lstm python

以下是一个基本的LSTM的Python实现：

import numpy as np

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

        # 初始化权重
        self.Wf = np.random.randn(input_size + hidden_size, hidden_size)
        self.Wi = np.random.randn(input_size + hidden_size, hidden_size)
        self.Wc = np.random.randn(input_size + hidden_size, hidden_size)
        self.Wo = np.random.randn(input_size + hidden_size, hidden_size)
        self.Wy = np.random.randn(hidden_size, output_size)

        # 初始化偏差
        self.bf = np.zeros((1, hidden_size))
        self.bi = np.zeros((1, hidden_size))
        self.bc = np.zeros((1, hidden_size))
        self.bo = np.zeros((1, hidden_size))
        self.by = np.zeros((1, output_size))

    def sigmoid(self, x):
        return 1 / (1 + np.exp(-x))

    def forward(self, x, h_prev, c_prev):
        # 合并输入和前一个隐藏层状态
        input = np.column_stack((h_prev, x))

        # 计算遗忘门
        f = self.sigmoid(np.dot(input, self.Wf) + self.bf)

        # 计算输入门
        i = self.sigmoid(np.dot(input, self.Wi) + self.bi)

        # 计算新候选值
        c_bar = np.tanh(np.dot(input, self.Wc) + self.bc)

        # 计算新的细胞状态
        c = f * c_prev + i * c_bar

        # 计算输出门
        o = self.sigmoid(np.dot(input, self.Wo) + self.bo)

        # 计算新的隐藏状态
        h = o * np.tanh(c)

        # 计算输出
        output = np.dot(h, self.Wy) + self.by

        # 保存状态
        self.x = x
        self.h_prev = h
        self.c_prev = c

        return output, h, c

    def backward(self, output, y, dh_next, dc_next, learning_rate):
        # 计算输出误差
        dout = output - y

        # 计算Wy和by的梯度
        dWy = np.dot(self.h_prev.T, dout)
        dby = np.sum(dout, axis=0, keepdims=True)

        # 计算dh和dc的梯度
        dh = np.dot(dout, self.Wy.T) + dh_next
        dc = dc_next

        # 计算输出门的梯度
        do = dh * np.tanh(self.c_prev)
        do = do * (1 - self.sigmoid(np.dot(self.x, self.Wo) + self.bo))
        dWo = np.dot(self.x.T, do)
        dbo = np.sum(do, axis=0, keepdims=True)

        # 计算新候选值的梯度
        dc_bar = dh * self.sigmoid(np.dot(self.x, self.Wc) + self.bc)
        dc_bar = dc_bar * (1 - np.tanh(np.dot(self.x, self.Wc) + self.bc) ** 2)
        dWc = np.dot(self.x.T, dc_bar)
        dbc = np.sum(dc_bar, axis=0, keepdims=True)

        # 计算输入门的梯度
        di = dh * self.tanh(self.c_bar)
        di = di * (1 - self.sigmoid(np.dot(self.x, self.Wi) + self.bi))
        dWi = np.dot(self.x.T, di)
        dbi = np.sum(di, axis=0, keepdims=True)

        # 计算遗忘门的梯度
        df = dc_prev * self.c_prev
        df = df * (1 - self.sigmoid(np.dot(self.x, self.Wf) + self.bf))
        dWf = np.dot(self.x.T, df)
        dbf = np.sum(df, axis=0, keepdims=True)

        # 计算x的梯度
        dx = np.dot(di, self.Wi.T) + np.dot(df, self.Wf.T) + \
             np.dot(dc_bar, self.Wc.T) + np.dot(do, self.Wo.T)

        # 保存梯度
        self.dWf = dWf
        self.dWi = dWi
        self.dWc = dWc
        self.dWo = dWo
        self.dWy = dWy

        self.dbf = dbf
        self.dbi = dbi
        self.dbc = dbc
        self.dbo = dbo
        self.dby = dby

        # 更新权重和偏差
        self.Wf -= learning_rate * self.dWf
        self.Wi -= learning_rate * self.dWi
        self.Wc -= learning_rate * self.dWc
        self.Wo -= learning_rate * self.dWo
        self.Wy -= learning_rate * self.dWy

        self.bf -= learning_rate * self.dbf
        self.bi -= learning_rate * self.dbi
        self.bc -= learning_rate * self.dbc
        self.bo -= learning_rate * self.dbo
        self.by -= learning_rate * self.dby

        return dx, dh_prev, dc_prev

这个实现包含了前向传播和反向传播的代码。如果你想使用这个LSTM实现，你需要在初始化时指定输入大小、隐藏层大小和输出大小。然后在训练时，你需要传入输入、前一个隐藏状态和前一个细胞状态，然后调用`forward`方法计算输出并返回当前的隐藏状态和细胞状态。接着，你需要计算输出误差并调用`backward`方法计算梯度并更新权重和偏差。最后，你需要将当前的隐藏状态和细胞状态传递到下一个时间步骤。