template<typename AReal = Real_t>
class TMVA::DNN::TCpu< AReal >

The TCpu architecture class.

Low-level interface class for multi-threaded CPU architectures. Contains as public types the declaration of the scalar, matrix and data loader types for this architecture as well as the remaining functions in the low-level interface in the form of static members.

Definition at line 37 of file Cpu.h.

Public Types
using	DeviceBuffer_t = TCpuBuffer< AReal >

using	HostBuffer_t = TCpuBuffer< AReal >

using	Matrix_t = TCpuMatrix< AReal >

using	Scalar_t = AReal

Static Public Member Functions
Forward Propagation
Low-level functions required for the forward propagation of activations through the network.
static void	MultiplyTranspose (TCpuMatrix< Scalar_t > &output, const TCpuMatrix< Scalar_t > &input, const TCpuMatrix< Scalar_t > &weights)
	Matrix-multiply `input` with the transpose of and write the results into `output`. More...

static void	AddRowWise (TCpuMatrix< Scalar_t > &output, const TCpuMatrix< Scalar_t > &biases)
	Add the vectors biases row-wise to the matrix output. More...

Backward Propagation
Low-level functions required for the forward propagation of activations through the network.
static void	Backward (TCpuMatrix< Scalar_t > &activationGradientsBackward, TCpuMatrix< Scalar_t > &weightGradients, TCpuMatrix< Scalar_t > &biasGradients, TCpuMatrix< Scalar_t > &df, const TCpuMatrix< Scalar_t > &activationGradients, const TCpuMatrix< Scalar_t > &weights, const TCpuMatrix< Scalar_t > &activationBackward)
	Perform the complete backward propagation step. More...

static void	ScaleAdd (TCpuMatrix< Scalar_t > &A, const TCpuMatrix< Scalar_t > &B, Scalar_t beta=1.0)
	Adds a the elements in matrix B scaled by c to the elements in the matrix A. More...

static void	Copy (TCpuMatrix< Scalar_t > &B, const TCpuMatrix< Scalar_t > &A)

Activation Functions
For each activation function, the low-level interface contains two routines. One that applies the acitvation function to a matrix and one that evaluate the derivatives of the activation function at the elements of a given matrix and writes the results into the result matrix.
static void	IdentityDerivative (TCpuMatrix< Scalar_t > &B, const TCpuMatrix< Scalar_t > &A)

static void	Relu (TCpuMatrix< Scalar_t > &B)

static void	ReluDerivative (TCpuMatrix< Scalar_t > &B, const TCpuMatrix< Scalar_t > &A)

static void	Sigmoid (TCpuMatrix< Scalar_t > &B)

static void	SigmoidDerivative (TCpuMatrix< Scalar_t > &B, const TCpuMatrix< Scalar_t > &A)

static void	Tanh (TCpuMatrix< Scalar_t > &B)

static void	TanhDerivative (TCpuMatrix< Scalar_t > &B, const TCpuMatrix< Scalar_t > &A)

static void	SymmetricRelu (TCpuMatrix< Scalar_t > &B)

static void	SymmetricReluDerivative (TCpuMatrix< Scalar_t > &B, const TCpuMatrix< Scalar_t > &A)

static void	SoftSign (TCpuMatrix< Scalar_t > &B)

static void	SoftSignDerivative (TCpuMatrix< Scalar_t > &B, const TCpuMatrix< Scalar_t > &A)

static void	Gauss (TCpuMatrix< Scalar_t > &B)

static void	GaussDerivative (TCpuMatrix< Scalar_t > &B, const TCpuMatrix< Scalar_t > &A)

Loss Functions
Loss functions compute a scalar value given the `output` of the network for a given training input and the expected network prediction `Y` that quantifies the quality of the prediction. For each function also a routing that computes the gradients (suffixed by Gradients) must be provided for the starting of the backpropagation algorithm.
static Scalar_t	MeanSquaredError (const TCpuMatrix< Scalar_t > &Y, const TCpuMatrix< Scalar_t > &output)

static void	MeanSquaredErrorGradients (TCpuMatrix< Scalar_t > &dY, const TCpuMatrix< Scalar_t > &Y, const TCpuMatrix< Scalar_t > &output)

static Scalar_t	CrossEntropy (const TCpuMatrix< Scalar_t > &Y, const TCpuMatrix< Scalar_t > &output)
	Sigmoid transformation is implicitly applied, thus `output` should hold the linear activations of the last layer in the net. More...

