ParallelReverseAutoDiff

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.

Supported Operations

AmplifiedSigmoidOperation - Used for gradient amplification

ApplyDropoutOperation

HadamardProductOperation

LayerNormalizationOperation

LeakyReLUOperation

MatrixAddOperation

MatrixAddThreeOperation

MatrixMultiplyOperation

MatrixMultiplyScalarOperation

MatrixTransposeOperation

SigmoidOperation

SoftmaxOperation

StretchedSigmoidOperation

TanhOperation

Usage

Create architecture JSON file

Here is an example:

{ "timeSteps": [ { "startOperations": [ { "id": "projectedInput", "description": "Multiply the input with the weight matrix", "type": "MatrixMultiplyOperation", "inputs": [ "We", "inputSequence[t]" ], "gradientResultTo": [ "dWe", null ] }, { "id": "embeddedInput", "description": "Add the bias", "type": "MatrixAddOperation", "inputs": [ "projectedInput", "be" ], "gradientResultTo": [ null, "dbe" ] } ], "layers": [ { "operations": [ { "id": "wf_currentInput", "type": "MatrixMultiplyOperation", "inputs": [ "Wf[layerIndex]", "currentInput" ], "gradientResultTo": [ "dWf[layerIndex]", null ] }, { "id": "uf_previousHiddenState", "type": "MatrixMultiplyOperation", "inputs": [ "Uf[layerIndex]", "previousHiddenState" ], "gradientResultTo": [ "dUf[layerIndex]", null ] }, { "id": "f_add", "type": "MatrixAddThreeOperation", "inputs": [ "wf_currentInput", "uf_previousHiddenState", "bf[layerIndex]" ], "gradientResultTo": [ null, null, "dbf[layerIndex]" ] }, { "id": "intermediate_f_1", "description": "Compute the forget gate", "type": "MatrixTransposeOperation", "inputs": [ "f_add" ] }, { "id": "intermediate_f_2", "description": "Compute the forget gate", "type": "LayerNormalizationOperation", "inputs": [ "intermediate_f_1" ] }, { "id": "intermediate_f_3", "description": "Compute the forget gate", "type": "MatrixTransposeOperation", "inputs": [ "intermediate_f_2" ] }, { "id": "f", "description": "Compute the forget gate", "type": "AmplifiedSigmoidOperation", "inputs": [ "intermediate_f_3" ], "setResultTo": "f[t][layerIndex]" }, { "id": "wi_currentInput", "type": "MatrixMultiplyOperation", "inputs": [ "Wi[layerIndex]", "currentInput" ], "gradientResultTo": [ "dWi[layerIndex]", null ] }, { "id": "ui_previousHiddenState", "type": "MatrixMultiplyOperation", "inputs": [ "Ui[layerIndex]", "previousHiddenState" ], "gradientResultTo": [ "dUi[layerIndex]", null ] }, { "id": "i_add", "type": "MatrixAddThreeOperation", "inputs": [ "wi_currentInput", "ui_previousHiddenState", "bi[layerIndex]" ], "gradientResultTo": [ null, null, "dbi[layerIndex]" ] }, { "id": "intermediate_i_1", "description": "Compute the input gate", "type": "MatrixTransposeOperation", "inputs": [ "i_add" ] }, { "id": "intermediate_i_2", "description": "Compute the input gate", "type": "LayerNormalizationOperation", "inputs": [ "intermediate_i_1" ] }, { "id": "intermediate_i_3", "description": "Compute the input gate", "type": "MatrixTransposeOperation", "inputs": [ "intermediate_i_2" ] }, { "id": "i", "description": "Compute the input gate", "type": "AmplifiedSigmoidOperation", "inputs": [ "intermediate_i_3" ], "setResultTo": "i[t][layerIndex]" }, { "id": "wc_currentInput", "type": "MatrixMultiplyOperation", "inputs": [ "Wc[layerIndex]", "currentInput" ], "gradientResultTo": [ "dWc[layerIndex]", null ] }, { "id": "uc_previousHiddenState", "type": "MatrixMultiplyOperation", "inputs": [ "Uc[layerIndex]", "previousHiddenState" ], "gradientResultTo": [ "dUc[layerIndex]", null ] }, { "id": "cHat_add", "type": "MatrixAddThreeOperation", "inputs": [ "wc_currentInput", "uc_previousHiddenState", "bc[layerIndex]" ], "gradientResultTo": [ null, null, "dbc[layerIndex]" ] }, { "id": "intermediate_cHat_1", "description": "Compute the candidate memory cell state", "type": "MatrixTransposeOperation", "inputs": [ "cHat_add" ] }, { "id": "intermediate_cHat_2", "description": "Compute the candidate memory cell state", "type": "LayerNormalizationOperation", "inputs": [ "intermediate_cHat_1" ] }, { "id": "intermediate_cHat_3", "description": "Compute the candidate memory cell state", "type": "MatrixTransposeOperation", "inputs": [ "intermediate_cHat_2" ] }, { "id": "cHat", "description": "Compute the candidate memory cell state", "type": "TanhOperation", "inputs": [ "intermediate_cHat_3" ], "setResultTo": "cHat[t][layerIndex]" }, { "id": "f_previousMemoryCellState", "type": "HadamardProductOperation", "inputs": [ "f[t][layerIndex]", "previousMemoryCellState" ] }, { "id": "i_cHat", "type": "HadamardProductOperation", "inputs": [ "i[t][layerIndex]", "cHat[t][layerIndex]" ] }, { "id": "newC", "description": "Compute the memory cell state", "type": "MatrixAddOperation", "inputs": [ "f_previousMemoryCellState", "i_cHat" ] }, { "id": "newCTransposed", "type": "MatrixTransposeOperation", "inputs": [ "newC" ] }, { "id": "newCNormalized", "type": "LayerNormalizationOperation", "inputs": [ "newCTransposed" ] }, { "id": "c", "type": "MatrixTransposeOperation", "inputs": [ "newCNormalized" ], "setResultTo": "c[t][layerIndex]" }, { "id": "wo_currentInput", "type": "MatrixMultiplyOperation", "inputs": [ "Wo[layerIndex]", "currentInput" ], "gradientResultTo": [ "dWo[layerIndex]", null ] }, { "id": "uo_previousHiddenState", "type": "MatrixMultiplyOperation", "inputs": [ "Uo[layerIndex]", "previousHiddenState" ], "gradientResultTo": [ "dUo[layerIndex]", null ] }, { "id": "o_add", "type": "MatrixAddThreeOperation", "inputs": [ "wo_currentInput", "uo_previousHiddenState", "bo[layerIndex]" ], "gradientResultTo": [ null, null, "dbo[layerIndex]" ] }, { "id": "o", "description": "Compute the output gate", "type": "LeakyReLUOperation", "inputs": [ "o_add" ], "setResultTo": "o[t][layerIndex]" }, { "id": "c_tanh", "type": "TanhOperation", "inputs": [ "c" ] }, { "id": "newH", "type": "HadamardProductOperation", "inputs": [ "o[t][layerIndex]", "c_tanh" ] }, { "id": "keys", "type": "MatrixMultiplyOperation", "inputs": [ "Wk[layerIndex]", "embeddedInput" ], "gradientResultTo": [ "dWk[layerIndex]", null ] }, { "id": "queries", "type": "MatrixMultiplyOperation", "inputs": [ "Wq[layerIndex]", "previousHiddenState" ], "gradientResultTo": [ "dWq[layerIndex]", null ] }, { "id": "values", "type": "MatrixMultiplyOperation", "inputs": [ "Wv[layerIndex]", "embeddedInput" ], "gradientResultTo": [ "dWv[layerIndex]", null ] }, { "id": "queriesTranspose", "type": "MatrixTransposeOperation", "inputs": [ "queries" ] }, { "id": "dotProduct", "description": "Compute the dot product of the queries and keys", "type": "MatrixMultiplyOperation", "inputs": [ "keys", "queriesTranspose" ] }, { "id": "scaledDotProduct", "description": "Scale the dot product", "type": "MatrixMultiplyScalarOperation", "inputs": [ "dotProduct", "scaledDotProductScalar" ] }, { "id": "scaledDotProductTranspose", "type": "MatrixTransposeOperation", "inputs": [ "scaledDotProduct" ] }, { "id": "attentionWeights", "type": "SoftmaxOperation", "inputs": [ "scaledDotProductTranspose" ] }, { "id": "attentionOutput", "type": "MatrixMultiplyOperation", "inputs": [ "attentionWeights", "values" ] }, { "id": "newHWithAttentionOutput", "type": "MatrixAddOperation", "inputs": [ "newH", "attentionOutput" ] }, { "id": "newHWithAttentionOutputTranspose", "type": "MatrixTransposeOperation", "inputs": [ "newHWithAttentionOutput" ] }, { "id": "normalizedNewH", "type": "LayerNormalizationOperation", "inputs": [ "newHWithAttentionOutputTranspose" ] }, { "id": "h", "type": "MatrixTransposeOperation", "inputs": [ "normalizedNewH" ], "setResultTo": "h[t][layerIndex]" } ] } ], "endOperations": [ { "id": "v_h", "type": "MatrixMultiplyOperation", "inputs": [ "V", "hFromCurrentTimeStepAndLastLayer" ], "gradientResultTo": [ "dV", null ] }, { "id": "v_h_b", "type": "MatrixAddOperation", "inputs": [ "v_h", "b" ], "gradientResultTo": [ null, "db" ] }, { "id": "output_t", "type": "AmplifiedSigmoidOperation", "inputs": [ "v_h_b" ], "setResultTo": "output[t]" } ] } ] }