public void testFeedForwardAndBAckLoopWorksWithMomentum()
{
// example 11.14 of Neural Network Design by Hagan, Demuth and Beale
Matrix hiddenLayerWeightMatrix = new Matrix(2, 1);
hiddenLayerWeightMatrix.set(0, 0, -0.27);
hiddenLayerWeightMatrix.set(1, 0, -0.41);
Vector hiddenLayerBiasVector = new Vector(2);
hiddenLayerBiasVector.setValue(0, -0.48);
hiddenLayerBiasVector.setValue(1, -0.13);
Vector input = new Vector(1);
input.setValue(0, 1);
Matrix outputLayerWeightMatrix = new Matrix(1, 2);
outputLayerWeightMatrix.set(0, 0, 0.09);
outputLayerWeightMatrix.set(0, 1, -0.17);
Vector outputLayerBiasVector = new Vector(1);
outputLayerBiasVector.setValue(0, 0.48);
Vector error = new Vector(1);
error.setValue(0, 1.261);
double learningRate = 0.1;
double momentumFactor = 0.5;
FeedForwardNeuralNetwork ffnn = new FeedForwardNeuralNetwork(
hiddenLayerWeightMatrix, hiddenLayerBiasVector,
outputLayerWeightMatrix, outputLayerBiasVector);
ffnn.setTrainingScheme(new BackPropLearning(learningRate,
momentumFactor));
ffnn.processInput(input);
ffnn.processError(error);
Matrix finalHiddenLayerWeights = ffnn.getHiddenLayerWeights();
Assert.AreEqual(-0.2675, finalHiddenLayerWeights.get(0, 0), 0.001);
Assert.AreEqual(-0.4149, finalHiddenLayerWeights.get(1, 0), 0.001);
Vector hiddenLayerBias = ffnn.getHiddenLayerBias();
Assert.AreEqual(-0.4775, hiddenLayerBias.getValue(0), 0.001);
Assert.AreEqual(-0.1349, hiddenLayerBias.getValue(1), 0.001);
Matrix finalOutputLayerWeights = ffnn.getOutputLayerWeights();
Assert.AreEqual(0.1304, finalOutputLayerWeights.get(0, 0), 0.001);
Assert.AreEqual(-0.1235, finalOutputLayerWeights.get(0, 1), 0.001);
Vector outputLayerBias = ffnn.getOutputLayerBias();
Assert.AreEqual(0.6061, outputLayerBias.getValue(0), 0.001);
}
/*
* ------------------------ Constructors ------------------------
*/
/** Construct a diagonal Matrix from the given List of doubles */
public static Matrix createDiagonalMatrix(List <Double> values)
{
Matrix m = new Matrix(values.Count, values.Count, 0);
for (int i = 0; i < values.Count; i++)
{
m.set(i, i, values[i]);
}
return(m);
}
public void testFeedForward()
{
// example 11.14 of Neural Network Design by Hagan, Demuth and Beale
// lots of tedious tests necessary to ensure nn is fundamentally correct
Matrix weightMatrix1 = new Matrix(2, 1);
weightMatrix1.set(0, 0, -0.27);
weightMatrix1.set(1, 0, -0.41);
Vector biasVector1 = new Vector(2);
biasVector1.setValue(0, -0.48);
biasVector1.setValue(1, -0.13);
Layer layer1 = new Layer(weightMatrix1, biasVector1,
new LogSigActivationFunction());
Vector inputVector1 = new Vector(1);
inputVector1.setValue(0, 1);
Vector expected = new Vector(2);
expected.setValue(0, 0.321);
expected.setValue(1, 0.368);
Vector result1 = layer1.feedForward(inputVector1);
Assert.AreEqual(expected.getValue(0), result1.getValue(0), 0.001);
Assert.AreEqual(expected.getValue(1), result1.getValue(1), 0.001);
Matrix weightMatrix2 = new Matrix(1, 2);
weightMatrix2.set(0, 0, 0.09);
weightMatrix2.set(0, 1, -0.17);
Vector biasVector2 = new Vector(1);
biasVector2.setValue(0, 0.48);
Layer layer2 = new Layer(weightMatrix2, biasVector2,
new PureLinearActivationFunction());
Vector inputVector2 = layer1.getLastActivationValues();
Vector result2 = layer2.feedForward(inputVector2);
Assert.AreEqual(0.446, result2.getValue(0), 0.001);
}