static void	CrossEntropyGradients (TCpuMatrix< Scalar_t > &dY, const TCpuMatrix< Scalar_t > &Y, const TCpuMatrix< Scalar_t > &output)

static Scalar_t	SoftmaxCrossEntropy (const TCpuMatrix< Scalar_t > &Y, const TCpuMatrix< Scalar_t > &output)
	Softmax transformation is implicitly applied, thus `output` should hold the linear activations of the last layer in the net. More...

static void	SoftmaxCrossEntropyGradients (TCpuMatrix< Scalar_t > &dY, const TCpuMatrix< Scalar_t > &Y, const TCpuMatrix< Scalar_t > &output)

Output Functions
Output functions transform the activations `output` of the output layer in the network to a valid prediction `YHat` for the desired usage of the network, e.g. the identity function for regression or the sigmoid transformation for two-class classification.
static void	Sigmoid (TCpuMatrix< Scalar_t > &YHat, const TCpuMatrix< Scalar_t > &)

static void	Softmax (TCpuMatrix< Scalar_t > &YHat, const TCpuMatrix< Scalar_t > &)

Regularization
For each regularization type two functions are required, one named `<Type>Regularization` that evaluates the corresponding regularization functional for a given weight matrix and the `Add<Type>RegularizationGradients`, that adds the regularization component in the gradients to the provided matrix.
static Scalar_t	L1Regularization (const TCpuMatrix< Scalar_t > &W)

static void	AddL1RegularizationGradients (TCpuMatrix< Scalar_t > &A, const TCpuMatrix< Scalar_t > &W, Scalar_t weightDecay)

static Scalar_t	L2Regularization (const TCpuMatrix< Scalar_t > &W)

static void	AddL2RegularizationGradients (TCpuMatrix< Scalar_t > &A, const TCpuMatrix< Scalar_t > &W, Scalar_t weightDecay)

Initialization
For each initialization method, one function in the low-level interface is provided. The naming scheme is Initialize<Type> for a given initialization method Type.
static void	InitializeGauss (TCpuMatrix< Scalar_t > &A)

static void	InitializeUniform (TCpuMatrix< Scalar_t > &A)

static void	InitializeIdentity (TCpuMatrix< Scalar_t > &A)

static void	InitializeZero (TCpuMatrix< Scalar_t > &A)

Dropout
static void	Dropout (TCpuMatrix< Scalar_t > &A, Scalar_t p)
	Apply dropout with activation probability `p` to the given matrix `A` and scale the result by reciprocal of `p`. More...

Additional Arithmetic Functions
Additional arithmetic on CUDA matrices used to implement the low-level interface.
static void	Multiply (TCpuMatrix< Scalar_t > &C, const TCpuMatrix< Scalar_t > &A, const TCpuMatrix< Scalar_t > &B)
	Standard multiplication of two matrices `A` and `B` with the result being written into C. More...

static void	TransposeMultiply (TCpuMatrix< Scalar_t > &output, const TCpuMatrix< Scalar_t > &input, const TCpuMatrix< Scalar_t > &Weights)
	Matrix multiplication of two matrices `A` and `B^T` (transposed) with the result being written into C. More...

static void	Hadamard (TCpuMatrix< Scalar_t > &A, const TCpuMatrix< Scalar_t > &B)
	In-place Hadamard (element-wise) product of matrices `A` and `B` with the result being written into `A`. More...

static void	SumColumns (TCpuMatrix< Scalar_t > &B, const TCpuMatrix< Scalar_t > &A)
	Sum columns of (m x n) matrixx `A` and write the results into the first m elements in `A`. More...

static Scalar_t	Sum (const TCpuMatrix< Scalar_t > &A)
	Compute the sum of all elements in `A`. More...

#include <TMVA/DNN/Architectures/Cpu.h>

Member Typedef Documentation

◆ DeviceBuffer_t

template<typename AReal = Real_t>

using TMVA::DNN::TCpu< AReal >::DeviceBuffer_t = TCpuBuffer<AReal>

Definition at line 44 of file Cpu.h.

◆ HostBuffer_t

template<typename AReal = Real_t>

using TMVA::DNN::TCpu< AReal >::HostBuffer_t = TCpuBuffer<AReal>

Definition at line 43 of file Cpu.h.

◆ Matrix_t

template<typename AReal = Real_t>

using TMVA::DNN::TCpu< AReal >::Matrix_t = TCpuMatrix<AReal>

Definition at line 42 of file Cpu.h.

◆ Scalar_t

template<typename AReal = Real_t>

using TMVA::DNN::TCpu< AReal >::Scalar_t = AReal

Definition at line 41 of file Cpu.h.

