【python实现卷积神经网络】全连接层实现

代码来源：https://github.com/eriklindernoren/ML-From-Scratch

卷积神经网络中卷积层Conv2D（带stride、padding）的具体实现：https://www.cnblogs.com/xiximayou/p/12706576.html

激活函数的实现（sigmoid、softmax、tanh、relu、leakyrelu、elu、selu、softplus）：https://www.cnblogs.com/xiximayou/p/12713081.html

损失函数定义（均方误差、交叉熵损失）：https://www.cnblogs.com/xiximayou/p/12713198.html

优化器的实现（SGD、Nesterov、Adagrad、Adadelta、RMSprop、Adam）：https://www.cnblogs.com/xiximayou/p/12713594.html

卷积层反向传播过程：https://www.cnblogs.com/xiximayou/p/12713930.html

全连接层实现代码：

class Dense(Layer):
    """A fully-connected NN layer.
    Parameters:
    -----------
    n_units: int
        The number of neurons in the layer.
    input_shape: tuple
        The expected input shape of the layer. For dense layers a single digit specifying
        the number of features of the input. Must be specified if it is the first layer in
        the network.
    """
    def __init__(self, n_units, input_shape=None):
        self.layer_input = None
        self.input_shape = input_shape
        self.n_units = n_units
        self.trainable = True
        self.W = None
        self.w0 = None

    def initialize(self, optimizer):
        # Initialize the weights
        limit = 1 / math.sqrt(self.input_shape[0])
        self.W  = np.random.uniform(-limit, limit, (self.input_shape[0], self.n_units))
        self.w0 = np.zeros((1, self.n_units))
        # Weight optimizers
        self.W_opt  = copy.copy(optimizer)
        self.w0_opt = copy.copy(optimizer)

    def parameters(self):
        return np.prod(self.W.shape) + np.prod(self.w0.shape)

    def forward_pass(self, X, training=True):
        self.layer_input = X
        return X.dot(self.W) + self.w0

    def backward_pass(self, accum_grad):
        # Save weights used during forwards pass
        W = self.W

        if self.trainable:
            # Calculate gradient w.r.t layer weights
            grad_w = self.layer_input.T.dot(accum_grad)
            grad_w0 = np.sum(accum_grad, axis=0, keepdims=True)

            # Update the layer weights
            self.W = self.W_opt.update(self.W, grad_w)
            self.w0 = self.w0_opt.update(self.w0, grad_w0)

        # Return accumulated gradient for next layer
        # Calculated based on the weights used during the forward pass
        accum_grad = accum_grad.dot(W.T)
        return accum_grad

    def output_shape(self):
        return (self.n_units, )