Parallel Reverse Mode Automatic Differentiation in C#
ParallelAutoDiff is a thread-safe C# library for reverse mode automatic differentiation, optimized for parallel computation. It leverages semaphores and locks to coordinate between threads, ensuring accuracy during gradient accumulation. Each operation in the library is implemented as a node with a forward and a backward function, facilitating efficient calculation of derivatives. A unique aspect of this library is its use of the visitor pattern: it includes a specialized 'Neural Network Visitor' which traverses neural network nodes across different threads. This visitor is responsible for gradient accumulation on nodes shared across multiple threads. This design allows for parallelized computations while maintaining consistency and avoiding race conditions. The result is an efficient, scalable automatic differentiation solution, ideal for machine learning applications and neural network training.
Prerequisites
Download and install the Cuda Toolkit 12.0 if you want to use the CudaMatrixMultiplyOperation.
Supported Operations
Regular Operations
AmplifiedSigmoidOperation - Used for gradient amplification.
ApplyDropoutOperation
BatchNormalizationOperation
CudaMatrixMultiplyOperation - Leverages the GPU for fast computation.
HadamardProductOperation
LayerNormalizationOperation
LeakyReLUOperation
MatrixAddOperation
MatrixAddThreeOperation
MatrixMultiplyOperation
MatrixMultiplyScalarOperation
MatrixTransposeOperation
ReLUOperation
ScaleAndShiftOperation
SigmoidOperation
SoftmaxOperation
StretchedSigmoidOperation
TanhOperation
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.
Use a JSON serialization library like Newtonsoft.JSON to deserialize the JSON file to a JsonArchitecure object.
Instantiate the computational graph
this.computationGraph = new SelfAttentionMultiLayerLSTMComputationGraph(this);
var zeroMatrixHiddenSize = new Matrix(this.hiddenSize, 1);
this.computationGraph
.AddIntermediate("inputSequence", x => this.Parameters.InputSequence[x.TimeStep])
.AddIntermediate("output", x => this.output[x.TimeStep])
.AddIntermediate("c", x => this.c[x.TimeStep][x.Layer])
.AddIntermediate("h", x => this.h[x.TimeStep][x.Layer])
.AddScalar("scaledDotProductScalar", x => 1.0d / Math.Sqrt(this.hiddenSize))
.AddWeight("Wf", x => this.Wf[x.Layer]).AddGradient("dWf", x => this.dWf[x.Layer])
.AddWeight("Wi", x => this.Wi[x.Layer]).AddGradient("dWi", x => this.dWi[x.Layer])
.AddWeight("Wc", x => this.Wc[x.Layer]).AddGradient("dWc", x => this.dWc[x.Layer])
.AddWeight("Wo", x => this.Wo[x.Layer]).AddGradient("dWo", x => this.dWo[x.Layer])
.AddWeight("Uf", x => this.Uf[x.Layer]).AddGradient("dUf", x => this.dUf[x.Layer])
.AddWeight("Ui", x => this.Ui[x.Layer]).AddGradient("dUi", x => this.dUi[x.Layer])
.AddWeight("Uc", x => this.Uc[x.Layer]).AddGradient("dUc", x => this.dUc[x.Layer])
.AddWeight("Uo", x => this.Uo[x.Layer]).AddGradient("dUo", x => this.dUo[x.Layer])
.AddWeight("bf", x => this.bf[x.Layer]).AddGradient("dbf", x => this.dbf[x.Layer])
.AddWeight("bi", x => this.bi[x.Layer]).AddGradient("dbi", x => this.dbi[x.Layer])
.AddWeight("bc", x => this.bc[x.Layer]).AddGradient("dbc", x => this.dbc[x.Layer])
.AddWeight("bo", x => this.bo[x.Layer]).AddGradient("dbo", x => this.dbo[x.Layer])
.AddWeight("Wq", x => this.Wq[x.Layer]).AddGradient("dWq", x => this.dWq[x.Layer])
.AddWeight("Wk", x => this.Wk[x.Layer]).AddGradient("dWk", x => this.dWk[x.Layer])
.AddWeight("Wv", x => this.Wv[x.Layer]).AddGradient("dWv", x => this.dWv[x.Layer])
