ParallelReverseAutoDiff (PRAD) is a thread-safe C# library designed for reverse mode automatic differentiation, optimized for parallel computation and primed for the demands of modern machine learning applications and neural network training. It leverages semaphores and locks to orchestrate between threads, ensuring precision during gradient accumulation.

Upon the realm of code, a gem does shine,

PRAD, a library so divine.

In C# it's crafted, threads align,

Parallel tasks in order, by design.

Reverse mode diff, its core decree,

For neural nets, the key to see.

With batch operations, swift and free,

And ILGPU's might, a sight to be.

From JSON springs architecture grand,

A computational graph, complex and planned.

In the realm of AI, it takes a stand,

A tool of power, in your hand.

So sing we now of PRAD's great glory,

Etched forever in code's vast story.

API Documentation

Overview

Each operation in PRAD is embodied as a node with forward and backward functions, facilitating the efficient calculation of derivatives. This design is particularly beneficial for large-scale problems and complex neural network architectures, where computational efficiency is paramount.

A standout feature of PRAD is its innovative use of the visitor pattern. The library includes a specialized 'Neural Network Visitor' which traverses neural network nodes across different threads. This visitor is tasked with gradient accumulation on nodes shared across multiple threads, allowing for parallelized computations while maintaining consistency and avoiding race conditions.

Moreover, PRAD introduces a data-driven approach to neural network architecture design, allowing for rapid prototyping and experimentation. The library leverages the power of ILGPU, a high-performance GPU-accelerated library for .NET programs, to perform complex computations on the GPU, further enhancing its performance and scalability.

PRAD's dynamic computational graph, constructed from JSON architecture, allows for the efficient computation of gradients, a crucial aspect of the backpropagation process used in training neural networks. This unique blend of features makes PRAD an efficient, scalable, and groundbreaking automatic differentiation solution.

Prerequisites

Download and install the Cuda Toolkit 12.0 if you want to use the CudaMatrixMultiplyOperation.

Regular Operations

AddGaussianNoiseOperation

AmplifiedSigmoidOperation - Used for gradient amplification.

ApplyDropoutOperation

BatchNormalizationOperation

CosineProjectionOperation

CosineScalingOperation

CudaMatrixMultiplyOperation - Leverages NVIDIA GPUs for fast computation.

DualWeightedOperation

ElementwiseMultiplyAndSumOperation

EmbeddingOperation - Used for word or subword embeddings.

FeatureAggregationOperation - Used for GATs

GELUOperation

GpuMatrixMultiplyAndSumOperation - Leverages NVIDIA, AMD, or Intel GPUs for fast computation.

GpuMatrixMultiplyOperation - Leverages NVIDIA, AMD, or Intel GPUs for fast computation.

GraphAttentionOperation - Used for GATs

HadamardProductOperation

HierarchicalScalingOperation - For increased interpretability.

LayerNormalizationOperation

LeakyReLUOperation

MatrixAddOperation

MatrixAddBroadcastingOperation

MatrixAddThreeOperation

MatrixAverageOperation

MatrixBroadcastOperation

MatrixConcatenateOperation

MatrixDiagonalFilterOperation

MatrixHorizontalConcatenateOperation

MatrixMultiplyOperation

MatrixMultiplyAndSumOperation

MatrixMultiplyAndSumRowsOperation

MatrixMultiplyScalarOperation

MatrixSumOperation

MatrixTransposeOperation

MatrixRowConcatenateOperation

MatrixVectorConcatenateOperation

MatrixVerticalConcatenateOperation

MultiQuerySelfAttentionOperation

PaddingMaskOperation

ReLUOperation

RMSNormOperation

ScaleAndShiftOperation

SigmoidOperation

SineSoftmaxOperation - Reduces the vanishing gradient problem with traditional softmax.

SoftmaxOperation

StretchedSigmoidOperation

SwigLUOperation

SwishOperation

TanhOperation

VariedSoftmaxOperation

Deep Operations

These types of operations operate on instances of the DeepMatrix class which is a 3-D matrix. The first dimension is the channel size and the second and third dimensions are the row and column sizes respectively.

DeepBatchNormalizationOperation

DeepConcatenateOperation

DeepConvolutionOperation

DeepLeakyReLUOperation

DeepMatrixElementwiseAddOperation

DeepMatrixElementWiseMultiplySumOperation

DeepMaxPoolOperation

DeepPairwiseAttentionOperation

DeepReLUOperation

DeepScaleAndShiftOperation

FlattenOperation

Vector Neural Network (VNN) Operations

These types of operations typically operate on instances of the Matrix class where the left half are magnitudes and the right half are angles in radians. Learn more about Vector Neural Networks here.

