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LSTM的记忆能力实验

news 2026/2/10 1:16:30

长短期记忆网络（Long Short-Term Memory Network，LSTM）是一种可以有效缓解长程依赖问题的循环神经网络．LSTM 的特点是引入了一个新的内部状态（Internal State) $C\xi R ^{D}$ 和门控机制（Gating Mechanism）．不同时刻的内部状态以近似线性的方式进行传递，从而缓解梯度消失或梯度爆炸问题．同时门控机制进行信息筛选，可以有效地增加记忆能力．例如，输入门可以让网络忽略无关紧要的输入信息，遗忘门可以使得网络保留有用的历史信息．在上一节的数字求和任务中，如果模型能够记住前两个非零数字，同时忽略掉一些不重要的干扰信息，那么即时序列很长，模型也有效地进行预测.

LSTM 模型在第 t 步时，循环单元的内部结构如图6.10所示．

图6.10 LSTM网络的循环单元结构

提醒：为了和代码的实现保存一致性，这里使用形状为 (样本数量 × 序列长度 × 特征维度) 的张量来表示一组样本.

6.3.1 模型构建

在本实验中，我们将使用第6.1.2.4节中定义Model_RNN4SeqClass模型，并构建 LSTM 算子．只需要实例化 LSTM 算，并传入Model_RNN4SeqClass模型，就可以用 LSTM 进行数字求和实验

6.3.1.1 LSTM层

LSTM层的代码与SRN层结构相似，只是在SRN层的基础上增加了内部状态、输入门、遗忘门和输出门的定义和计算。这里LSTM层的输出也依然为序列的最后一个位置的隐状态向量。代码实现如下：

import torch
import torch.nn.functional as F
from torch import nn# 声明LSTM和相关参数
class LSTM(nn.Module):def __init__(self, input_size, hidden_size, Wi_attr=None, Wf_attr=None, Wo_attr=None, Wc_attr=None,Ui_attr=None, Uf_attr=None, Uo_attr=None, Uc_attr=None, bi_attr=None, bf_attr=None,bo_attr=None, bc_attr=None):super(LSTM, self).__init__()self.input_size = input_sizeself.hidden_size = hidden_sizeW_i = torch.randn([input_size, hidden_size])W_f = torch.randn([input_size, hidden_size])W_o = torch.randn([input_size, hidden_size])W_c = torch.randn([input_size, hidden_size])U_i = torch.randn([hidden_size, hidden_size])U_f = torch.randn([hidden_size, hidden_size])U_o = torch.randn([hidden_size, hidden_size])U_c = torch.randn([hidden_size, hidden_size])b_i = torch.randn([1, hidden_size])b_f = torch.randn([1, hidden_size])b_o = torch.randn([1, hidden_size])b_c = torch.randn([1, hidden_size])self.W_i = torch.nn.Parameter(torch.nn.init.xavier_uniform_(torch.as_tensor(W_i, dtype=torch.float32), gain=1.0))# 初始化模型参数self.W_f = torch.nn.Parameter(torch.nn.init.xavier_uniform_(torch.as_tensor(W_f, dtype=torch.float32), gain=1.0))self.W_o = torch.nn.Parameter(torch.nn.init.xavier_uniform_(torch.as_tensor(W_o, dtype=torch.float32), gain=1.0))self.W_c = torch.nn.Parameter(torch.nn.init.xavier_uniform_(torch.as_tensor(W_c, dtype=torch.float32), gain=1.0))self.U_i = torch.nn.Parameter(torch.nn.init.xavier_uniform_(torch.as_tensor(U_i, dtype=torch.float32), gain=1.0))self.U_f = torch.nn.Parameter(torch.nn.init.xavier_uniform_(torch.as_tensor(U_f, dtype=torch.float32), gain=1.0))self.U_o = torch.nn.Parameter(torch.nn.init.xavier_uniform_(torch.as_tensor(U_o, dtype=torch.float32), gain=1.0))self.U_c = torch.nn.Parameter(torch.nn.init.xavier_uniform_(torch.as_tensor(U_c, dtype=torch.float32), gain=1.0))self.b_i = torch.nn.Parameter(torch.nn.init.xavier_uniform_(torch.as_tensor(b_i, dtype=torch.float32), gain=1.0))self.b_f = torch.nn.Parameter(torch.nn.init.xavier_uniform_(torch.as_tensor(b_f, dtype=torch.float32), gain=1.0))self.b_o = torch.nn.Parameter(torch.nn.init.xavier_uniform_(torch.as_tensor(b_o, dtype=torch.float32), gain=1.0))self.b_c = torch.nn.Parameter(torch.nn.init.xavier_uniform_(torch.as_tensor(b_c, dtype=torch.float32), gain=1.0))# 初始化状态向量和隐状态向量def init_state(self, batch_size):hidden_state = torch.zeros(size=[batch_size, self.hidden_size], dtype=torch.float32)cell_state = torch.zeros(size=[batch_size, self.hidden_size], dtype=torch.float32)return hidden_state, cell_state# 定义前向计算def forward(self, inputs, states=None):# inputs: 输入数据，其shape为batch_size x seq_len x input_sizebatch_size, seq_len, input_size = inputs.shape# 初始化起始的单元状态和隐状态向量，其shape为batch_size x hidden_sizeif states is None:states = self.init_state(batch_size)hidden_state, cell_state = states# 执行LSTM计算，包括：输入门、遗忘门和输出门、候选内部状态、内部状态和隐状态向量for step in range(seq_len):# 获取当前时刻的输入数据step_input: 其shape为batch_size x input_sizestep_input = inputs[:, step, :]# 计算输入门, 遗忘门和输出门, 其shape为：batch_size x hidden_sizeI_gate = F.sigmoid(torch.matmul(step_input, self.W_i) + torch.matmul(hidden_state, self.U_i) + self.b_i)F_gate = F.sigmoid(torch.matmul(step_input, self.W_f) + torch.matmul(hidden_state, self.U_f) + self.b_f)O_gate = F.sigmoid(torch.matmul(step_input, self.W_o) + torch.matmul(hidden_state, self.U_o) + self.b_o)# 计算候选状态向量, 其shape为：batch_size x hidden_sizeC_tilde = F.tanh(torch.matmul(step_input, self.W_c) + torch.matmul(hidden_state, self.U_c) + self.b_c)# 计算单元状态向量, 其shape为：batch_size x hidden_sizecell_state = F_gate * cell_state + I_gate * C_tilde# 计算隐状态向量，其shape为：batch_size x hidden_sizehidden_state = O_gate * F.tanh(cell_state)return hidden_stateWi_attr = torch.tensor([[0.1, 0.2], [0.1, 0.2]])
Wf_attr = torch.tensor([[0.1, 0.2], [0.1, 0.2]])
Wo_attr = torch.tensor([[0.1, 0.2], [0.1, 0.2]])
Wc_attr = torch.tensor([[0.1, 0.2], [0.1, 0.2]])
Ui_attr = torch.tensor([[0.0, 0.1], [0.1, 0.0]])
Uf_attr = torch.tensor([[0.0, 0.1], [0.1, 0.0]])
Uo_attr = torch.tensor([[0.0, 0.1], [0.1, 0.0]])
Uc_attr = torch.tensor([[0.0, 0.1], [0.1, 0.0]])
bi_attr = torch.tensor([[0.1, 0.1]])
bf_attr = torch.tensor([[0.1, 0.1]])
bo_attr = torch.tensor([[0.1, 0.1]])
bc_attr = torch.tensor([[0.1, 0.1]])lstm = LSTM(2, 2, Wi_attr=Wi_attr, Wf_attr=Wf_attr, Wo_attr=Wo_attr, Wc_attr=Wc_attr,Ui_attr=Ui_attr, Uf_attr=Uf_attr, Uo_attr=Uo_attr, Uc_attr=Uc_attr,bi_attr=bi_attr, bf_attr=bf_attr, bo_attr=bo_attr, bc_attr=bc_attr)inputs = torch.tensor([[[1, 0]]], dtype=torch.float32)
hidden_state = lstm(inputs)
print(hidden_state)

