Implementing a Neural Network in Java: Training and Backpropagation issues
I'm trying to implement a feed-forward neural network in Java. I've created three classes NNeuron, NLayer and NNetwork. The "simple" calculations seem fine (I get correct sums/activations/outputs), but when it comes to the training process, I don't seem to get correct results. Can anyone, please tell what I'm doing wrong ? The whole code for the NNetwork class is quite long, so I'm posting the part that is causing the problem: [EDIT]: this is actually pretty much all of the NNetwork class
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
public class NNetwork
{
public static final double defaultLearningRate = 0.4;
public static final double defaultMomentum = 0.8;
private NLayer inputLayer;
private ArrayList<NLayer> hiddenLayers;
private NLayer outputLayer;
private ArrayList<NLayer> layers;
private double momentum = NNetwork1.defaultMomentum; // alpha: momentum, default! 0.3
private ArrayList<Double> learningRates;
public NNetwork (int nInputs, int nOutputs, Integer... neuronsPerHiddenLayer)
{
this(nInputs, nOutputs, Arrays.asList(neuronsPerHiddenLayer));
}
public NNetwork (int nInputs, int nOutputs, List<Integer> neuronsPerHiddenLayer)
{
// the number of neurons on the last layer build so far (i.e. the number of inputs for each neuron of the next layer)
int prvOuts = 1;
this.layers = new ArrayList<>();
// input layer
this.inputLayer = new NLayer(nInputs, prvOuts, this);
this.inputLayer.setAllWeightsTo(1.0);
this.inputLayer.setAllBiasesTo(0.0);
this.inputLayer.useSigmaForOutput(false);
prvOuts = nInputs;
this.layers.add(this.inputLayer);
// hidden layers
this.hiddenLayers = new ArrayList<>();
for (int i=0 ; i<neuronsPerHiddenLayer.size() ; i++)
{
this.hiddenLayers.add(new NLayer(neuronsPerHiddenLayer.get(i), prvOuts, this));
prvOuts = neuronsPerHiddenLayer.get(i);
}
this.layers.addAll(this.hiddenLayers);
// output layer
this.outputLayer = new NLayer(nOutputs, prvOuts, this);
this.layers.add(this.outputLayer);
this.initCoeffs();
}
private void initCoeffs ()
{
this.learningRates = new ArrayList<>();
// learning rates of the hidden layers
for (int i=0 ; i<this.hiddenLayers.size(); i++)
this.learningRates.add(NNetwork1.defaultLearningRate);
// learning rate of the output layer
this.learningRates.add(NNetwork1.defaultLearningRate);
}
public double getLearningRate (int layerIndex)
{
if (layerIndex > 0 && layerIndex <= this.hiddenLayers.size()+1)
{
return this.learningRates.get(layerIndex-1);
}
else
{
return 0;
}
}
public ArrayList<Double> getLearningRates ()
{
return this.learningRates;
}
public void setLearningRate (int layerIndex, double newLearningRate)
{
if (layerIndex > 0 && layerIndex <= this.hiddenLayers.size()+1)
{
this.learningRates.set(
layerIndex-1,
newLearningRate);
}
}
public void setLearningRates (Double... newLearningRates)
{
this.setLearningRates(Arrays.asList(newLearningRates));
}
public void setLearningRates (List<Double> newLearningRates)
{
int len = (this.learningRates.size() <= newLearningRates.size())
? this.learningRates.size()
: newLearningRates.size();
for (int i=0; i<len; i++)
this.learningRates
.set(i,
newLearningRates.get(i));
}
public double getMomentum ()
{
return this.momentum;
}
public void setMomentum (double momentum)
{
this.momentum = momentum;
}
public NNeuron getNeuron (int layerIndex, int neuronIndex)
{
if (layerIndex == 0)
return this.inputLayer.getNeurons().get(neuronIndex);
else if (layerIndex == this.hiddenLayers.size()+1)
return this.outputLayer.getNeurons().get(neuronIndex);
else
return this.hiddenLayers.get(layerIndex-1).getNeurons().get(neuronIndex);
}
public ArrayList<Double> getOutput (ArrayList<Double> inputs)
{
ArrayList<Double> lastOuts = inputs; // the last computed outputs of the last 'called' layer so far