ElementwiseSquareOperation

ElementwiseVectorAddOperation

ElementwiseVectorCartesianSummationOperation

ElementwiseVectorConstituentMultiplyOperation

ElementwiseVectorDecompositionOperation

ElementwiseVectorMiniDecompositionOperation

PairwiseSineSoftmaxOperation

VectorAttentionBinaryOperation

VectorAttentionOperation

VectorizeOperation

Neural Network Parameters

Each neural network base class has a set of parameters that can be used to configure the neural network. They are as follows:

Usage

Building your Neural Network Model

Each model element group needs a unique identifier, a size array, and an initialization type.

The three possible initialization types are Xavier, He, and Zeroes.

The group consists of weights, gradients, and moments for Adam optimization.

The initialization type is used to initialize the model element group's weights.

The model element group's elements are stored in a matrix whose size is specified by the size array.

In this example, for the hidden layer, the first dimension is the number of layers and the second and third dimensions are the row and column sizes respectively.

Understanding the JSON Architecture

Here is an example:

Each operation in the JSON represents a step in a computational graph used for automatic differentiation. Here's what each field means:

• "timeSteps": This is an array that represents the sequence of computational operations. Each element in the array is an object that corresponds to a computational timestep.

• "startOperations": This is an array that defines the initial operations for the current timestep.

• "layers": This represents a sequence of operations corresponding to the layers of the network. Each operation in a layer is a step in the computation, and the order of operations matters, as some operations depend on the results of previous operations.

• "endOperations": This is an array that defines the final operations for the current timestep.

Each operation object in "startOperations", "layers", or "endOperations" has several fields:

• "id": This is a unique identifier for the operation.

• "description": This is a human-readable description of what the operation does.

• "type": This specifies the type of the operation.

• "inputs": This is an array that lists the inputs for the operation. These are the identifiers of other nodes in the computational graph. The identifiers are either defined in the computational graph, or in operation finders declared in code when building an instance of the ComputationGraph class, for example the SelfAttentionMultiLayerLSTMComputationGraph class which is a subclass of ComputationGraph.

• "gradientResultTo": This is an array that specifies where the results of the backward pass (i.e., the computed gradients) should be stored. A null value means that the gradient with respect to the input is not stored. There is an implicit mapping between the gradient and the input based on its position in the array.

• "setResultTo": This is used to store the result of the operation for later use.

The JSON defines the steps in a machine learning model's forward pass and also specifies how the backward pass (which computes gradients for optimization) should be carried out.

By defining the operations and their connections in a JSON file, the graph can be easily constructed and modified, and the computations can be automatically differentiated and parallelized. This representation makes it possible to define a wide variety of models in a modular way, using the building blocks provided by the library.

Instantiating the Architecture

Use a JSON serialization library like Newtonsoft.JSON to deserialize the JSON file to a JsonArchitecture object.

There are other JSON architectures available as well.

These include the 'NestedLayersJsonArchitecture', 'DualLayersJsonArchitecture', and 'TripleLayersJsonArchitecture'.

Instantiating the Computational Graph

Operation finders are a key component used to define and locate different operations in a neural network's computational graph. They're essentially functions that link to specific operations at different layers or time steps within the network. This is achieved by mapping string identifiers (IDs) to these operations, which are then used within a JSON architecture to establish the network's structure and sequence of computations. For example, an operation finder could link to a matrix multiplication operation in a specific layer of the network. By using these operation finders, developers can effectively manage complex computational graphs.

Populating the Backward Dependency Counts

Then populate the backward dependency counts by running the following code. It only has to be run once to set up the backward dependency counts.

Running the Forward Pass

Creating a Loss Function

Create a loss function like mean squared error, cross-entropy loss or using policy gradient methods.

Then calculate the gradient of the loss with respect to the output.

Plug the result in as the backward input for the backward start operation.

Running the Backward Pass

Clipping the Gradients

Updating the Weights

Using CUDA Operations

PradOp

PradOp is a 'pretty rad' automatic differentiation operation class in the ParallelReverseAutoDiff (PRAD) library, providing a lightweight reverse-mode automatic differentiation implementation. It supports various tensor operations and manages the computation graph for efficient gradient calculations. It is meant to be used within both the Forward and Backward functions for custom neural network operations to simplify the code, especially the backward pass, by leveraging automatic differentiation.

