用python实现LSTM

版权声明：本文为博主原创文章，转载请注明出处！ https://blog.csdn.net/PoGeN1/article/details/85137125

import numpy as np


# 定义一个LSTM类（input_width是输入数据的张量大小，state_width是状态向量的维度，learning_rate是学习率）
class LstmLayer(object):
    def __init__(self, input_width, state_width, learning_rate):
        self.input_width = input_width
        self.state_width = state_width
        self.learning_rate = learning_rate
        # 门的激活函数
        self.gate_activator = SigmoidActivator()
        # 输出的激活函数
        self.output_activator = TanhActivator()
        # 当前时刻初始化为t0
        self.times = 0
        # 各个时刻的单元状态向量c
        self.c_list = self.init_state_vec()
        # 各个时刻的输出向量h
        self.h_list = self.init_state_vec()
        # 各个时刻的遗忘门f
        self.f_list = self.init_state_vec()
        # 各个时刻的输入门i
        self.i_list = self.init_state_vec()
        # 各个时刻的输出门o
        self.o_list = self.init_state_vec()
        # 各个时刻的即时状态c~
        self.ct_list = self.init_state_vec()
        # 遗忘门权重矩阵Wfh, Wfx, 偏置项bf
        self.Wfh, self.Wfx, self.bf = (self.init_weight_mat())
        # 输入门权重矩阵Wfh, Wfx, 偏置项bf
        self.Wih, self.Wix, self.bi = (self.init_weight_mat())
        # 输出门权重矩阵Wfh, Wfx, 偏置项bf
        self.Woh, self.Wox, self.bo = (self.init_weight_mat())
        # 单元状态权重矩阵Wfh, Wfx, 偏置项bf
        self.Wch, self.Wcx, self.bc = (self.init_weight_mat())

    def init_state_vec(self):
        # 初始化保存状态的向量为0

        state_vec_list = []
        state_vec_list.append(np.zeros((self.state_width, 1)))
        return state_vec_list

    def init_weight_mat(self):
        # 初始化权重矩阵

        Wh = np.random.uniform(-1e-4, 1e-4, (self.state_width, self.state_width))
        Wx = np.random.uniform(-1e-4, 1e-4, (self.state_width, self.input_width))
        b = np.zeros((self.state_width, 1))
        return Wh, Wx, b

    def forward(self, x):
        # 根据公式1-式6进行前向计算

        self.times += 1
        # 遗忘门
        fg = self.calc_gate(x, self.Wfx, self.Wfh, self.bf, self.gate_activator)
        self.f_list.append(fg)
        # 输入门
        ig = self.calc_gate(x, self.Wix, self.Wih, self.bi, self.gate_activator)
        self.i_list.append(ig)
        # 输出门
        og = self.calc_gate(x, self.Wox, self.Woh, self.bo, self.gate_activator)
        self.o_list.append(og)
        # 即时状态
        ct = self.calc_gate(x, self.Wcx, self.Wch, self.bc, self.output_activator)
        self.ct_list.append(ct)
        # 单元状态
        c = fg * self.c_list[self.times - 1] + ig * ct
        self.c_list.append(c)
        # 输出
        h = og * self.output_activator.forward(c)
        self.h_list.append(h)

    def calc_gate(self, x, Wx, Wh, b, activator):
        # 计算门

        h = self.h_list[self.times - 1]  # 上次的LSTM输出
        net = np.dot(Wh, h) + np.dot(Wx, x) + b
        gate = activator.forward(net)
        return gate

    def backward(self, x, delta_h, activator):
        # 实现LSTM训练算法

        self.calc_delta(delta_h, activator)
        self.calc_gradient(x)

    def update(self):
        # 按照梯度下降，更新权重

        self.Wfh -= self.learning_rate * self.Whf_grad
        self.Wfx -= self.learning_rate * self.Whx_grad
        self.bf -= self.learning_rate * self.bf_grad
        self.Wih -= self.learning_rate * self.Whi_grad
        self.Wix -= self.learning_rate * self.Whi_grad
        self.bi -= self.learning_rate * self.bi_grad
        self.Woh -= self.learning_rate * self.Wof_grad
        self.Wox -= self.learning_rate * self.Wox_grad
        self.bo -= self.learning_rate * self.bo_grad
        self.Wch -= self.learning_rate * self.Wcf_grad
        self.Wcx -= self.learning_rate * self.Wcx_grad
        self.bc -= self.learning_rate * self.bc_grad

