1.简单层的实现

# coding: utf-8

class MulLayer:
    def __init__(self):
        self.x = None
        self.y = None

    def forward(self, x, y):
        self.x = x
        self.y = y
        out = x * y

        return out

    def backward(self, dout):
        dx = dout * self.y
        dy = dout * self.x

        return dx, dy


class AddLayer:
    def __init__(self):
        pass

    def forward(self, x, y):
        out = x + y

        return out

    def backward(self, dout):
        dx = dout * 1
        dy = dout * 1

        return dx, dy


apple = 100
apple_num = 2
orange = 150
orange_num = 3
tax = 1.1

# layer
mul_apple_layer = MulLayer()
mul_orange_layer = MulLayer()
add_apple_orange_layer = AddLayer()
mul_tax_layer = MulLayer()

# forward
apple_price = mul_apple_layer.forward(apple, apple_num)  # (1)
orange_price = mul_orange_layer.forward(orange, orange_num)  # (2)
all_price = add_apple_orange_layer.forward(apple_price, orange_price)  # (3)
price = mul_tax_layer.forward(all_price, tax)  # (4)

# backward
dprice = 1
dall_price, dtax = mul_tax_layer.backward(dprice)  # (4)
dapple_price, dorange_price = add_apple_orange_layer.backward(dall_price)  # (3)
dorange, dorange_num = mul_orange_layer.backward(dorange_price)  # (2)
dapple, dapple_num = mul_apple_layer.backward(dapple_price)  # (1)

print("price:", int(price))
print("dApple:", dapple)
print("dApple_num:", int(dapple_num))
print("dOrange:", dorange)
print("dOrange_num:", int(dorange_num))
print("dTax:", dtax)

2.激活函数层的实现

把计算图的思路应用到神经网络中。把构成神经网络的层实现为一个类。

class Relu:
    def __init__(self):
        self.mask = None

    def forward(self, x):
        self.mask = (x <= 0)
        out = x.copy()
        out[self.mask] = 0

        return out

    def backward(self, dout):
        dout[self.mask] = 0
        dx = dout

        return dx


class Sigmoid:
    def __init__(self):
        self.out = None

    def forward(self, x):
        out = sigmoid(x)
        self.out = out
        return out

    def backward(self, dout):
        dx = dout * (1.0 - self.out) * self.out

        return dx

3.Affine/Softmax层的实现

矩阵的乘积运算在几何学中被称为“仿射变换”，仿射变换包括一次线性变换和一次平移。分别对应神经网络的加权和运算与加偏置运算。

将进行仿射变换的处理实现为“Affine”层

class Affine:
    def __init__(self, W, b):
        self.W =W
        self.b = b
        
        self.x = None
        self.original_x_shape = None
        # 权重和偏置参数的导数
        self.dW = None
        self.db = None

    def forward(self, x):
        # 对应张量
        self.original_x_shape = x.shape
        x = x.reshape(x.shape[0], -1)
        self.x = x

        out = np.dot(self.x, self.W) + self.b

        return out

    def backward(self, dout):
        dx = np.dot(dout, self.W.T)
        self.dW = np.dot(self.x.T, dout)
        self.db = np.sum(dout, axis=0)
        
        dx = dx.reshape(*self.original_x_shape)  # 还原输入数据的形状（对应张量）
        return dx

Softmax-with-Loss层（Softmax函数和交叉熵误差，Softmax函数记为Softmax层，交叉熵误差记为Cross Entropy Error层）

class SoftmaxWithLoss:
    def __init__(self):
        self.loss = None
        self.y = None # softmax的输出
        self.t = None # 监督数据

    def forward(self, x, t):
        self.t = t
        self.y = softmax(x)
        self.loss = cross_entropy_error(self.y, self.t)
        
        return self.loss

    def backward(self, dout=1):
        batch_size = self.t.shape[0]
        if self.t.size == self.y.size: # 监督数据是one-hot-vector的情况
            dx = (self.y - self.t) / batch_size
        else:
            dx = self.y.copy()
            dx[np.arange(batch_size), self.t] -= 1
            dx = dx / batch_size
        
        return dx

4.误差反向传播法的实现（求梯度）

两种求梯度的方法，一种是基于的数值微分的方法，另一种是误差反向传播法。

数值微分的优点是实现简单，一般情况下不太容易出错；

误差反向传播法的实现很复杂，容易出错。

在确认误差反向传播法的实现是否正确时，需要用数值微分求出的梯度结果来进行“梯度确认”（gradient check）