使用numpy實現一個簡單的2層神經網絡

import numpy as np

def main():
    # 2層神經網絡，64個輸入1000維，1個隱藏層100維，輸出10維
    N, D_in, H, D_out = 64, 1000, 100, 10
    # 隨機初始化樣本
    x = np.random.randn(N, D_in)
    y = np.random.randn(N, D_out)

    # 隨機初始化權重
    w1 = np.random.randn(D_in, H)
    w2 = np.random.randn(H, D_out)
    # 學習率一般選擇1e-6~1e-4
    learning_rate = 1e-6
    # 循環迭代學習500次
    for t in range(500):
        # forward pass
        h = x.dot(w1) # N * H
        h_relu = np.maximum(h,0) # N * H
        y_pred = h_relu.dot(w2) # H * D_out

        # compute loss
        loss = np.square(y_pred - y).sum()
        print(t, loss)

        # backward pass
        # compute the gradient
        grad_y_pred = 2.0 * (y_pred - y)
        grad_w2 = h_relu.T.dot(grad_y_pred)
        grad_h_relu = grad_y_pred.dot(w2.T)
        grad_h = grad_h_relu.copy()
        grad_h[h<0] = 0
        grad_w1 = x.T.dot(grad_h)

        # update weights of w1 and w2
        w1 -= learning_rate * grad_w1
        w2 -= learning_rate * grad_w2
        
    # 使用訓練好的數據進行預測
    h = x.dot(w1)
    h_relu = np.maximum(h, 0)
    y_pred = h_relu.dot(w2)
    
    # 打印出預測值與實際值的誤差
    print(y - y_pred)


if __name__ == '__main__':
    main()

經過500次迭代，損失逐漸減小

490 6.488345724242929e-07
491 6.189309834083105e-07
492 5.904337869152525e-07
493 5.632434702894173e-07
494 5.373005118562679e-07
495 5.125660475282727e-07
496 4.889721590543996e-07
497 4.6647564933752185e-07
498 4.4502716144784435e-07
499 4.245642390520534e-07

進行預測測試，部分結果如下，可見誤差已經非常小了

 [-4.05827834e-06 -2.08487774e-05 -1.08563393e-05  2.56239401e-05
   1.21532941e-05  8.19823028e-06 -3.31557266e-05 -5.22064015e-06
  -2.07082664e-05 -9.00997895e-06]
 [ 7.89988666e-06  6.81363721e-06 -1.28522000e-06 -1.39193166e-05
  -1.49279614e-05  1.09177779e-05  2.73508543e-05 -3.20825669e-06
  -6.57302516e-07  4.38394831e-06]]