Implementing a Neural Network in Java: Training and Backpropagation issues

Question

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 1

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]);
    }
   }
  }
 }
}

Answer 2

I tried going over your code, but as you stated, it was pretty long.

Here's what I suggest:

• To verify that your network is learning properly, try to train a simple network, like a network that recognizes the XOR operator. This shouldn't take all that long.
• Use the simplest back-propagation algorithm. Stochastic backpropagation (where the weights are updated after the presentation of each training input) is the easiest. Implement the algorithm without the momentum term initially, and with a constant learning rate (i.e., don't start with adaptive learning-rates). Once you're satisfied that the algorithm is working, you can introduce the momentum term. Doing too many things at the same time increases the chances that more than one thing can go wrong. This makes it harder for you to see where you went wrong.
• If you want to go over some code, you can check out some code that I wrote; you want to look at Backpropagator.java. I've basically implemented the stochastic backpropagation algorithm with a momentum term. I also have a video where I provide a quick explanation of my implementation of the backpropagation algorithm.

Hopefully this is of some help!