main.c

#include <time.h>
#include <stdlib.h>
#include <stdio.h>
#include <math.h>

typedef float sample[3];

typedef struct
{
    float w1;
    float w2;
    float b;
} Model;

// modulable by a single neuron
sample or_train[] = {
    { 0, 0, 0 },
    { 0, 1, 1 },
    { 1, 0, 1 },
    { 1, 1, 1 }
};

// modulable by a single neuron
sample and_train[] = {
    { 0, 0, 0 },
    { 0, 1, 0 },
    { 1, 0, 0 },
    { 1, 1, 1 }
};

// modulable by a single neuron
sample nand_train[] = {
    { 0, 0, 1 },
    { 0, 1, 1 },
    { 1, 0, 1 },
    { 1, 1, 0 }
};

sample *train;
size_t train_count = 4;

float sigmoidf(float x)
{
    return 1.f / (1.f + expf(-x));
}

float random_float()
{
    return (float)rand() / (float)(RAND_MAX);
}

float cost(float w1, float w2, float b)
{
    float result = 0.0f;

    for (size_t i = 0; i < train_count; i++)
    {
        float x1 = train[i][0];
        float x2 = train[i][1];
        float y = sigmoidf(x1*w1 + x2*w2 + b);

        float d = y - train[i][2];

        result += d*d;
    }

    return result / train_count;
}

Model train_model()
{
    Model model;

    model.w1 = random_float();
    model.w2 = random_float();
    model.b = random_float();

    float eps = 1e-3;
    float rate = 1e-1;
    size_t epochs = 2000*2000;

    for (size_t i = 0; i < epochs; i++)
    {
        float c = cost(model.w1, model.w2, model.b);

        float dw1 = (cost(model.w1 + eps, model.w2, model.b) - c) / eps;
        float dw2 = (cost(model.w1, model.w2 + eps, model.b) - c) / eps;
        float db = (cost(model.w1, model.w2, model.b + eps) - c) / eps;

        model.w1 -= rate*dw1;
        model.w2 -= rate*dw2;
        model.b -= rate*db;
    }

    return model;
}

void predict(char* label, char symbol, sample data[])
{
    printf("\n%s:\n", label);

    train = data;

    Model model = train_model();

    printf("\ncost = %f\n", cost(model.w1, model.w2, model.b));
    printf("\nPREDICTIONS:\n\n");

    for (size_t i = 0; i < 2; i++)
        for (size_t j = 0; j < 2; j++)
            printf("%zu %c %zu = %f\n", i, symbol, j, sigmoidf(i * model.w1 + j * model.w2 + model.b));
}

int main(int argc, char** argv)
{
    predict("And", '&', and_train);
    predict("Nand", '~', nand_train);
    predict("Or", '|', or_train);
}