org.deeplearning4j.nn.layers.recurrent.LSTMHelpers Maven / Gradle / Ivy
package org.deeplearning4j.nn.layers.recurrent;
import org.deeplearning4j.berkeley.Pair;
import org.deeplearning4j.exception.DL4JInvalidInputException;
import org.deeplearning4j.nn.api.Layer;
import org.deeplearning4j.nn.conf.NeuralNetConfiguration;
import org.deeplearning4j.nn.gradient.DefaultGradient;
import org.deeplearning4j.nn.gradient.Gradient;
import org.deeplearning4j.util.Dropout;
import org.nd4j.linalg.activations.IActivation;
import org.nd4j.linalg.activations.impl.ActivationSigmoid;
import org.nd4j.linalg.api.blas.Level1;
import org.nd4j.linalg.api.ndarray.INDArray;
import org.nd4j.linalg.api.ops.impl.transforms.TimesOneMinus;
import org.nd4j.linalg.api.ops.impl.transforms.arithmetic.MulOp;
import org.nd4j.linalg.api.shape.Shape;
import org.nd4j.linalg.factory.Nd4j;
import org.nd4j.linalg.indexing.NDArrayIndex;
import java.util.Arrays;
import java.util.Map;
import static org.nd4j.linalg.indexing.NDArrayIndex.interval;
import static org.nd4j.linalg.indexing.NDArrayIndex.point;
/**
*
* RNN tutorial: http://deeplearning4j.org/usingrnns.html
* READ THIS FIRST if you want to understand what the heck is happening here.
*
* Shared code for the standard "forwards" LSTM RNN and the bidirectional LSTM RNN
* This was extracted from GravesLSTM and refactored into static helper functions. The general reasoning for this was
* so we only have math in one place, instead of two.
*
* Based on Graves: Supervised Sequence Labelling with Recurrent Neural Networks
* http://www.cs.toronto.edu/~graves/phd.pdf
* See also for full/vectorized equations (and a comparison to other LSTM variants):
* Greff et al. 2015, "LSTM: A Search Space Odyssey", pg11. This is the "vanilla" variant in said paper
* http://arxiv.org/pdf/1503.04069.pdf
*
* Please note that truncated backpropagation through time (BPTT) will not work with the bidirectional layer as-is.
* Additionally, variable length data sets will also not work with the bidirectional layer.
*
* @author Alex Black (LSTM implementation)
* @author Benjamin Joseph (refactoring for bidirectional LSTM)
*/
public class LSTMHelpers {
// public static final String SIGMOID = "sigmoid";
private LSTMHelpers() {
}
/**
* Returns FwdPassReturn object with activations/INDArrays. Allows activateHelper to be used for forward pass, backward pass
* and rnnTimeStep whilst being reasonably efficient for all
*/
static public FwdPassReturn activateHelper(final Layer layer,
final NeuralNetConfiguration conf,
final IActivation gateActivationFn, //Activation function for the gates - sigmoid or hard sigmoid (must be found in range 0 to 1)
final INDArray input,
final INDArray recurrentWeights, //Shape: [hiddenLayerSize,4*hiddenLayerSize+3]; order: [wI,wF,wO,wG,wFF,wOO,wGG]
final INDArray originalInputWeights, //Shape: [n^(L-1),4*hiddenLayerSize]; order: [wi,wf,wo,wg]
final INDArray biases, //Shape: [4,hiddenLayerSize]; order: [bi,bf,bo,bg]^T
final boolean training,
final INDArray originalPrevOutputActivations,
final INDArray originalPrevMemCellState,
boolean forBackprop,
boolean forwards,
final String inputWeightKey) {
//Mini-batch data format: for mini-batch size m, nIn inputs, and T time series length
