山东大学人工智能导论实验2工程文件-前向传播和反向传播

import os import numpy as np import math def sigmoid(x): """ Compute the sigmoid of x Arguments: x -- A scalar or numpy array of any size Return: s -- sigmoid(x) """ # write your code here sig = 1 / (1 + np.exp(-x)) return sig def softmax(x): """Calculates the softmax for the input x. Argument: x -- A numpy matrix of shape (n,) Returns: s -- A numpy matrix equal to the softmax of x, of shape (n,) """ # write your code here x = np.exp(x) / np.sum(np.exp(x), axis=0, keepdims=True) return x def cross_entropy_loss(target, prediction): """ Compute the cross entropy loss between target and prediction Arguments: target -- the real label, a scalar or numpy array size = (n,) prediction -- the output of model, a scalar or numpy array, size=(n, c) Return: mean loss -- cross_entropy_loss(target, prediction) """ # write your code here delta = 1e-6 return -np.sum(prediction * np.log(target + delta)) def forward(w, b, x): """ Arguments: w -- weights, a numpy array of size (m, 1) b -- bias, a scalar x -- data of size (n, m) Return: prediction """ ## write your code here prediction = sigmoid(x @ w + b) # print(prediction.shape) return prediction def backward(x, target, prediction): """ Arguments: x -- data of size (n, m) target -- data of size (n, num_class) prediction -- data of size (n, num_class) Return: dw, db """ delta = target - prediction db = delta dw = sigmoid(x.T) @ delta return dw, db # don't edit if __name__ == '__main__': ## three samples x = np.array([[12, 3, 7, 4], [3, 10, 4, 9], [9, 6, 2, 0]]) target = np.array([0, 1, 2]) num_class = 3 ## learning rate of the gradient descent update rule learning_rate = 0.001 ## one-hot label target = np.eye(num_class)[target] n, m = x.shape w = np.zeros([m, num_class]) b = 0 # three iterations of forward and backward for i in range(3): prediction = forward(w, b, x) loss = cross_entropy_loss(target, softmax(prediction)) dw, db = backward(x, target, prediction) # update w and b w = w - learning_rate * dw b = b - learning_rate * db print("iter = {}, w = {}, b = {}, loss= {}".format(i, w, b, loss))