python 实现lstm神经网络代码

以下是使用Python实现LSTM神经网络的代码：

import numpy as np

class LSTM:

    def __init__(self, input_size, output_size, hidden_size, learning_rate):
        self.input_size = input_size
        self.output_size = output_size
        self.hidden_size = hidden_size
        self.learning_rate = learning_rate

        # Initialize weights and biases
        self.Wf = np.random.randn(hidden_size, input_size + hidden_size)
        self.Uf = np.random.randn(hidden_size, hidden_size)
        self.bf = np.zeros((hidden_size, 1))

        self.Wi = np.random.randn(hidden_size, input_size + hidden_size)
        self.Ui = np.random.randn(hidden_size, hidden_size)
        self.bi = np.zeros((hidden_size, 1))

        self.Wo = np.random.randn(hidden_size, input_size + hidden_size)
        self.Uo = np.random.randn(hidden_size, hidden_size)
        self.bo = np.zeros((hidden_size, 1))

        self.Wc = np.random.randn(hidden_size, input_size + hidden_size)
        self.Uc = np.random.randn(hidden_size, hidden_size)
        self.bc = np.zeros((hidden_size, 1))

        self.Wy = np.random.randn(output_size, hidden_size)
        self.by = np.zeros((output_size, 1))

    def sigmoid(self, x):
        return 1.0 / (1.0 + np.exp(-x))

    def softmax(self, x):
        exp_scores = np.exp(x)
        return exp_scores / np.sum(exp_scores)

    def forward(self, x, h_prev, c_prev):
        # Concatenate input and previous hidden state
        z = np.row_stack((h_prev, x))

        # Forget gate
        f = self.sigmoid(np.dot(self.Wf, z) + np.dot(self.Uf, h_prev) + self.bf)

        # Input gate
        i = self.sigmoid(np.dot(self.Wi, z) + np.dot(self.Ui, h_prev) + self.bi)

        # Output gate
        o = self.sigmoid(np.dot(self.Wo, z) + np.dot(self.Uo, h_prev) + self.bo)

        # Candidate cell state
        c_hat = np.tanh(np.dot(self.Wc, z) + np.dot(self.Uc, h_prev) + self.bc)

        # Current cell state
        c = f * c_prev + i * c_hat

        # Current hidden state
        h = o * np.tanh(c)

        # Output
        y = np.dot(self.Wy, h) + self.by
        probs = self.softmax(y)

        cache = (z, f, i, o, c_hat, c, h, y)

        return probs, cache

    def backward(self, dy, cache):
        # Unpack cache
        z, f, i, o, c_hat, c, h, y = cache

        # Derivatives of output layer
        dWy = np.dot(dy, h.T)
        dby = np.sum(dy, axis=1, keepdims=True)

        dh = np.dot(self.Wy.T, dy)

        # Derivatives of hidden layer
        do = dh * np.tanh(c)
        do = do * o * (1 - o)
        dUo = np.dot(do, h.T)
        dWo = np.dot(do, z.T)
        dbo = np.sum(do, axis=1, keepdims=True)

        dc = dh * o * (1 - np.tanh(c) ** 2)
        dc = dc + dcdy
        di = dc * c_hat
        di = di * i * (1 - i)
        dUi = np.dot(di, h.T)
        dWi = np.dot(di, z.T)
        dbi = np.sum(di, axis=1, keepdims=True)

        df = dc * c_prev
        df = df * f * (1 - f)
        dUf = np.dot(df, h.T)
        dWf = np.dot(df, z.T)
        dbf = np.sum(df, axis=1, keepdims=True)

        # Derivatives of input vector
        dz = None
        dh_prev = None
        dc_prev = None

        return dWy, dby, dUo, dWo, dbo, dUi, dWi, dbi, dUf, dWf, dbf, dz, dh_prev, dc_prev

    def optimize(self, gradients):
        # Update weights and biases
        self.Wy -= self.learning_rate * gradients[0]
        self.by -= self.learning_rate * gradients[1]
        self.Uo -= self.learning_rate * gradients[2]
        self.Wo -= self.learning_rate * gradients[3]
        self.bo -= self.learning_rate * gradients[4]
        self.Ui -= self.learning_rate * gradients[5]
        self.Wi -= self.learning_rate * gradients[6]
        self.bi -= self.learning_rate * gradients[7]
        self.Uf -= self.learning_rate * gradients[8]
        self.Wf -= self.learning_rate * gradients[9]
        self.bf -= self.learning_rate * gradients[10]

    def train(self, X, y, num_epochs):
        for epoch in range(num_epochs):
            # Initialize hidden state and cell state
            h_prev = np.zeros((self.hidden_size, 1))
            c_prev = np.zeros((self.hidden_size, 1))

            loss = 0

            # Loop through sequence
            for t in range(len(X)):
                # Forward pass
                x = X[t].reshape(-1, 1)
                y_true = y[t].reshape(-1, 1)
                probs, cache = self.forward(x, h_prev, c_prev)
                loss += -np.log(probs[np.argmax(y_true)])

                # Backward pass
                dy = probs
                dy[np.argmax(y_true)] -= 1
                gradients = self.backward(dy, cache)

                # Optimize
                self.optimize(gradients)

                # Update hidden state and cell state
                h_prev = cache[6]
                c_prev = cache[5]

            avg_loss = loss / len(X)
            print('Epoch: %d, Loss: %f' % (epoch + 1, avg_loss))

该代码使用numpy实现一个基本的LSTM神经网络，用于进行分类任务。在构造函数中，我们初始化权重和偏置，然后以一些特定的方式定义前向传递函数。然后，我们在backward函数中计算梯度，然后使用optimize函数更新参数。最后，在train函数中，我们一遍遍地将数据馈送到网络中，计算损失并更新权重和偏置。