//Data has shape [m,nIn,T]. Layer activations/output has shape [m,nHiddenUnits,T]
if(input == null || input.length() == 0) throw new IllegalArgumentException("Invalid input: not set or 0 length");
INDArray inputWeights = originalInputWeights;
INDArray prevOutputActivations = originalPrevOutputActivations;
boolean is2dInput = input.rank() < 3; //Edge case of T=1, may have shape [m,nIn], equiv. to [m,nIn,1]
int timeSeriesLength = (is2dInput ? 1 : input.size(2));
int hiddenLayerSize = recurrentWeights.size(0);
int miniBatchSize = input.size(0);
INDArray prevMemCellState;
if (originalPrevMemCellState == null) {
prevMemCellState = Nd4j.create(new int[]{miniBatchSize, hiddenLayerSize},'f');
} else {
prevMemCellState = originalPrevMemCellState.dup('f');
}
INDArray recurrentWeightsIFOG = recurrentWeights.get(NDArrayIndex.all(), NDArrayIndex.interval(0,4*hiddenLayerSize)).dup('f');
//Apply dropconnect to input (not recurrent) weights only:
if (conf.isUseDropConnect() && training && conf.getLayer().getDropOut() > 0) {
inputWeights = Dropout.applyDropConnect(layer, inputWeightKey);
}
INDArray wFFTranspose = recurrentWeights.get(NDArrayIndex.all(), interval(4 * hiddenLayerSize, 4 * hiddenLayerSize + 1)).transpose(); //current
INDArray wOOTranspose = recurrentWeights.get(NDArrayIndex.all(), interval(4 * hiddenLayerSize + 1, 4 * hiddenLayerSize + 2)).transpose(); //current
INDArray wGGTranspose = recurrentWeights.get(NDArrayIndex.all(), interval(4 * hiddenLayerSize + 2, 4 * hiddenLayerSize + 3)).transpose(); //previous
if (timeSeriesLength > 1 || forBackprop) {
wFFTranspose = Shape.toMmulCompatible(wFFTranspose);
wOOTranspose = Shape.toMmulCompatible(wOOTranspose);
wGGTranspose = Shape.toMmulCompatible(wGGTranspose);
}
//Allocate arrays for activations:
boolean sigmoidGates = gateActivationFn instanceof ActivationSigmoid;
IActivation afn = conf.getLayer().getActivationFn();
INDArray outputActivations = null;
FwdPassReturn toReturn = new FwdPassReturn();
if (forBackprop) {
toReturn.fwdPassOutputAsArrays = new INDArray[timeSeriesLength];
toReturn.memCellState = new INDArray[timeSeriesLength];
toReturn.memCellActivations = new INDArray[timeSeriesLength];
toReturn.iz = new INDArray[timeSeriesLength];
toReturn.ia = new INDArray[timeSeriesLength];
toReturn.fa = new INDArray[timeSeriesLength];
toReturn.oa = new INDArray[timeSeriesLength];
toReturn.ga = new INDArray[timeSeriesLength];
if(!sigmoidGates){
toReturn.fz = new INDArray[timeSeriesLength];
toReturn.oz = new INDArray[timeSeriesLength];
toReturn.gz = new INDArray[timeSeriesLength];
}
} else {
outputActivations = Nd4j.create(new int[]{miniBatchSize, hiddenLayerSize, timeSeriesLength},'f'); //F order to keep time steps together
toReturn.fwdPassOutput = outputActivations;
}
Level1 l1BLAS = Nd4j.getBlasWrapper().level1();
//Input validation: check input data matches nIn
if(input.size(1) != inputWeights.size(0)){
throw new DL4JInvalidInputException("Received input with size(1) = " + input.size(1) + " (input array shape = "
+ Arrays.toString(input.shape()) + "); input.size(1) must match layer nIn size (nIn = " + inputWeights.size(0) + ")");
}
//Input validation: check that if past state is provided, that it has same