public void testSensitivityMatrixCalculationFromErrorVector()
{
Matrix weightMatrix1 = new Matrix(2, 1);
weightMatrix1.set(0, 0, -0.27);
weightMatrix1.set(1, 0, -0.41);
Vector biasVector1 = new Vector(2);
biasVector1.setValue(0, -0.48);
biasVector1.setValue(1, -0.13);
Layer layer1 = new Layer(weightMatrix1, biasVector1,
new LogSigActivationFunction());
Vector inputVector1 = new Vector(1);
inputVector1.setValue(0, 1);
layer1.feedForward(inputVector1);
Matrix weightMatrix2 = new Matrix(1, 2);
weightMatrix2.set(0, 0, 0.09);
weightMatrix2.set(0, 1, -0.17);
Vector biasVector2 = new Vector(1);
biasVector2.setValue(0, 0.48);
Layer layer2 = new Layer(weightMatrix2, biasVector2,
new PureLinearActivationFunction());
Vector inputVector2 = layer1.getLastActivationValues();
layer2.feedForward(inputVector2);
Vector errorVector = new Vector(1);
errorVector.setValue(0, 1.261);
LayerSensitivity layer2Sensitivity = new LayerSensitivity(layer2);
layer2Sensitivity.sensitivityMatrixFromErrorMatrix(errorVector);
Matrix sensitivityMatrix = layer2Sensitivity.getSensitivityMatrix();
Assert.AreEqual(-2.522, sensitivityMatrix.get(0, 0), 0.0001);
}
public Matrix asMatrix(String action)
{
Matrix transitionMatrix = new Matrix(states.Count, states.Count);
for (int i = 0; i < states.Count; i++)
{
String oldState = states[i];
String old_state_action = String.Concat(oldState,action);
for (int j = 0; j < states.Count; j++)
{
String newState = states[j];
double transitionProbability = get(old_state_action, newState);
transitionMatrix.set(i, j, transitionProbability);
}
}
return transitionMatrix;
}
/*
* ------------------------ Constructors ------------------------
*/
/** Construct a diagonal Matrix from the given List of doubles */
public static Matrix createDiagonalMatrix(List<Double> values) {
Matrix m = new Matrix(values.Count, values.Count, 0);
for (int i = 0; i < values.Count; i++) {
m.set(i, i, values[i]);
}
return m;
}
public void testWeightsAndBiasesUpdatedCorrectly()
{
Matrix weightMatrix1 = new Matrix(2, 1);
weightMatrix1.set(0, 0, -0.27);
weightMatrix1.set(1, 0, -0.41);
Vector biasVector1 = new Vector(2);
biasVector1.setValue(0, -0.48);
biasVector1.setValue(1, -0.13);
Layer layer1 = new Layer(weightMatrix1, biasVector1,
new LogSigActivationFunction());
LayerSensitivity layer1Sensitivity = new LayerSensitivity(layer1);
Vector inputVector1 = new Vector(1);
inputVector1.setValue(0, 1);
layer1.feedForward(inputVector1);
Matrix weightMatrix2 = new Matrix(1, 2);
weightMatrix2.set(0, 0, 0.09);
weightMatrix2.set(0, 1, -0.17);
Vector biasVector2 = new Vector(1);
biasVector2.setValue(0, 0.48);
Layer layer2 = new Layer(weightMatrix2, biasVector2,
new PureLinearActivationFunction());
Vector inputVector2 = layer1.getLastActivationValues();
layer2.feedForward(inputVector2);
Vector errorVector = new Vector(1);
errorVector.setValue(0, 1.261);
LayerSensitivity layer2Sensitivity = new LayerSensitivity(layer2);
layer2Sensitivity.sensitivityMatrixFromErrorMatrix(errorVector);
layer1Sensitivity
.sensitivityMatrixFromSucceedingLayer(layer2Sensitivity);
BackPropLearning.calculateWeightUpdates(layer2Sensitivity, layer1
.getLastActivationValues(), 0.1);
BackPropLearning.calculateBiasUpdates(layer2Sensitivity, 0.1);
BackPropLearning.calculateWeightUpdates(layer1Sensitivity,
inputVector1, 0.1);