    def calc_delta(self, delta_h, activator):
        # 初始化各个时刻的误差项

        self.delta_h_list = self.init_delta()  # 输出误差项
        self.delta_o_list = self.init_delta()  # 输出门误差项
        self.delta_i_list = self.init_delta()  # 输入门误差项
        self.delta_f_list = self.init_delta()  # 遗忘门误差项
        self.delta_ct_list = self.init_delta()  # 即时输出误差项

        # 保存从上一层传递下来的当前时刻的误差项
        self.delta_h_list[-1] = delta_h

        # 迭代计算每个时刻的误差项
        for k in range(self.times, 0, -1):
            self.calc_delta_k(k)

    def init_delta(self):
        #初始化误差项

        delta_list = []
        for i in range(self.times + 1):
            delta_list.append(np.zeros((self.state_width, 1)))
        return delta_list

    def calc_delta_k(self, k):
        # 根据k时刻的delta_h，计算k时刻的delta_f、delta_i、delta_o、delta_ct，以及k-1时刻的delta_h

        # 获得k时刻前向计算的值
        ig = self.i_list[k]
        og = self.o_list[k]
        fg = self.f_list[k]
        ct = self.ct_list[k]
        c = self.c_list[k]
        c_prev = self.c_list[k - 1]
        tanh_c = self.output_activator.forward(c)
        delta_k = self.delta_h_list[k]

        # 根据式9计算delta_o
        delta_o = (delta_k * tanh_c * self.gate_activator.backward(og))
        delta_f = (delta_k * og * (1 - tanh_c * tanh_c) * c_prev * self.gate_activator.backward(fg))
        delta_i = (delta_k * og * (1 - tanh_c * tanh_c) * ct * self.gate_activator.backward(ig))
        delta_ct = (delta_k * og * (1 - tanh_c * tanh_c) * ig * self.output_activator.backward(ct))
        delta_h_prev = (np.dot(delta_o.transpose(), self.Woh) + np.dot(delta_i.transpose(), self.Wih) +
            np.dot(delta_f.transpose(), self.Wfh) +  np.dot(delta_ct.transpose(), self.Wch)).transpose()

        # 保存全部delta值
        self.delta_h_list[k - 1] = delta_h_prev
        self.delta_f_list[k] = delta_f
        self.delta_i_list[k] = delta_i
        self.delta_o_list[k] = delta_o
        self.delta_ct_list[k] = delta_ct

    def calc_gradient(self, x):
        # 初始化遗忘门权重梯度矩阵和偏置项
        self.Wfh_grad, self.Wfx_grad, self.bf_grad = (self.init_weight_gradient_mat())
        # 初始化输入门权重梯度矩阵和偏置项
        self.Wih_grad, self.Wix_grad, self.bi_grad = (self.init_weight_gradient_mat())
        # 初始化输出门权重梯度矩阵和偏置项
        self.Woh_grad, self.Wox_grad, self.bo_grad = (self.init_weight_gradient_mat())
        # 初始化单元状态权重梯度矩阵和偏置项
        self.Wch_grad, self.Wcx_grad, self.bc_grad = (self.init_weight_gradient_mat())

        # 计算对上一次输出h的权重梯度
        for t in range(self.times, 0, -1):
            # 计算各个时刻的梯度
            (Wfh_grad, bf_grad,
             Wih_grad, bi_grad,
             Woh_grad, bo_grad,
             Wch_grad, bc_grad) = (self.calc_gradient_t(t))
            # 实际梯度是各时刻梯度之和
            self.Wfh_grad += Wfh_grad
            self.bf_grad += bf_grad
            self.Wih_grad += Wih_grad
            self.bi_grad += bi_grad
            self.Woh_grad += Woh_grad
            self.bo_grad += bo_grad
            self.Wch_grad += Wch_grad
            self.bc_grad += bc_grad