//These can be different if user forgets to call rnnClearPreviousState() between calls of rnnTimeStep
if(prevOutputActivations != null && prevOutputActivations.size(0) != input.size(0)){
throw new DL4JInvalidInputException("Previous activations (stored state) number of examples = " + prevOutputActivations.size(0)
+ " but input array number of examples = " + input.size(0) + ". Possible cause: using rnnTimeStep() without calling"
+ " rnnClearPreviousState() between different sequences?");
}
//initialize prevOutputActivations to zeroes
if (prevOutputActivations == null) {
prevOutputActivations = Nd4j.zeros(new int[]{miniBatchSize, hiddenLayerSize});
}
for (int iTimeIndex = 0; iTimeIndex < timeSeriesLength; iTimeIndex++) {
int time = iTimeIndex;
if (!forwards) {
time = timeSeriesLength - iTimeIndex - 1;
}
INDArray miniBatchData = (is2dInput ? input : input.tensorAlongDimension(time, 1, 0)); //[Expected shape: [m,nIn]. Also deals with edge case of T=1, with 'time series' data of shape [m,nIn], equiv. to [m,nIn,1]
miniBatchData = Shape.toMmulCompatible(miniBatchData);
//Calculate activations for: network input + forget, output, input modulation gates. Next 3 lines are first part of those
INDArray ifogActivations = miniBatchData.mmul(inputWeights); //Shape: [miniBatch,4*layerSize]
Nd4j.gemm(prevOutputActivations, recurrentWeightsIFOG, ifogActivations, false, false, 1.0, 1.0);
ifogActivations.addiRowVector(biases);
INDArray inputActivations = ifogActivations.get(NDArrayIndex.all(), NDArrayIndex.interval(0,hiddenLayerSize));
if (forBackprop) toReturn.iz[time] = inputActivations.dup('f');
conf.getLayer().getActivationFn().getActivation(inputActivations, training);
if (forBackprop) toReturn.ia[time] = inputActivations;
INDArray forgetGateActivations = ifogActivations.get(NDArrayIndex.all(), NDArrayIndex.interval(hiddenLayerSize,2*hiddenLayerSize));
INDArray pmcellWFF = prevMemCellState.dup('f').muliRowVector(wFFTranspose);
l1BLAS.axpy(pmcellWFF.length(), 1.0, pmcellWFF, forgetGateActivations); //y = a*x + y i.e., forgetGateActivations.addi(pmcellWFF)
//Above line: treats matrix as a vector. Can only do this because we're sure both pwcelWFF and forgetGateACtivations are f order, offset 0 and have same strides
if(forBackprop && !sigmoidGates){
toReturn.fz[time] = forgetGateActivations.dup('f'); //Forget gate pre-out (z)
}
gateActivationFn.getActivation(forgetGateActivations, training);
if (forBackprop) toReturn.fa[time] = forgetGateActivations;
INDArray inputModGateActivations = ifogActivations.get(NDArrayIndex.all(), NDArrayIndex.interval(3*hiddenLayerSize,4*hiddenLayerSize));
INDArray pmcellWGG = prevMemCellState.dup('f').muliRowVector(wGGTranspose);
l1BLAS.axpy(pmcellWGG.length(), 1.0, pmcellWGG, inputModGateActivations); //inputModGateActivations.addi(pmcellWGG)
if(forBackprop && !sigmoidGates){
toReturn.gz[time] = inputModGateActivations.dup('f'); //Input modulation gate pre-out (z)
}
gateActivationFn.getActivation(inputModGateActivations, training);
if (forBackprop) toReturn.ga[time] = inputModGateActivations;
//Memory cell state
INDArray currentMemoryCellState;
INDArray inputModMulInput;
if(forBackprop){
currentMemoryCellState = prevMemCellState.dup('f').muli(forgetGateActivations);