BackPropLearning.calculateBiasUpdates(layer1Sensitivity, 0.1);
layer2.updateWeights();
Matrix newWeightMatrix2 = layer2.getWeightMatrix();
Assert.AreEqual(0.171, newWeightMatrix2.get(0, 0), 0.001);
Assert.AreEqual(-0.0772, newWeightMatrix2.get(0, 1), 0.001);
layer2.updateBiases();
Vector newBiasVector2 = layer2.getBiasVector();
Assert.AreEqual(0.7322, newBiasVector2.getValue(0), 0.00001);
layer1.updateWeights();
Matrix newWeightMatrix1 = layer1.getWeightMatrix();
Assert.AreEqual(-0.265, newWeightMatrix1.get(0, 0), 0.001);
Assert.AreEqual(-0.419, newWeightMatrix1.get(1, 0), 0.001);
layer1.updateBiases();
Vector newBiasVector1 = layer1.getBiasVector();
Assert.AreEqual(-0.475, newBiasVector1.getValue(0), 0.001);
Assert.AreEqual(-0.139, newBiasVector1.getValue(1), 0.001);
}
public void testBiasUpdateMatrixesFormedCorrectly()
{
Matrix weightMatrix1 = new Matrix(2, 1);
weightMatrix1.set(0, 0, -0.27);
weightMatrix1.set(1, 0, -0.41);
Vector biasVector1 = new Vector(2);
biasVector1.setValue(0, -0.48);
biasVector1.setValue(1, -0.13);
Layer layer1 = new Layer(weightMatrix1, biasVector1,
new LogSigActivationFunction());
LayerSensitivity layer1Sensitivity = new LayerSensitivity(layer1);
Vector inputVector1 = new Vector(1);
inputVector1.setValue(0, 1);
layer1.feedForward(inputVector1);
Matrix weightMatrix2 = new Matrix(1, 2);
weightMatrix2.set(0, 0, 0.09);
weightMatrix2.set(0, 1, -0.17);
Vector biasVector2 = new Vector(1);
biasVector2.setValue(0, 0.48);
Layer layer2 = new Layer(weightMatrix2, biasVector2,
new PureLinearActivationFunction());
LayerSensitivity layer2Sensitivity = new LayerSensitivity(layer2);
Vector inputVector2 = layer1.getLastActivationValues();
layer2.feedForward(inputVector2);
Vector errorVector = new Vector(1);
errorVector.setValue(0, 1.261);
layer2Sensitivity.sensitivityMatrixFromErrorMatrix(errorVector);
layer1Sensitivity
.sensitivityMatrixFromSucceedingLayer(layer2Sensitivity);
Vector biasUpdateVector2 = BackPropLearning.calculateBiasUpdates(
layer2Sensitivity, 0.1);
Assert.AreEqual(0.2522, biasUpdateVector2.getValue(0), 0.001);
Vector lastBiasUpdateVector2 = layer2.getLastBiasUpdateVector();
Assert.AreEqual(0.2522, lastBiasUpdateVector2.getValue(0), 0.001);
Vector penultimateBiasUpdateVector2 = layer2
.getPenultimateBiasUpdateVector();
Assert.AreEqual(0.0, penultimateBiasUpdateVector2.getValue(0),
0.001);
Vector biasUpdateVector1 = BackPropLearning.calculateBiasUpdates(
layer1Sensitivity, 0.1);
Assert.AreEqual(0.00495, biasUpdateVector1.getValue(0), 0.001);
Assert.AreEqual(-0.00997, biasUpdateVector1.getValue(1), 0.001);
Vector lastBiasUpdateVector1 = layer1.getLastBiasUpdateVector();
Assert.AreEqual(0.00495, lastBiasUpdateVector1.getValue(0), 0.001);
Assert.AreEqual(-0.00997, lastBiasUpdateVector1.getValue(1), 0.001);
Vector penultimateBiasUpdateVector1 = layer1
.getPenultimateBiasUpdateVector();
Assert.AreEqual(0.0, penultimateBiasUpdateVector1.getValue(0),
0.001);
Assert.AreEqual(0.0, penultimateBiasUpdateVector1.getValue(1),
0.001);
}
//
// PRIVATE METHODS
//
private static void initializeMatrix(Matrix aMatrix, double lowerLimit,
double upperLimit) {
for (int i = 0; i < aMatrix.getRowDimension(); i++) {
for (int j = 0; j < aMatrix.getColumnDimension(); j++) {
double random = Util.generateRandomDoubleBetween(lowerLimit,
upperLimit);
aMatrix.set(i, j, random);
}
}
}
