/// <summary>
/// Create a feedforward neural network, train it, and run some test examples.
/// </summary>
public FeedForwardXor()
{
// Create the data set
// Frame the problem as a regression problem; two inputs (x, y) and one output (z)
DataSet.Regression dataSet = new DataSet.Regression(2, 1);
// Populate data set - data point takes a double array for inputs and outputs
dataSet.AddDataPoint(new double[] { 0, 0 }, new double[] { 0 });
dataSet.AddDataPoint(new double[] { 1, 0 }, new double[] { 1 });
dataSet.AddDataPoint(new double[] { 0, 1 }, new double[] { 1 });
dataSet.AddDataPoint(new double[] { 1, 1 }, new double[] { 0 });
// Split the data points randomly into training, validation, and test sets
// Here, put all data points into the training set
dataSet.AssignDataPoints(1, 0, 0);
// Create feedforward network
// Create a network with two inputs and one output
FeedForwardNetwork network = new FeedForwardNetwork(2, 1);
// Add five hidden nodes, and connect them to the output layer using sigmoid activation
network.AddHiddenLayer(5, new ActivationFunction.Sigmoid())
.AddOutputLayer(new ActivationFunction.Sigmoid());
// Set up the backpropagation trainer
// Create the batch selector - here, select the whole training set, but this can be
// used to select mini-batches, single points, etc.
DataPoint[] select(DataSet data) => data.TrainingSet;
BackpropagationTrainer trainer = new BackpropagationTrainer()
{
// Set the learning rate
LearningRate = 0.09,
// Initialise network weights using a uniform distribution
initialiser = new Initialiser.Uniform(-0.2, 0.2, false),
// Update weights after the whole batch rather than after each point
stochastic = false,
// Train on the whole training set each iteration
batchSelector = new BackpropagationTrainer.BatchSelector(select),
// Use squared error as the loss function
lossFunction = new LossFunction.SquaredError(),
// Log training data every 5000 epochs; access this with trainer.evaluations
evaluationFrequency = 8000
};
// Add a termination condition to the trainer; it will stop after 50,000 epochs
trainer.terminationConditions.Add(new TerminationCondition.EpochLimit(80000));
// Troubleshoot trainer (this will notify you of any missing required settings)
foreach (string s in trainer.Troubleshoot())
{
Console.WriteLine();
}
// Start training
// Train the network on the data set
trainer.Train(network, dataSet);
// Print training data to the console
List <double[]> evals = trainer.evaluations;
foreach (double[] arr in evals)
{
Console.WriteLine("epoch={0}, training error={1}, " +
"validation error={2}", arr[0], arr[1], arr[2]);
}
Console.WriteLine();
// Test
foreach (DataPoint dataPoint in dataSet.TrainingSet)
{
// Feed the network a test point and record the output
double output = network.GetOutput(Matrix.ToColumnMatrix(dataPoint.input))[0, 0];
Console.WriteLine("({0}, {1}) -> {2} : expected {3}",
dataPoint.input[0], dataPoint.input[1], output, dataPoint.output[0]);
}
Console.WriteLine();
}
/// <summary>
/// Create a feedforward neural network, train it, and run some test examples.
/// </summary>
public FeedForwardRegression()
{
// Define the function we are trying to model in the range [0, 1]
double TestFunction(double x)
{
return(Math.Sqrt(x) + 0.3 * Math.Sin(6 * Math.Sqrt(x)));
}
// Create the data set
// Frame the problem as a regression problem; one input (x) and one output (y)
DataSet.Regression dataSet = new DataSet.Regression(1, 1);
// Populate data set - data point takes a double array for inputs and outputs
Random random = new Random(421);
for (int i = 0; i < 10000; i++)
{
double nextDouble = random.NextDouble(); // In the range [0, 1]
dataSet.AddDataPoint(new double[] { nextDouble },
new double[] { TestFunction(nextDouble) });
}
// Split the data points randomly into training, validation, and test sets in the ratio
// 7:2:1
dataSet.AssignDataPoints(0.7, 0.2, 0.1);
// Create feedforward network
// Create a network with one input and one output
FeedForwardNetwork network = new FeedForwardNetwork(1, 1);
// Add five hidden nodes, and connect them to the output layer using sigmoid activation
network.AddHiddenLayer(32, new ActivationFunction.Sigmoid())
.AddOutputLayer(new ActivationFunction.Sigmoid());
// Set up the backpropagation trainer
// Create the batch selector - here, select a random mini-batch from the training set
// with 32 examples in it
DataPoint[] select(DataSet data) => data.GetRandomTrainingSubset(32);
BackpropagationTrainer trainer = new BackpropagationTrainer()
{
// Set the learning rate
LearningRate = 0.1,
// Initialise network weights using a uniform distribution
initialiser = new Initialiser.Uniform(-0.01, 0.01, false),
// Update weights after the whole batch rather than after each point
stochastic = false,
// Train on the whole training set each iteration
batchSelector = new BackpropagationTrainer.BatchSelector(select),
// Use squared error as the loss function
lossFunction = new LossFunction.SquaredError(),
// Log training data every 5000 epochs; access this with trainer.evaluations
evaluationFrequency = 50
};
// Add a termination condition to the trainer; it will stop after 1200 epochs
trainer.terminationConditions.Add(new TerminationCondition.EpochLimit(1200));
// Troubleshoot trainer (this will notify you of any missing required settings)
foreach (string s in trainer.Troubleshoot())
{
Console.WriteLine();
}
// Start training
// Train the network on the data set
trainer.Train(network, dataSet);
// Print training data to the console
List <double[]> evals = trainer.evaluations;
foreach (double[] arr in evals)
{
Console.WriteLine("epoch={0}, training error={1}, " +
"validation error={2}", arr[0], arr[1], arr[2]);
}
Console.WriteLine();
// Test
// Print the test set loss
Console.WriteLine("Mean test loss per point: " + trainer.TestLoss() + "\n");
// Print 64 samples from the test set
foreach (DataPoint dataPoint in dataSet.GetRandomTestSubset(64))
{
// Feed the network a test point and record the output
double output = network.GetOutput(Matrix.ToColumnMatrix(dataPoint.input))[0, 0];
Console.WriteLine("({0}) -> {1} : expected {2}",
dataPoint.input[0], output, dataPoint.output[0]);
}
Console.WriteLine();
// If training takes a long time, this will notify you when it finishes
Console.Beep(880, 2000);
}