward	(	O &&	output,
		E &&	errors
	)		-> detail::left_binary_helper<O, E, sigmoid_derivative_binary_op>

Return the backward activation of the sigmoid function.

Parameters

output	The output of the forward activation function
errors	The errors at output of this activation function

Returns: the backward activation of the activation function

◆ sigmoid_derivative_out()

template<etl_expr E>

auto etl::ml::sigmoid_derivative_out ( E && value ) -> decltype(value >> (1.0 - value))

Return the derivative of the logistic sigmoid of the given ETL expression, with respect to the output value.

Parameters

value The ETL expression

Returns: An ETL expression representing the derivative of the logistic sigmoid of the input.

◆ softmax_backward()

template<typename O , typename E >

decltype(auto) etl::ml::softmax_backward	(	[[maybe_unused] ] O &&	output,
		E &&	errors
	)

Return the backward activation of the softmax function.

Parameters

output	The output of the forward activation function
errors	The errors at output of this activation function

Returns: the backward activation of the activation function

◆ softmax_derivative_out()

template<typename E >

auto etl::ml::softmax_derivative_out ( [[maybe_unused] ] E && e )

Return the derivative of the softmax function of the given ETL expression, with respect to output values.

Parameters

e	The ETL expression

Returns: An ETL expression representing the derivative of the softmax function of the input.

◆ tanh_backward()

template<typename O , etl_expr E>

auto etl::ml::tanh_backward	(	O &&	output,
		E &&	errors
	)

Return the backward activation of the tanh function.

Parameters

output	The output of the forward activation function
errors	The errors at output of this activation function

Returns: the backward activation of the activation function

◆ tanh_derivative_out()

template<etl_expr E>

auto etl::ml::tanh_derivative_out ( E && value ) -> decltype(1.0 - (value >> value))

Return the derivative of the tanh function of the given ETL expression, with respect to the output values.

Parameters

value The ETL expression

Returns: An ETL expression representing the derivative of the tanh function of the input.

Functions

Detailed Description

Function Documentation

◆ avg_pool_3d_backward() [1/2]

◆ avg_pool_3d_backward() [2/2]

◆ avg_pool_3d_forward() [1/2]

◆ avg_pool_3d_forward() [2/2]

◆ avg_pool_backward() [1/3]

◆ avg_pool_backward() [2/3]

◆ avg_pool_backward() [3/3]

◆ avg_pool_forward() [1/3]

◆ avg_pool_forward() [2/3]

◆ avg_pool_forward() [3/3]

◆ bce()

◆ bce_error()

◆ bce_loss()

◆ cce()

◆ cce_error()

◆ cce_loss()

◆ convolution_backward() [1/2]

◆ convolution_backward() [2/2]

◆ convolution_backward_filter() [1/2]

◆ convolution_backward_filter() [2/2]

◆ convolution_forward() [1/2]

◆ convolution_forward() [2/2]

◆ identity_backward()

◆ identity_derivative_out()

◆ max_pool_3d_backward() [1/2]

◆ max_pool_3d_backward() [2/2]

◆ max_pool_3d_forward() [1/2]

◆ max_pool_3d_forward() [2/2]

◆ max_pool_backward() [1/3]

◆ max_pool_backward() [2/3]

◆ max_pool_backward() [3/3]

◆ max_pool_forward() [1/3]

◆ max_pool_forward() [2/3]

◆ max_pool_forward() [3/3]

◆ mse()

◆ mse_error()

◆ mse_loss()

◆ relu_backward()

◆ relu_derivative_out()

◆ sigmoid_backward()

◆ sigmoid_derivative_out()

◆ softmax_backward()

◆ softmax_derivative_out()

◆ tanh_backward()

◆ tanh_derivative_out()