Member Function Documentation

◆ AddL1RegularizationGradients()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::AddL1RegularizationGradients	(	TCpuMatrix< Scalar_t > &	A,
		const TCpuMatrix< Scalar_t > &	W,
		Scalar_t	weightDecay
	)

static

Definition at line 52 of file Regularization.cxx.

◆ AddL2RegularizationGradients()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::AddL2RegularizationGradients	(	TCpuMatrix< Scalar_t > &	A,
		const TCpuMatrix< Scalar_t > &	W,
		Scalar_t	weightDecay
	)

static

Definition at line 98 of file Regularization.cxx.

◆ AddRowWise()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::AddRowWise	(	TCpuMatrix< Scalar_t > &	output,
		const TCpuMatrix< Scalar_t > &	biases
	)

static

Add the vectors biases row-wise to the matrix output.

Definition at line 50 of file Propagation.cxx.

◆ Backward()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::Backward	(	TCpuMatrix< Scalar_t > &	activationGradientsBackward,
		TCpuMatrix< Scalar_t > &	weightGradients,
		TCpuMatrix< Scalar_t > &	biasGradients,
		TCpuMatrix< Scalar_t > &	df,
		const TCpuMatrix< Scalar_t > &	activationGradients,
		const TCpuMatrix< Scalar_t > &	weights,
		const TCpuMatrix< Scalar_t > &	activationBackward
	)

static

Perform the complete backward propagation step.

If the provided activationGradientsBackward matrix is not empty, compute the gradients of the objective function with respect to the activations of the previous layer (backward direction). Also compute the weight and the bias gradients. Modifies the values in df and thus produces only a valid result, if it is applied the first time after the corresponding forward propagation has been per- formed.

Definition at line 68 of file Propagation.cxx.

◆ Copy()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< Real_t >::Copy	(	TCpuMatrix< Scalar_t > &	B,
		const TCpuMatrix< Scalar_t > &	A
	)

static

Definition at line 129 of file Arithmetic.cxx.

◆ CrossEntropy()

template<typename AReal = Real_t>

AFloat TMVA::DNN::TCpu< AFloat >::CrossEntropy	(	const TCpuMatrix< Scalar_t > &	Y,
		const TCpuMatrix< Scalar_t > &	output
	)

static

Sigmoid transformation is implicitly applied, thus output should hold the linear activations of the last layer in the net.

Definition at line 77 of file LossFunctions.cxx.

◆ CrossEntropyGradients()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::CrossEntropyGradients	(	TCpuMatrix< Scalar_t > &	dY,
		const TCpuMatrix< Scalar_t > &	Y,
		const TCpuMatrix< Scalar_t > &	output
	)

static

Definition at line 109 of file LossFunctions.cxx.

◆ Dropout()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::Dropout	(	TCpuMatrix< Scalar_t > &	A,
		Scalar_t	p
	)

static

Apply dropout with activation probability p to the given matrix A and scale the result by reciprocal of p.

Definition at line 24 of file Dropout.cxx.

◆ Gauss()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::Gauss ( TCpuMatrix< Scalar_t > & B )

static

Definition at line 133 of file ActivationFunctions.cxx.

◆ GaussDerivative()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::GaussDerivative	(	TCpuMatrix< Scalar_t > &	B,
		const TCpuMatrix< Scalar_t > &	A
	)

static

Definition at line 141 of file ActivationFunctions.cxx.

◆ Hadamard()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< Real_t >::Hadamard	(	TCpuMatrix< Scalar_t > &	A,
		const TCpuMatrix< Scalar_t > &	B
	)

static

In-place Hadamard (element-wise) product of matrices A and B with the result being written into A.

Definition at line 76 of file Arithmetic.cxx.

◆ IdentityDerivative()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::IdentityDerivative	(	TCpuMatrix< Scalar_t > &	B,
		const TCpuMatrix< Scalar_t > &	A
	)

static

Definition at line 27 of file ActivationFunctions.cxx.

◆ InitializeGauss()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::InitializeGauss ( TCpuMatrix< Scalar_t > & A )

static

Definition at line 27 of file Initialization.cxx.

◆ InitializeIdentity()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::InitializeIdentity ( TCpuMatrix< Scalar_t > & A )

static

Definition at line 65 of file Initialization.cxx.

◆ InitializeUniform()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::InitializeUniform ( TCpuMatrix< Scalar_t > & A )

static

Definition at line 46 of file Initialization.cxx.

◆ InitializeZero()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::InitializeZero ( TCpuMatrix< Scalar_t > & A )

static

Definition at line 84 of file Initialization.cxx.