// input layer
//lastOuts = this.inputLayer.getOutput(lastOuts);
lastOuts = this.getInputLayerOutputs(lastOuts);
// hidden layers
for (NLayer layer : this.hiddenLayers)
lastOuts = layer.getOutput(lastOuts);
// output layer
lastOuts = this.outputLayer.getOutput(lastOuts);
return lastOuts;
}
public ArrayList<ArrayList<Double>> getAllOutputs (ArrayList<Double> inputs)
{
ArrayList<ArrayList<Double>> outs = new ArrayList<>();
// input layer
outs.add(this.getInputLayerOutputs(inputs));
// hidden layers
for (NLayer layer : this.hiddenLayers)
outs.add(layer.getOutput(outs.get(outs.size()-1)));
// output layer
outs.add(this.outputLayer.getOutput(outs.get(outs.size()-1)));
return outs;
}
public ArrayList<ArrayList<Double>> getAllSums (ArrayList<Double> inputs)
{
//*
ArrayList<ArrayList<Double>> sums = new ArrayList<>();
ArrayList<Double> lastOut;
// input layer
sums.add(inputs);
lastOut = this.getInputLayerOutputs(inputs);
// hidden nodes
for (NLayer layer : this.hiddenLayers)
{
sums.add(layer.getSums(lastOut));
lastOut = layer.getOutput(lastOut);
}
// output layer
sums.add(this.outputLayer.getSums(lastOut));
return sums;
}
public ArrayList<Double> getInputLayerOutputs (ArrayList<Double> inputs)
{
ArrayList<Double> outs = new ArrayList<>();
for (int i=0 ; i<this.inputLayer.getNeurons().size() ; i++)
outs.add(this
.inputLayer
.getNeuron(i)
.getOutput(inputs.get(i)));
return outs;
}
public void changeWeights (
ArrayList<ArrayList<Double>> deltaW,
ArrayList<ArrayList<Double>> inputSet,
ArrayList<ArrayList<Double>> targetSet,
boolean checkError)
{
for (int i=0 ; i<deltaW.size()-1 ; i++)
this.hiddenLayers.get(i).changeWeights(deltaW.get(i), inputSet, targetSet, checkError);
this.outputLayer.changeWeights(deltaW.get(deltaW.size()-1), inputSet, targetSet, checkError);
}
public int train2 (
ArrayList<ArrayList<Double>> inputSet,
ArrayList<ArrayList<Double>> targetSet,
double maxError,
int maxIterations)
{
ArrayList<Double>
input,
target;
ArrayList<ArrayList<ArrayList<Double>>> prvNetworkDeltaW = null;
double error;
int i = 0, j = 0, traininSetLength = inputSet.size();
do // during each itreration...
{
error = 0.0;
for (j = 0; j < traininSetLength; j++) // ... for each training element...
{
input = inputSet.get(j);
target = targetSet.get(j);
prvNetworkDeltaW = this.train2_bp(input, target, prvNetworkDeltaW); // ... do backpropagation, and return the new weight deltas
error += this.getInputMeanSquareError(input, target);
}
i++;
} while (error > maxError && i < maxIterations); // iterate as much as necessary/possible
return i;
}
public ArrayList<ArrayList<ArrayList<Double>>> train2_bp (
ArrayList<Double> input,
ArrayList<Double> target,
ArrayList<ArrayList<ArrayList<Double>>> prvNetworkDeltaW)
{
ArrayList<ArrayList<Double>> layerSums = this.getAllSums(input); // the sums for each layer
ArrayList<ArrayList<Double>> layerOutputs = this.getAllOutputs(input); // the outputs of each layer
// get the layer deltas (inc the input layer that is null)
ArrayList<ArrayList<Double>> layerDeltas = this.train2_getLayerDeltas(layerSums, layerOutputs, target);
// get the weight deltas
ArrayList<ArrayList<ArrayList<Double>>> networkDeltaW = this.train2_getWeightDeltas(layerOutputs, layerDeltas, prvNetworkDeltaW);
// change the weights
this.train2_updateWeights(networkDeltaW);
return networkDeltaW;
}
public void train2_updateWeights (ArrayList<ArrayList<ArrayList<Double>>> networkDeltaW)
{
for (int i=1; i<this.layers.size(); i++)
this.layers.get(i).train2_updateWeights(networkDeltaW.get(i));
}
public ArrayList<ArrayList<ArrayList<Double>>> train2_getWeightDeltas (
ArrayList<ArrayList<Double>> layerOutputs,
ArrayList<ArrayList<Double>> layerDeltas,
ArrayList<ArrayList<ArrayList<Double>>> prvNetworkDeltaW)