.AddWeight("We", x => this.We).AddGradient("dWe", x => this.dWe)
.AddWeight("be", x => this.be).AddGradient("dbe", x => this.dbe)
.AddWeight("V", x => this.V).AddGradient("dV", x => this.dV)
.AddWeight("b", x => this.b).AddGradient("db", x => this.db)
.AddOperationFinder("i", x => this.computationGraph[$"i_{x.TimeStep}_{x.Layer}"])
.AddOperationFinder("f", x => this.computationGraph[$"f_{x.TimeStep}_{x.Layer}"])
.AddOperationFinder("cHat", x => this.computationGraph[$"cHat_{x.TimeStep}_{x.Layer}"])
.AddOperationFinder("o", x => this.computationGraph[$"o_{x.TimeStep}_{x.Layer}"])
.AddOperationFinder("embeddedInput", x => this.computationGraph[$"embeddedInput_{x.TimeStep}_0"])
.AddOperationFinder("hFromCurrentTimeStepAndLastLayer", x => this.computationGraph[$"h_{x.TimeStep}_{this.numLayers - 1}"])
.AddOperationFinder("currentInput", x => x.Layer == 0 ? this.computationGraph[$"embeddedInput_{x.TimeStep}_0"] : this.computationGraph[$"h_{x.TimeStep}_{x.Layer - 1}"])
.AddOperationFinder("previousHiddenState", x => x.TimeStep == 0 ? zeroMatrixHiddenSize : this.computationGraph[$"h_{x.TimeStep - 1}_{x.Layer}"])
.AddOperationFinder("previousMemoryCellState", x => x.TimeStep == 0 ? zeroMatrixHiddenSize : this.computationGraph[$"c_{x.TimeStep - 1}_{x.Layer}"])
.ConstructFromArchitecture(jsonArchitecture, this.numTimeSteps, this.numLayers);
Populate 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.
IOperationBase? backwardStartOperation = null;
for (int t = this.Parameters.NumTimeSteps - 1; t >= 0; t--)
{
backwardStartOperation = this.computationGraph[$"output_t_{t}_0"];
OperationGraphVisitor opVisitor = new OperationGraphVisitor(Guid.NewGuid().ToString(), backwardStartOperation, t);
await opVisitor.TraverseAsync();
await opVisitor.ResetVisitedCountsAsync(backwardStartOperation);
}
Run the forward pass
var op = this.computationGraph.StartOperation ?? throw new Exception("Start operation should not be null.");
IOperationBase? currOp = null;
do
{
var parameters = this.LookupParameters(op);
var forwardMethod = op.OperationType.GetMethod("Forward") ?? throw new Exception($"Forward method should exist on operation of type {op.OperationType.Name}.");
forwardMethod.Invoke(op, parameters);
if (op.ResultToName != null)
{
var split = op.ResultToName.Split(new[] { '[', ']' }, StringSplitOptions.RemoveEmptyEntries);
var oo = this.computationGraph[MatrixType.Intermediate, split[0], op.LayerInfo];
op.CopyResult(oo);
}
currOp = op;
if (op.HasNext)
{
op = op.Next;
}
}
while (currOp.Next != null);
Create a loss function
Create a loss function like mean squared error 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.
Run the backward pass utilizing inherent parallelization
IOperationBase? backwardStartOperation = null;
for (int t = this.Parameters.NumTimeSteps - 1; t >= 0; t--)
{
backwardStartOperation = this.computationGraph[$"output_t_{t}_0"];
if (gradientOfLossWrtOutput[t][0] != 0.0d)
{
var backwardInput = new Matrix(1, 1);
backwardInput[0] = gradientOfLossWrtOutput[t];
backwardStartOperation.BackwardInput = backwardInput;
OperationNeuralNetworkVisitor opVisitor = new OperationNeuralNetworkVisitor(Guid.NewGuid().ToString(), backwardStartOperation, t);
await opVisitor.TraverseAsync();
opVisitor.Reset();
traverseCount++;
}
}
Using CUDA operations
Cudablas.Instance.DeviceId = 0; // set the GPU to use, defaults to 0
Cudablas.Instance.Initialize(); // initialize the CUDA library
// ... <Run CUDA operations> ...
Cudablas.Instance.Dispose(); // dispose the CUDA library
