import numpy as np from functools import reduce from model import element_wise_op, ReluActivator, IdentityActivator, SigmoidActivator, TanhActivator class LstmLayer(object): """ 实现LSTM层 """ def __init__(self, input_width, state_width, learning_rate): """设置超参数，初始化LSTM层 :param input_width: 输入维度 :param state_width: 保存状态的向量维度 :param learning_rate: 学习速率 """ 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 :return: """ state_vec_list = [np.zeros((self.state_width, 1))] return state_vec_list def init_weight_mat(self): """初始化权重矩阵 :return: """ 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): """前向计算 :param x: 输入 :return: """ 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 :param x: 输入 :param Wx: 权重矩阵Wx :param Wh: 权重矩阵Wh :param b: 偏置值 :param activator: 激活函数 :return: """ 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 :param x: 输入 :param delta_h: 上层误差矩阵 :param activator: 激活函数 :return: """ self.calc_delta(delta_h, activator) self.calc_gradient(x) def calc_delta(self, delta_h, activator): """计算误差 :param delta_h: 上层误差矩阵 :param activator: 激活函数 :return: """ # 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 :param k: 时刻 :return: """ # 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): """计算梯度 :param x: 输入 :return: """ # 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 :param t: 时刻 :return: """ 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 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 reset_state(self): """ 重置内部状态 """ # 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()