inputModMulInput = inputModGateActivations.dup('f').muli(inputActivations);
} else {
currentMemoryCellState = forgetGateActivations.muli(prevMemCellState);
inputModMulInput = inputModGateActivations.muli(inputActivations);
}
l1BLAS.axpy(currentMemoryCellState.length(), 1.0, inputModMulInput, currentMemoryCellState); //currentMemoryCellState.addi(inputModMulInput)
INDArray outputGateActivations = ifogActivations.get(NDArrayIndex.all(), NDArrayIndex.interval(2*hiddenLayerSize,3*hiddenLayerSize));
INDArray pmcellWOO = currentMemoryCellState.dup('f').muliRowVector(wOOTranspose);
l1BLAS.axpy(pmcellWOO.length(), 1.0, pmcellWOO, outputGateActivations); //outputGateActivations.addi(pmcellWOO)
if(forBackprop && !sigmoidGates){
toReturn.oz[time] = outputGateActivations.dup('f'); //Output gate activations
}
gateActivationFn.getActivation(outputGateActivations, training);
if (forBackprop) toReturn.oa[time] = outputGateActivations;
//LSTM unit outputs:
INDArray currMemoryCellActivation = afn.getActivation(currentMemoryCellState.dup('f'), training);
INDArray currHiddenUnitActivations;
if(forBackprop){
currHiddenUnitActivations = currMemoryCellActivation.dup('f').muli(outputGateActivations); //Expected shape: [m,hiddenLayerSize]
} else {
currHiddenUnitActivations = currMemoryCellActivation.muli(outputGateActivations); //Expected shape: [m,hiddenLayerSize]
}
if (forBackprop) {
toReturn.fwdPassOutputAsArrays[time] = currHiddenUnitActivations;
toReturn.memCellState[time] = currentMemoryCellState;
toReturn.memCellActivations[time] = currMemoryCellActivation;
} else {
outputActivations.tensorAlongDimension(time, 1, 0).assign(currHiddenUnitActivations);
}
prevOutputActivations = currHiddenUnitActivations;
prevMemCellState = currentMemoryCellState;
toReturn.lastAct = currHiddenUnitActivations;
toReturn.lastMemCell = currentMemoryCellState;
}
return toReturn;
}
static public Pair backpropGradientHelper(final NeuralNetConfiguration conf,
final IActivation gateActivationFn,
final INDArray input,
final INDArray recurrentWeights, //Shape: [hiddenLayerSize,4*hiddenLayerSize+3]; order: [wI,wF,wO,wG,wFF,wOO,wGG]
final INDArray inputWeights, //Shape: [n^(L-1),4*hiddenLayerSize]; order: [wi,wf,wo,wg]
final INDArray epsilon,
final boolean truncatedBPTT,
final int tbpttBackwardLength,
final FwdPassReturn fwdPass,
final boolean forwards,
final String inputWeightKey,
final String recurrentWeightKey,
final String biasWeightKey,
final Map gradientViews) {
//Expect errors to have shape: [miniBatchSize,n^(L+1),timeSeriesLength]
int hiddenLayerSize = recurrentWeights.size(0); //i.e., n^L
int prevLayerSize = inputWeights.size(0); //n^(L-1)
int miniBatchSize = epsilon.size(0);
boolean is2dInput = epsilon.rank() < 3; //Edge case: T=1 may have shape [miniBatchSize,n^(L+1)], equiv. to [miniBatchSize,n^(L+1),1]
int timeSeriesLength = (is2dInput ? 1 : epsilon.size(2));
INDArray wFFTranspose = recurrentWeights.get(NDArrayIndex.all(), point(4 * hiddenLayerSize)).transpose();
INDArray wOOTranspose = recurrentWeights.get(NDArrayIndex.all(), point(4 * hiddenLayerSize+1)).transpose();
INDArray wGGTranspose = recurrentWeights.get(NDArrayIndex.all(), point(4 * hiddenLayerSize+2)).transpose();