◆ L1Regularization()

template<typename AReal = Real_t>

AFloat TMVA::DNN::TCpu< AFloat >::L1Regularization ( const TCpuMatrix< Scalar_t > & W )

static

Definition at line 26 of file Regularization.cxx.

◆ L2Regularization()

template<typename AReal = Real_t>

AFloat TMVA::DNN::TCpu< AFloat >::L2Regularization ( const TCpuMatrix< Scalar_t > & W )

static

Definition at line 72 of file Regularization.cxx.

◆ MeanSquaredError()

template<typename AReal = Real_t>

AFloat TMVA::DNN::TCpu< AFloat >::MeanSquaredError	(	const TCpuMatrix< Scalar_t > &	Y,
		const TCpuMatrix< Scalar_t > &	output
	)

static

Definition at line 26 of file LossFunctions.cxx.

◆ MeanSquaredErrorGradients()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::MeanSquaredErrorGradients	(	TCpuMatrix< Scalar_t > &	dY,
		const TCpuMatrix< Scalar_t > &	Y,
		const TCpuMatrix< Scalar_t > &	output
	)

static

Definition at line 55 of file LossFunctions.cxx.

◆ Multiply()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< Real_t >::Multiply	(	TCpuMatrix< Scalar_t > &	C,
		const TCpuMatrix< Scalar_t > &	A,
		const TCpuMatrix< Scalar_t > &	B
	)

static

Standard multiplication of two matrices A and B with the result being written into C.

Definition at line 28 of file Arithmetic.cxx.

◆ MultiplyTranspose()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::MultiplyTranspose	(	TCpuMatrix< Scalar_t > &	output,
		const TCpuMatrix< Scalar_t > &	input,
		const TCpuMatrix< Scalar_t > &	weights
	)

static

Matrix-multiply input with the transpose of and write the results into output.

Definition at line 27 of file Propagation.cxx.

◆ Relu()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::Relu ( TCpuMatrix< Scalar_t > & B )

static

Definition at line 36 of file ActivationFunctions.cxx.

◆ ReluDerivative()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::ReluDerivative	(	TCpuMatrix< Scalar_t > &	B,
		const TCpuMatrix< Scalar_t > &	A
	)

static

Definition at line 44 of file ActivationFunctions.cxx.

◆ ScaleAdd()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< Real_t >::ScaleAdd	(	TCpuMatrix< Scalar_t > &	A,
		const TCpuMatrix< Scalar_t > &	B,
		Scalar_t	beta = `1.0`
	)

static

Adds a the elements in matrix B scaled by c to the elements in the matrix A.

This is required for the weight update in the gradient descent step.

Definition at line 114 of file Arithmetic.cxx.

◆ Sigmoid() [1/2]

template<typename AReal = Real_t>

static void TMVA::DNN::TCpu< AReal >::Sigmoid ( TCpuMatrix< Scalar_t > & B )

static

◆ Sigmoid() [2/2]

template<typename AReal = Real_t>

static void TMVA::DNN::TCpu< AReal >::Sigmoid	(	TCpuMatrix< Scalar_t > &	YHat,
		const TCpuMatrix< Scalar_t > &
	)

static

◆ SigmoidDerivative()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::SigmoidDerivative	(	TCpuMatrix< Scalar_t > &	B,
		const TCpuMatrix< Scalar_t > &	A
	)

static

Definition at line 61 of file ActivationFunctions.cxx.

◆ Softmax()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::Softmax	(	TCpuMatrix< Scalar_t > &	YHat,
		const TCpuMatrix< Scalar_t > &
	)

static

Definition at line 33 of file OutputFunctions.cxx.

◆ SoftmaxCrossEntropy()

template<typename AReal = Real_t>

AFloat TMVA::DNN::TCpu< AFloat >::SoftmaxCrossEntropy	(	const TCpuMatrix< Scalar_t > &	Y,
		const TCpuMatrix< Scalar_t > &	output
	)

static

Softmax transformation is implicitly applied, thus output should hold the linear activations of the last layer in the net.

Definition at line 132 of file LossFunctions.cxx.

◆ SoftmaxCrossEntropyGradients()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::SoftmaxCrossEntropyGradients	(	TCpuMatrix< Scalar_t > &	dY,
		const TCpuMatrix< Scalar_t > &	Y,
		const TCpuMatrix< Scalar_t > &	output
	)

static

Definition at line 171 of file LossFunctions.cxx.

◆ SoftSign()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::SoftSign ( TCpuMatrix< Scalar_t > & B )

static

Definition at line 112 of file ActivationFunctions.cxx.