        # 计算对本次输入x的权重梯度
        xt = x.transpose()
        self.Wfx_grad = np.dot(self.delta_f_list[-1], xt)
        self.Wix_grad = np.dot(self.delta_i_list[-1], xt)
        self.Wox_grad = np.dot(self.delta_o_list[-1], xt)
        self.Wcx_grad = np.dot(self.delta_ct_list[-1], xt)

    def init_weight_gradient_mat(self):
        # 初始化权重矩阵

        Wh_grad = np.zeros((self.state_width, self.state_width))
        Wx_grad = np.zeros((self.state_width, self.input_width))
        b_grad = np.zeros((self.state_width, 1))
        return Wh_grad, Wx_grad, b_grad

    def calc_gradient_t(self, t):
        # 计算每个时刻t权重的梯度

        h_prev = self.h_list[t - 1].transpose()
        Wfh_grad = np.dot(self.delta_f_list[t], h_prev)
        bf_grad = self.delta_f_list[t]
        Wih_grad = np.dot(self.delta_i_list[t], h_prev)
        bi_grad = self.delta_f_list[t]
        Woh_grad = np.dot(self.delta_o_list[t], h_prev)
        bo_grad = self.delta_f_list[t]
        Wch_grad = np.dot(self.delta_ct_list[t], h_prev)
        bc_grad = self.delta_ct_list[t]
        return Wfh_grad, bf_grad, Wih_grad, bi_grad, Woh_grad, bo_grad, Wch_grad, bc_grad

    def reset_state(self):
        # 当前时刻初始化为t0
        self.times = 0
        # 各个时刻的单元状态向量c
        self.c_list = self.init_state_vec()
        # 各个时刻的输出向量h
        self.h_list = self.init_state_vec()
        # 各个时刻的遗忘门f
        self.f_list = self.init_state_vec()
        # 各个时刻的输入门i
        self.i_list = self.init_state_vec()
        # 各个时刻的输出门o
        self.o_list = self.init_state_vec()
        # 各个时刻的即时状态c~
        self.ct_list = self.init_state_vec()


def data_set():
    x = [np.array([[1], [2], [3]]),
         np.array([[2], [3], [4]])]
    d = np.array([[1], [2]])
    return x, d


class IdentityActivator():
    def forward(self, weight_input):
        return weight_input

    def backward(self, weighted_input):
        return 1.0


# 激活函数sigmoid和tanh
class SigmoidActivator(object):
    def forward(self, weighted_input):
        return 1.0 / (1.0 + np.exp(-weighted_input))

    def backward(self, output):
        return output * (1 - output)


class TanhActivator(object):
    def forward(self, weighted_input):
        return 2.0 / (1.0 + np.exp(-2 * weighted_input)) - 1.0

    def backward(self, output):
        return 1 - output * output


def gradient_check():
    #梯度检查

    # 设计一个误差函数，取所有节点输出项之和
    error_function = lambda o: o.sum()

    lstm = LstmLayer(3, 2, 1e-3)

    # 计算forward值
    x, d = data_set()
    lstm.forward(x[0])
    lstm.forward(x[1])

    # 求取sensitivity map
    sensitivity_array = np.ones(lstm.h_list[-1].shape,dtype=np.float64)
    # 计算梯度
    lstm.backward(x[1], sensitivity_array, IdentityActivator())

    # 检查梯度
    epsilon = 10e-4
    for i in range(lstm.Wfh.shape[0]):
        for j in range(lstm.Wfh.shape[1]):
            lstm.Wfh[i, j] += epsilon
            lstm.reset_state()
            lstm.forward(x[0])
            lstm.forward(x[1])
            err1 = error_function(lstm.h_list[-1])
            lstm.Wfh[i, j] -= 2 * epsilon
            lstm.reset_state()
            lstm.forward(x[0])
            lstm.forward(x[1])
            err2 = error_function(lstm.h_list[-1])
            expect_grad = (err1 - err2) / (2 * epsilon)
            lstm.Wfh[i, j] += epsilon
            print('weights(%d,%d): expected - actural %.4e - %.4e' % (
                i, j, expect_grad, lstm.Wfh_grad[i, j]))

    return lstm


def test():
    l = LstmLayer(3, 2, 1e-3)
    x, d = data_set()
    l.forward(x[0])
    l.forward(x[1])
    l.backward(x[1], d, IdentityActivator())
    return l



gradient_check()