INDArray wIFOG = recurrentWeights.get(NDArrayIndex.all(), NDArrayIndex.interval(0,4*hiddenLayerSize));
//F order here so that content for time steps are together
INDArray epsilonNext = Nd4j.create(new int[]{miniBatchSize, prevLayerSize, timeSeriesLength},'f'); //i.e., what would be W^L*(delta^L)^T. Shape: [m,n^(L-1),T]
INDArray nablaCellStateNext = null;
INDArray deltaifogNext = Nd4j.create(new int[]{miniBatchSize,4*hiddenLayerSize},'f');
INDArray deltaiNext = deltaifogNext.get(NDArrayIndex.all(), NDArrayIndex.interval(0,hiddenLayerSize));
INDArray deltafNext = deltaifogNext.get(NDArrayIndex.all(), NDArrayIndex.interval(hiddenLayerSize,2*hiddenLayerSize));
INDArray deltaoNext = deltaifogNext.get(NDArrayIndex.all(), NDArrayIndex.interval(2*hiddenLayerSize,3*hiddenLayerSize));
INDArray deltagNext = deltaifogNext.get(NDArrayIndex.all(), NDArrayIndex.interval(3*hiddenLayerSize,4*hiddenLayerSize));
Level1 l1BLAS = Nd4j.getBlasWrapper().level1();
int endIdx = 0;
if (truncatedBPTT) {
endIdx = Math.max(0, timeSeriesLength - tbpttBackwardLength);
}
//Get gradients. Note that we have to manually zero these, as they might not be initialized (or still has data from last iteration)
//Also note that they are in f order (as per param initializer) so can be used in gemm etc
INDArray iwGradientsOut = gradientViews.get(inputWeightKey);
INDArray rwGradientsOut = gradientViews.get(recurrentWeightKey); //Order: {I,F,O,G,FF,OO,GG}
INDArray bGradientsOut = gradientViews.get(biasWeightKey);
iwGradientsOut.assign(0);
rwGradientsOut.assign(0);
bGradientsOut.assign(0);
INDArray rwGradientsIFOG = rwGradientsOut.get(NDArrayIndex.all(), NDArrayIndex.interval(0,4*hiddenLayerSize));
INDArray rwGradientsFF = rwGradientsOut.get(NDArrayIndex.all(), NDArrayIndex.point(4 * hiddenLayerSize));
INDArray rwGradientsOO = rwGradientsOut.get(NDArrayIndex.all(), NDArrayIndex.point(4 * hiddenLayerSize + 1));
INDArray rwGradientsGG = rwGradientsOut.get(NDArrayIndex.all(), NDArrayIndex.point(4 * hiddenLayerSize + 2));
boolean sigmoidGates = gateActivationFn instanceof ActivationSigmoid;
IActivation afn = conf.getLayer().getActivationFn();
for (int iTimeIndex = timeSeriesLength - 1; iTimeIndex >= endIdx; iTimeIndex--) {
int time = iTimeIndex;
int inext = 1;
if (!forwards) {
time = timeSeriesLength - iTimeIndex - 1;
inext = -1;
}
//First: calclate the components of nablaCellState that relies on the next time step deltas, so we can overwrite the deltas
INDArray nablaCellState;
if(iTimeIndex != timeSeriesLength -1){
nablaCellState = deltafNext.dup('f').muliRowVector(wFFTranspose);
l1BLAS.axpy(nablaCellState.length(), 1.0, deltagNext.dup('f').muliRowVector(wGGTranspose), nablaCellState);
} else {
nablaCellState = Nd4j.create(new int[]{miniBatchSize,hiddenLayerSize},'f');
}
INDArray prevMemCellState = (iTimeIndex == 0 ? null : fwdPass.memCellState[time - inext]);
INDArray prevHiddenUnitActivation = (iTimeIndex == 0 ? null : fwdPass.fwdPassOutputAsArrays[time - inext]);
INDArray currMemCellState = fwdPass.memCellState[time];
//LSTM unit output errors (dL/d(a_out)); not to be confused with \delta=dL/d(z_out)
INDArray epsilonSlice = (is2dInput ? epsilon : epsilon.tensorAlongDimension(time, 1, 0)); //(w^{L+1}*(delta^{(L+1)t})^T)^T or equiv.