◆ SoftSignDerivative()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::SoftSignDerivative	(	TCpuMatrix< Scalar_t > &	B,
		const TCpuMatrix< Scalar_t > &	A
	)

static

Definition at line 120 of file ActivationFunctions.cxx.

◆ Sum()

template<typename AReal = Real_t>

static Scalar_t TMVA::DNN::TCpu< AReal >::Sum ( const TCpuMatrix< Scalar_t > & A )

static

Compute the sum of all elements in A.

◆ SumColumns()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< Real_t >::SumColumns	(	TCpuMatrix< Scalar_t > &	B,
		const TCpuMatrix< Scalar_t > &	A
	)

static

Sum columns of (m x n) matrixx A and write the results into the first m elements in A.

Definition at line 93 of file Arithmetic.cxx.

◆ SymmetricRelu()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::SymmetricRelu ( TCpuMatrix< Scalar_t > & B )

static

Definition at line 93 of file ActivationFunctions.cxx.

◆ SymmetricReluDerivative()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::SymmetricReluDerivative	(	TCpuMatrix< Scalar_t > &	B,
		const TCpuMatrix< Scalar_t > &	A
	)

static

Definition at line 101 of file ActivationFunctions.cxx.

◆ Tanh()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::Tanh ( TCpuMatrix< Scalar_t > & B )

static

Definition at line 73 of file ActivationFunctions.cxx.

◆ TanhDerivative()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< AFloat >::TanhDerivative	(	TCpuMatrix< Scalar_t > &	B,
		const TCpuMatrix< Scalar_t > &	A
	)

static

Definition at line 81 of file ActivationFunctions.cxx.

◆ TransposeMultiply()

template<typename AReal = Real_t>

void TMVA::DNN::TCpu< Real_t >::TransposeMultiply	(	TCpuMatrix< Scalar_t > &	output,
		const TCpuMatrix< Scalar_t > &	input,
		const TCpuMatrix< Scalar_t > &	Weights
	)

static

Matrix multiplication of two matrices A and B^T (transposed) with the result being written into C.

Definition at line 52 of file Arithmetic.cxx.

The documentation for this class was generated from the following files:

tmva/tmva/inc/TMVA/DNN/Architectures/Cpu.h
tmva/tmva/src/DNN/Architectures/Cpu/ActivationFunctions.cxx
tmva/tmva/src/DNN/Architectures/Cpu/Arithmetic.cxx
tmva/tmva/src/DNN/Architectures/Cpu/Dropout.cxx
tmva/tmva/src/DNN/Architectures/Cpu/Initialization.cxx
tmva/tmva/src/DNN/Architectures/Cpu/LossFunctions.cxx
tmva/tmva/src/DNN/Architectures/Cpu/OutputFunctions.cxx
tmva/tmva/src/DNN/Architectures/Cpu/Propagation.cxx
tmva/tmva/src/DNN/Architectures/Cpu/Regularization.cxx

template<typename AReal = Real_t> class TMVA::DNN::TCpu< AReal >

Public Types

Static Public Member Functions

Member Typedef Documentation

◆ DeviceBuffer_t

◆ HostBuffer_t

◆ Matrix_t

◆ Scalar_t

Member Function Documentation

◆ AddL1RegularizationGradients()

◆ AddL2RegularizationGradients()

◆ AddRowWise()

◆ Backward()

◆ Copy()

◆ CrossEntropy()

◆ CrossEntropyGradients()

◆ Dropout()

◆ Gauss()

◆ GaussDerivative()

◆ Hadamard()

◆ IdentityDerivative()

◆ InitializeGauss()

◆ InitializeIdentity()

◆ InitializeUniform()

◆ InitializeZero()

◆ L1Regularization()

◆ L2Regularization()

◆ MeanSquaredError()

◆ MeanSquaredErrorGradients()

◆ Multiply()

◆ MultiplyTranspose()

◆ Relu()

◆ ReluDerivative()

◆ ScaleAdd()

◆ Sigmoid() [1/2]

◆ Sigmoid() [2/2]

◆ SigmoidDerivative()

◆ Softmax()

◆ SoftmaxCrossEntropy()

◆ SoftmaxCrossEntropyGradients()

◆ SoftSign()

◆ SoftSignDerivative()

◆ Sum()

◆ SumColumns()

◆ SymmetricRelu()

◆ SymmetricReluDerivative()

◆ Tanh()

◆ TanhDerivative()

◆ TransposeMultiply()

template<typename AReal = Real_t>
class TMVA::DNN::TCpu< AReal >