牛客题解 | 实现长短期记忆（LSTM）网络

题目

题目链接

长短期记忆（LSTM）网络是循环神经网络的一种，其特点是能够处理长序列数据。LSTM网络的数学推导可以参考相关资料。
LSTM的具体步骤如下：

1. 计算遗忘门
   \[f_t = \sigma(W_f \cdot [h_{t-1}, x_t] + b_f) \]

2. 计算输入门
   \[i_t = \sigma(W_i \cdot [h_{t-1}, x_t] + b_i) \]

3. 计算细胞状态更新
   \[c_t = f_t \cdot c_{t-1} + i_t \cdot \tanh(W_c \cdot [h_{t-1}, x_t] + b_c) \]

4. 计算输出门
   \[o_t = \sigma(W_o \cdot [h_{t-1}, x_t] + b_o) \]

其中，\(\sigma\)是sigmoid函数，表达式为\(\sigma(x) = \frac{1}{1 + e^{-x}}\)，\(\tanh\)是tanh函数，表达式为\(\tanh(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}}\)。
5. 计算隐藏状态更新

\[h_t = o_t \cdot \tanh(c_t) \]

标准代码如下

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

        # Initialize weights and biases
        self.Wf = np.random.randn(hidden_size, input_size + hidden_size)
        self.Wi = np.random.randn(hidden_size, input_size + hidden_size)
        self.Wc = np.random.randn(hidden_size, input_size + hidden_size)
        self.Wo = np.random.randn(hidden_size, input_size + hidden_size)

        self.bf = np.zeros((hidden_size, 1))
        self.bi = np.zeros((hidden_size, 1))
        self.bc = np.zeros((hidden_size, 1))
        self.bo = np.zeros((hidden_size, 1))

    def forward(self, x, initial_hidden_state, initial_cell_state):
        h = initial_hidden_state
        c = initial_cell_state
        outputs = []

        for t in range(len(x)):
            xt = x[t].reshape(-1, 1)
            concat = np.vstack((h, xt))

            # Forget gate
            ft = self.sigmoid(np.dot(self.Wf, concat) + self.bf)

            # Input gate
            it = self.sigmoid(np.dot(self.Wi, concat) + self.bi)
            c_tilde = np.tanh(np.dot(self.Wc, concat) + self.bc)

            # Cell state update
            c = ft * c + it * c_tilde

            # Output gate
            ot = self.sigmoid(np.dot(self.Wo, concat) + self.bo)

            # Hidden state update
            h = ot * np.tanh(c)

            outputs.append(h)

        return np.array(outputs), h, c

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