johnBuffer/BackpropagationFFNN

BackpropagationFFNN

Simple backpropagation algorithm wrote from scratch in order to understand it.

Usage

Declare network architecture: 1 input, 3 units in hidden layer, 1 output

std::vector<uint32_t> architecture{ 1, 3, 1 };

Create the Network and the Optimizer (with a training rate of 0.01)

ffnn::FFNeuralNetwork network(architecture);
ffnn::Optimizer optimizer(0.01f);

A simple struct to handle training examples

struct Example
{
    ffnn::Vectorf input;
    // The expected output
    ffnn::Vectorf output;
};

Generate training set, here we just want the output to be equal to the input

NumberGenerator gen;
std::vector<Example> training_set;
uint64_t examples_count = 10000;
for (uint64_t i(examples_count); i--;) {
    const float a = gen.getUnder(1.0f);
    training_set.push_back({
        {a},
        {a}
    });
}

Train the network

const float threshold = 1.0f;
float error = threshold + 1.0f;
while (error > threshold) {
    error = 0.0f;
    for (const Example& example : training_set) {
        optimizer.train(network, example.input, example.output);
        error += optimizer.error;
    }
    // Monitor the error after each iteration
    std::cout << error << std::endl;
}

View results

for (uint32_t i(10); i--;) {
    const float a = gen.getUnder(1.0f);
    const ffnn::Vectorf r = network.execute({ a });
    const float error = 0.5f * std::pow(a - r[0], 2);
    std::cout << "Result for " << a << ": " << r[0]  << " error: " << error << std::endl;
}

Limitations

• Currently just sigmoid activation is supported
• Perf are probably very bad because of naive matrix operations