INDArray nablaOut = Shape.toOffsetZeroCopy(epsilonSlice, 'f'); //Shape: [m,n^L]
if (iTimeIndex != timeSeriesLength - 1) {
//if t == timeSeriesLength-1 then deltaiNext etc are zeros
Nd4j.gemm(deltaifogNext, wIFOG, nablaOut, false, true, 1.0, 1.0);
}
//Output gate deltas:
INDArray sigmahOfS = fwdPass.memCellActivations[time];
INDArray ao = fwdPass.oa[time];
//Normally would use zo.dup() in above line, but won't be using zo again (for this time step). Ditto for zf, zg, zi
INDArray deltao = deltaoNext;
Nd4j.getExecutioner().exec(new MulOp(nablaOut,sigmahOfS,deltao));
if(sigmoidGates){
INDArray sigmaoPrimeOfZo = Nd4j.getExecutioner().execAndReturn(new TimesOneMinus(ao.dup('f'))); //Equivalent to sigmoid deriv on zo
deltao.muli(sigmaoPrimeOfZo);
} else {
deltao.assign(gateActivationFn.backprop(fwdPass.oz[time], deltao).getFirst()); //Deltao needs to be modified in-place
//TODO: optimize (no assign)
}
//Memory cell error:
INDArray temp = afn.backprop(currMemCellState.dup('f'), ao.muli(nablaOut)).getFirst(); //TODO activation functions with params
l1BLAS.axpy(nablaCellState.length(), 1.0, temp, nablaCellState);
INDArray deltaMulRowWOO = deltao.dup('f').muliRowVector(wOOTranspose);
l1BLAS.axpy(nablaCellState.length(), 1.0, deltaMulRowWOO, nablaCellState); //nablaCellState.addi(deltao.mulRowVector(wOOTranspose));
if (iTimeIndex != timeSeriesLength - 1) {
INDArray nextForgetGateAs = fwdPass.fa[time + inext];
int length = nablaCellState.length();
l1BLAS.axpy(length, 1.0, nextForgetGateAs.muli(nablaCellStateNext), nablaCellState); //nablaCellState.addi(nextForgetGateAs.mul(nablaCellStateNext))
}
nablaCellStateNext = nablaCellState; //Store for use in next iteration
//Forget gate delta:
INDArray af = fwdPass.fa[time];
INDArray deltaf = null;
if (iTimeIndex > 0) {
deltaf = deltafNext;
if( sigmoidGates ) {
Nd4j.getExecutioner().exec(new TimesOneMinus(af, deltaf));
deltaf.muli(nablaCellState);
deltaf.muli(prevMemCellState);
} else {
INDArray temp2 = nablaCellState.mul(prevMemCellState);
deltaf.assign(gateActivationFn.backprop(fwdPass.fz[time].dup('f'), temp2).getFirst()); //deltaf needs to be modified in-place
//TODO activation functions with params
}
}
//Shape: [m,n^L]
//Input modulation gate delta:
INDArray ag = fwdPass.ga[time];
INDArray ai = fwdPass.ia[time];
INDArray deltag = deltagNext;
if( sigmoidGates ){
Nd4j.getExecutioner().exec(new TimesOneMinus(ag,deltag)); //Equivalent to sigmoid deriv on zg
deltag.muli(ai);
deltag.muli(nablaCellState);
} else {
INDArray temp2 = Nd4j.getExecutioner().execAndReturn(new MulOp(ai,nablaCellState,Nd4j.createUninitialized(ai.shape(), 'f')));
deltag.assign(gateActivationFn.backprop(fwdPass.gz[time],temp2).getFirst());
//TODO activation functions with params; optimize (no assign)
}
//Shape: [m,n^L]
//Network input delta:
INDArray zi = fwdPass.iz[time];
INDArray deltai = deltaiNext;
temp = Nd4j.getExecutioner().execAndReturn(new MulOp(ag,nablaCellState,Nd4j.createUninitialized(deltai.shape(), 'f')));
deltai.assign(afn.backprop(zi, temp).getFirst());
//TODO activation functions with params; also: optimize this (no assign)
//Shape: [m,n^L]
INDArray prevLayerActivationSlice = Shape.toMmulCompatible(is2dInput ? input : input.tensorAlongDimension(time, 1, 0));
if(iTimeIndex > 0){
//Again, deltaifog_current == deltaifogNext at this point... same array
Nd4j.gemm(prevLayerActivationSlice, deltaifogNext, iwGradientsOut, true, false, 1.0, 1.0);
} else {
INDArray iwGradients_i = iwGradientsOut.get(NDArrayIndex.all(), NDArrayIndex.interval(0,hiddenLayerSize));
Nd4j.gemm(prevLayerActivationSlice, deltai, iwGradients_i, true, false, 1.0, 1.0);
INDArray iwGradients_og = iwGradientsOut.get(NDArrayIndex.all(), NDArrayIndex.interval(2*hiddenLayerSize, 4*hiddenLayerSize));
INDArray deltaog = deltaifogNext.get(NDArrayIndex.all(), NDArrayIndex.interval(2*hiddenLayerSize,4*hiddenLayerSize));
Nd4j.gemm(prevLayerActivationSlice, deltaog, iwGradients_og, true, false, 1.0, 1.0);
}
if (iTimeIndex > 0) {
//If t==0, then prevHiddenUnitActivation==zeros(n^L,n^L), so dL/dW for recurrent weights will end up as 0 anyway
//At this point: deltaifog and deltaifogNext are the same thing...