{
ArrayList<ArrayList<ArrayList<Double>>> networkDeltaW = new ArrayList<>(this.layers.size());
ArrayList<ArrayList<Double>> layerDeltaW;
ArrayList<Double> neuronDeltaW;
for (int i=0; i<this.layers.size(); i++)
networkDeltaW.add(new ArrayList<ArrayList<Double>>());
double
deltaW, x, learningRate, prvDeltaW, d;
int i, j, k;
for (i=this.layers.size()-1; i>0; i--) // for each layer
{
learningRate = this.getLearningRate(i);
layerDeltaW = new ArrayList<>();
networkDeltaW.set(i, layerDeltaW);
for (j=0; j<this.layers.get(i).getNeurons().size(); j++) // for each neuron of this layer
{
neuronDeltaW = new ArrayList<>();
layerDeltaW.add(neuronDeltaW);
for (k=0; k<this.layers.get(i-1).getNeurons().size(); k++) // for each weight (i.e. each neuron of the previous layer)
{
d = layerDeltas.get(i).get(j);
x = layerOutputs.get(i-1).get(k);
prvDeltaW = (prvNetworkDeltaW != null)
? prvNetworkDeltaW.get(i).get(j).get(k)
: 0.0;
deltaW = -learningRate * d * x + this.momentum * prvDeltaW;
neuronDeltaW.add(deltaW);
}
// the bias !!
d = layerDeltas.get(i).get(j);
x = 1;
prvDeltaW = (prvNetworkDeltaW != null)
? prvNetworkDeltaW.get(i).get(j).get(prvNetworkDeltaW.get(i).get(j).size()-1)
: 0.0;
deltaW = -learningRate * d * x + this.momentum * prvDeltaW;
neuronDeltaW.add(deltaW);
}
}
return networkDeltaW;
}
ArrayList<ArrayList<Double>> train2_getLayerDeltas (
ArrayList<ArrayList<Double>> layerSums,
ArrayList<ArrayList<Double>> layerOutputs,
ArrayList<Double> target)
{
// get ouput deltas
ArrayList<Double> outputDeltas = new ArrayList<>(); // the output layer deltas
double
oErr, // output error given a target
s, // sum
o, // output
d; // delta
int
nOutputs = target.size(), // @TODO ?== this.outputLayer.size()
nLayers = this.hiddenLayers.size()+2; // @TODO ?== layerOutputs.size()
for (int i=0; i<nOutputs; i++) // for each neuron...
{
s = layerSums.get(nLayers-1).get(i);
o = layerOutputs.get(nLayers-1).get(i);
oErr = (target.get(i) - o);
d = -oErr * this.getNeuron(nLayers-1, i).sigmaPrime(s); // @TODO "s" or "o" ??
outputDeltas.add(d);
}
// get hidden deltas
ArrayList<ArrayList<Double>> hiddenDeltas = new ArrayList<>();
for (int i=0; i<this.hiddenLayers.size(); i++)
hiddenDeltas.add(new ArrayList<Double>());
NLayer nextLayer = this.outputLayer;
ArrayList<Double> nextDeltas = outputDeltas;
int
h, k,
nHidden = this.hiddenLayers.size(),
nNeurons = this.hiddenLayers.get(nHidden-1).getNeurons().size();
double
wdSum = 0.0;
for (int i=nHidden-1; i>=0; i--) // for each hidden layer
{
hiddenDeltas.set(i, new ArrayList<Double>());
for (h=0; h<nNeurons; h++)
{
wdSum = 0.0;
for (k=0; k<nextLayer.getNeurons().size(); k++)
{
wdSum += nextLayer.getNeuron(k).getWeight(h) * nextDeltas.get(k);
}
s = layerSums.get(i+1).get(h);
d = this.getNeuron(i+1, h).sigmaPrime(s) * wdSum;
hiddenDeltas.get(i).add(d);
}
nextLayer = this.hiddenLayers.get(i);
nextDeltas = hiddenDeltas.get(i);
}
ArrayList<ArrayList<Double>> deltas = new ArrayList<>();
// input layer deltas: void
deltas.add(null);
// hidden layers deltas
deltas.addAll(hiddenDeltas);
// output layer deltas
deltas.add(outputDeltas);
return deltas;
}
public double getInputMeanSquareError (ArrayList<Double> input, ArrayList<Double> target)
{
double diff, mse=0.0;
ArrayList<Double> output = this.getOutput(input);
for (int i=0; i<target.size(); i++)
{
diff = target.get(i) - output.get(i);
mse += (diff * diff);
}
mse /= 2.0;
return mse;
}
}
Some methods' names (with their return values/types) are quite self-explanatory, like "this.getAllSums" that returns the sums (sum(x_i*w_i) for each neuron) of each layer, "this.getAllOutputs" that return the outputs (sigmoid(sum) for each neuron) of each layer and "this.getNeuron(i,j)" that returns the j'th neuron of the i'th layer.