Features

• Efficient Tensor Operations: Leverages the Tensor class for fast, vectorized computations using the math kernel library (MKL.NET).
• Automatic Differentiation: Records operations for both forward and backward passes.
• Parallelization: Supports parallel execution of multiple operations for improved performance.
• Flexible Architecture: Can be used as a standalone mini-computation graph or integrated into larger systems.
• Rich Operation Set: Includes element-wise operations, reshaping, transposing, gathering, and more.
• Branching Support: Allows for creation of complex computational graphs with branching paths.
• Gradient Accumulation: Designed to work with systems that use gradient accumulation and optimization.
• Custom Operations: Supports implementation of custom operations with automatic gradient computation.

Key Components

PradOp

• Manages the computational graph and operations.
• Handles forward and backward passes.
• Supports branching and splitting for complex graph structures.

PradResult

• Encapsulates the result of a computation.
• Provides methods for backpropagation and chaining operations.

Constructor

Creates a new instance of the PradOp class with a seed tensor.

• seed: The initial tensor to start computations with.

Properties

Methods

Tensor Operations

Tensor Manipulation

Computation Graph Management

Static Operations

PradOp provides several static operation delegates that can be used with the Then method of PradResult:

• SquareRootOp
• AddOp
• MulOp
• SubOp
• DivOp
• SinOp
• CosOp
• GatherNdOp
• SumRowsOp
• SquareOp
• Atan2Op
• StackOp
• ConcatOp

PradResult.Then Method

The Then method in PradResult is a powerful feature that allows for elegant chaining of operations in the computational graph. It provides a fluent interface for applying successive operations to the result of previous computations.

Method Signatures

Functionality

1. Chaining Operations: The Then method allows you to apply a new operation to the result of the previous operation. This creates a chain of operations that can be read from left to right, improving code readability.

2. Static Operation Delegates: The method uses static operation delegates defined in PradOp (like AddOp, MulOp, SinOp, etc.) to determine which operation to apply. These static delegates act as keys to retrieve the corresponding instance method.

3. Flexible Input: The method can handle operations that require no additional input, a single additional tensor, or multiple additional tensors and an axis.

4. Dynamic Dispatch: The method uses the GetOperation<T> method of PradOp to dynamically retrieve the correct instance method based on the static delegate provided.

Usage Examples

Here are some examples of how to use PradOp:

Chaining Operations

PradResult allows for elegant chaining of operations:

Parallel Operations

PradOp supports parallel execution of multiple operations:

Custom Operations

PradOp allows you to define custom operations with their own forward and backward passes. Here's an example of a custom sigmoid operation:

Usage:

Branching

PradOp supports creating complex computational graphs with branching paths. Here's an example:

Splitting

PradOp allows you to split tensors and perform operations on the split parts. Here's an example:

These examples demonstrate the flexibility of PradOp in handling complex computational graphs, including custom operations, branching, and splitting/recombining tensors. The automatic differentiation system takes care of computing the correct gradients through these complex structures.

Customization

The ParallelReverseAutoDiff (PRAD) library is designed with customization at its core.

Understanding that the world of machine learning and neural networks is continually evolving, the library allows users to define their own neural network operations.

This feature provides an immense level of flexibility and control over the architecture and behavior of the networks, making it adaptable to both traditional and experimental models.

Custom Neural Network Operations

One of the standout features of PRAD is the ability to create custom operations.

These operations can encapsulate any computation or processing steps, including but not limited to, complex forward and backward calculations, and operations involving matrices, vectors, or scalars.

Creating a custom operation requires extending the Operation abstract class, which involves implementing two key methods:

• Forward(): This method is used to describe how your operation behaves during the forward pass of the neural network. It takes as input the relevant data, processes it as per the custom-defined operation, and produces the output.

• Backward(): This method is responsible for defining how your operation behaves during the backward pass of the neural network, i.e., how it contributes to the gradients during backpropagation. It receives the gradient of the output and uses it to compute the gradients of its inputs.

Let's look at an example custom operation, MatrixAverageOperation, which calculates the average of feature vectors across a matrix:

In this example, the Forward method calculates the average of the features for each path, while the Backward method spreads the gradient evenly across the features.

This level of customization allows PRAD to be a versatile tool in the field of machine learning, capable of being tailored to a wide range of tasks, datasets, and innovative architectures.

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