第1关：实现常见损失函数的前向传播

import numpy as np


def softmax(x):
    x = x - np.max(x, axis=1, keepdims=True)
    return np.exp(x) / np.sum(np.exp(x), axis=1, keepdims=True)


class SoftmaxWithLoss:
    def __init__(self):
        self.loss = None

    def forward(self, x, t):
        r'''
        SoftMax + Cross Entropy的前向传播

        Parameter:
        - x: numpy.array, (B, C)
        - t: numpy.array, (B)

        Return:
        - loss: float
        '''
        ########## Begin ##########
        y = softmax(x)  
        batch_size = y.shape[0]  
        # 为了避免log计算的时候y太小，所以加一个1e-7来避免算数错误  
        loss = -np.sum(np.log(y[np.arange(batch_size), t] + 1e-7)) / batch_size  
        self.loss = loss  
        return loss  


        ########## End ##########


class MeanSquaredError:
    def __init__(self):
        self.loss = None

    def forward(self, y, t):
        r'''
        Mean Squared Error的前向传播

        Parameter:
        - y: numpy.array, (B, N)
        - t: numpy.array, (B, N)

        Return:
        - loss: float
        '''
        ########## Begin ##########
        loss = 0.5 * np.sum((y - t) ** 2)  
        self.loss = loss  
        return loss  

        ########## End ##########

第2关：实现常见损失函数的反向传播

import numpy as np


def softmax(x):
    x = x - np.max(x, axis=1, keepdims=True)
    return np.exp(x) / np.sum(np.exp(x), axis=1, keepdims=True)


class SoftmaxWithLoss:
    def __init__(self):
        self.loss = None
        self.y = None
        self.t = None

    def forward(self, x, t):
        r'''
        SoftMax + Cross Entropy的前向传播

        Parameter:
        - x: numpy.array, (B, C)
        - t: numpy.array, (B)

        Return:
        - loss: float
        '''
        y = softmax(x)
        batch_size = y.shape[0]
        loss = -np.sum(np.log(y[np.arange(batch_size), t] + 1e-7)) / batch_size
        self.loss = loss
        self.y = y
        self.t = t
        return loss

    def backward(self):
        r'''
        SoftMax + Cross Entropy的反向传播

        Return:
        - dx: numpy.array, (B, C)
        '''
        ########## Begin ##########
        batch_size = self.t.shape[0]  
        dx = self.y.copy()  
        dx[np.arange(batch_size), self.t] -= 1  
        dx = dx / batch_size  
        return dx  

        ########## End ##########


class MeanSquaredError:
    def __init__(self):
        self.loss = None
        self.y = None
        self.t = None

    def forward(self, y, t):
        r'''
        Mean Squared Error的前向传播

        Parameter:
        - y: numpy.array, (B, N)
        - t: numpy.array, (B, N)

        Return:
        - loss: float
        '''
        loss = 0.5 * np.sum((y - t) ** 2)
        self.loss = loss
        self.y = y
        self.t = t
        return loss

    def backward(self):
        r'''
        Mean Squared Error的反向传播

        Return:
        - dy: numpy.array, (B, N)
        '''
        ########## Begin ##########
        y_grad = self.y - self.t  
        return y_grad

        ########## End ##########