Thank you in advance for your help :)
Answer
Here is a very simple java implementation with tests in the main method :
import java.util.Arrays;
import java.util.Random;
public class MLP {
public static class MLPLayer {
float[] output;
float[] input;
float[] weights;
float[] dweights;
boolean isSigmoid = true;
public MLPLayer(int inputSize, int outputSize, Random r) {
output = new float[outputSize];
input = new float[inputSize + 1];
weights = new float[(1 + inputSize) * outputSize];
dweights = new float[weights.length];
initWeights(r);
}
public void setIsSigmoid(boolean isSigmoid) {
this.isSigmoid = isSigmoid;
}
public void initWeights(Random r) {
for (int i = 0; i < weights.length; i++) {
weights[i] = (r.nextFloat() - 0.5f) * 4f;
}
}
public float[] run(float[] in) {
System.arraycopy(in, 0, input, 0, in.length);
input[input.length - 1] = 1;
int offs = 0;
Arrays.fill(output, 0);
for (int i = 0; i < output.length; i++) {
for (int j = 0; j < input.length; j++) {
output[i] += weights[offs + j] * input[j];
}
if (isSigmoid) {
output[i] = (float) (1 / (1 + Math.exp(-output[i])));
}
offs += input.length;
}
return Arrays.copyOf(output, output.length);
}
public float[] train(float[] error, float learningRate, float momentum) {
int offs = 0;
float[] nextError = new float[input.length];
for (int i = 0; i < output.length; i++) {
float d = error[i];
if (isSigmoid) {
d *= output[i] * (1 - output[i]);
}
for (int j = 0; j < input.length; j++) {
int idx = offs + j;
nextError[j] += weights[idx] * d;
float dw = input[j] * d * learningRate;
weights[idx] += dweights[idx] * momentum + dw;
dweights[idx] = dw;
}
offs += input.length;
}
return nextError;
}
}
MLPLayer[] layers;
public MLP(int inputSize, int[] layersSize) {
layers = new MLPLayer[layersSize.length];
Random r = new Random(1234);
for (int i = 0; i < layersSize.length; i++) {
int inSize = i == 0 ? inputSize : layersSize[i - 1];
layers[i] = new MLPLayer(inSize, layersSize[i], r);
}
}
public MLPLayer getLayer(int idx) {
return layers[idx];
}
public float[] run(float[] input) {
float[] actIn = input;
for (int i = 0; i < layers.length; i++) {
actIn = layers[i].run(actIn);
}
return actIn;
}
public void train(float[] input, float[] targetOutput, float learningRate, float momentum) {
float[] calcOut = run(input);
float[] error = new float[calcOut.length];
for (int i = 0; i < error.length; i++) {
error[i] = targetOutput[i] - calcOut[i]; // negative error
}
for (int i = layers.length - 1; i >= 0; i--) {
error = layers[i].train(error, learningRate, momentum);
}
}
public static void main(String[] args) throws Exception {
float[][] train = new float[][]{new float[]{0, 0}, new float[]{0, 1}, new float[]{1, 0}, new float[]{1, 1}};
float[][] res = new float[][]{new float[]{0}, new float[]{1}, new float[]{1}, new float[]{0}};
MLP mlp = new MLP(2, new int[]{2, 1});
mlp.getLayer(1).setIsSigmoid(false);
Random r = new Random();
int en = 500;
for (int e = 0; e < en; e++) {
for (int i = 0; i < res.length; i++) {
int idx = r.nextInt(res.length);
mlp.train(train[idx], res[idx], 0.3f, 0.6f);
}
if ((e + 1) % 100 == 0) {
System.out.println();
for (int i = 0; i < res.length; i++) {
float[] t = train[i];
System.out.printf("%d epoch\n", e + 1);
System.out.printf("%.1f, %.1f --> %.3f\n", t[0], t[1], mlp.run(t)[0]);
}
}
}
}
}