//So what we are actually doing here is sum of (prevAct^transpose * deltaifog_current)
Nd4j.gemm(prevHiddenUnitActivation, deltaifogNext, rwGradientsIFOG, true, false, 1.0, 1.0);
//Shape: [1,n^L]. sum(0) is sum over examples in mini-batch.
//Can use axpy here because result of sum and rwGradients[4 to 6] have order Nd4j.order(), via Nd4j.create()
INDArray dLdwFF = deltaf.dup('f').muli(prevMemCellState).sum(0); //mul not mmul because these weights are from unit j->j only (whereas other recurrent weights are i->j for all i,j)
l1BLAS.axpy(hiddenLayerSize,1.0,dLdwFF,rwGradientsFF); //rwGradients[4].addi(dLdwFF); //dL/dw_{FF}
INDArray dLdwGG = deltag.dup('f').muli(prevMemCellState).sum(0);
l1BLAS.axpy(hiddenLayerSize,1.0,dLdwGG,rwGradientsGG); //rwGradients[6].addi(dLdwGG);
}
INDArray dLdwOO = deltao.dup('f').muli(currMemCellState).sum(0); //Expected shape: [n^L,1]. sum(0) is sum over examples in mini-batch.
l1BLAS.axpy(hiddenLayerSize,1.0,dLdwOO,rwGradientsOO); //rwGradients[5].addi(dLdwOO); //dL/dw_{OOxy}
if(iTimeIndex > 0){
l1BLAS.axpy(4*hiddenLayerSize,1.0, deltaifogNext.sum(0), bGradientsOut);
} else {
l1BLAS.axpy(hiddenLayerSize,1.0,deltai.sum(0),bGradientsOut); //Sneaky way to do bGradients_i += deltai.sum(0)
INDArray ogBiasToAdd = deltaifogNext.get(NDArrayIndex.all(), NDArrayIndex.interval(2*hiddenLayerSize,4*hiddenLayerSize)).sum(0);
INDArray ogBiasGrad = bGradientsOut.get(NDArrayIndex.point(0), NDArrayIndex.interval(2*hiddenLayerSize,4*hiddenLayerSize));
l1BLAS.axpy(2*hiddenLayerSize,1.0,ogBiasToAdd,ogBiasGrad);
}
//Calculate epsilonNext - i.e., equiv. to what would be (w^L*(d^(Lt))^T)^T in a normal network
//But here, need to add 4 weights * deltas for the IFOG gates
INDArray epsilonNextSlice = epsilonNext.tensorAlongDimension(time, 1, 0); //This slice: f order and contiguous, due to epsilonNext being defined as f order.
if(iTimeIndex > 0){
Nd4j.gemm(deltaifogNext, inputWeights, epsilonNextSlice, false, true, 1.0, 1.0);
} else {
//No contribution from forget gate at t=0
INDArray wi = inputWeights.get(NDArrayIndex.all(), NDArrayIndex.interval(0,hiddenLayerSize));
Nd4j.gemm(deltai, wi, epsilonNextSlice, false, true, 1.0, 1.0);
INDArray deltaog = deltaifogNext.get(NDArrayIndex.all(), NDArrayIndex.interval(2*hiddenLayerSize,4*hiddenLayerSize));
INDArray wog = inputWeights.get(NDArrayIndex.all(), NDArrayIndex.interval(2*hiddenLayerSize,4*hiddenLayerSize));
Nd4j.gemm(deltaog, wog, epsilonNextSlice, false, true, 1.0, 1.0); //epsilonNextSlice.addi(deltao.mmul(woTranspose)).addi(deltag.mmul(wgTranspose));
}
}
Gradient retGradient = new DefaultGradient();
retGradient.gradientForVariable().put(inputWeightKey, iwGradientsOut);
retGradient.gradientForVariable().put(recurrentWeightKey, rwGradientsOut);
retGradient.gradientForVariable().put(biasWeightKey, bGradientsOut);
return new Pair<>(retGradient, epsilonNext);
}
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