tsoding.ml-notes/gates.c

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

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

typedef float sample[3];

// NAND-gate
sample or_train[] = {
    {0, 0, 0},
    {1, 0, 1},
    {0, 1, 1},
    {1, 1, 1},
};

sample and_train[] = {
    {0, 0, 0},
    {1, 0, 0},
    {0, 1, 0},
    {1, 1, 1},
};

sample nand_train[] = {
    {0, 0, 1},
    {1, 0, 1},
    {0, 1, 1},
    {1, 1, 0},
};

sample xor_train[] = {
    {0, 0, 0},
    {1, 0, 1},
    {0, 1, 1},
    {1, 1, 0},
};

sample *train = and_train;
size_t train_count = 4;

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;
    }
    result /= train_count;
    return result;
}

void dcost(float eps,
           float w1, float w2, float b,
           float *dw1, float *dw2, float *db)
{
    float c = cost(w1, w2, b);
    *dw1 = (cost(w1 + eps, w2, b) - c)/eps;
    *dw2 = (cost(w1, w2 + eps, b) - c)/eps;
    *db  = (cost(w1, w2, b + eps) - c)/eps;
}


void gcost(float w1, float w2, float b,
           float *dw1, float *dw2, float *db)
{
    *dw1 = 0;
    *dw2 = 0;
    *db = 0;
    size_t n = train_count;
    for (size_t i = 0; i < n; ++i) {
        float xi = train[i][0];
        float yi = train[i][1];
        float zi = train[i][2];
        float ai = sigmoidf(xi*w1 + yi*w2 + b);
        float di = 2*(ai - zi)*ai*(1 - ai);
        *dw1 += di*xi;
        *dw2 += di*yi;
        *db  += di;
    }
    *dw1 /= n;
    *dw2 /= n;
    *db /= n;
}

float rand_float(void)
{
    return (float) rand()/ (float) RAND_MAX;
}

int main2(void)
{
    // (x|y) & ~(x&y)
    for (size_t x = 0; x < 2; ++x) {
        for (size_t y = 0; y < 2; ++y) {
            printf("%zu ^ %zu = %zu\n", x, y, (x|y) & (~(x&y)));
        }
    }
    return 0;
}

int main(void)
{
    srand(time(0));
    float w1 = rand_float();
    float w2 = rand_float();
    float b  = rand_float();

    float rate = 1e-1;

    for (size_t i = 0; i < 10*1000; ++i) {
        float c = cost(w1, w2, b);
        printf("c = %f, w1 = %f, w2 = %f, b = %f\n", c, w1, w2, b);

        float dw1, dw2, db;
#if 1
        float eps = 1e-1;
        dcost(eps, w1, w2, b, &dw1, &dw2, &db);
#else
        gcost(w1, w2, b, &dw1, &dw2, &db);
#endif
        w1 -= rate*dw1;
        w2 -= rate*dw2;
        b  -= rate*db;
    }
    printf("c = %f, w1 = %f, w2 = %f, b = %f\n", cost(w1, w2, b), w1, w2, b);

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

    return 0;
}