这里我们可以将自己实现的SRN和Paddle框架内置的SRN返回的结果进行打印展示，实现代码如下。

# 这里创建一个随机数组作为测试数据，数据shape为batch_size x seq_len x input_size
batch_size, seq_len, input_size = 8, 20, 32
inputs = torch.randn(size=[batch_size, seq_len, input_size])# 设置模型的hidden_size
hidden_size = 32
torch_lstm = nn.LSTM(input_size, hidden_size)
self_lstm = LSTM(input_size, hidden_size)self_hidden_state = self_lstm(inputs)
torch_outputs, (torch_hidden_state, torch_cell_state) = torch_lstm(inputs)print("self_lstm hidden_state: ", self_hidden_state.shape)
print("torch_lstm outpus:", torch_outputs.shape)
print("torch_lstm hidden_state:", torch_hidden_state.shape)
print("torch_lstm cell_state:", torch_cell_state.shape)

可以看到，自己实现的LSTM由于没有考虑多层因素，因此没有层次这个维度，因此其输出shape为[8, 32]。同时由于在以上代码使用Paddle内置API实例化LSTM时，默认定义的是1层的单向SRN，因此其shape为[1, 8, 32]，同时隐状态向量为[8,20, 32].

接下来，我们可以将自己实现的LSTM与Paddle内置的LSTM在输出值的精度上进行对比 ,在进行实验时，首先定义输入数据inputs，然后将该数据分别传入Paddle内置的LSTM与自己实现的LSTM模型中，最后通过对比两者的隐状态输出向量。

import torchtorch.manual_seed(0)# 这里创建一个随机数组作为测试数据，数据shape为batch_size x seq_len x input_size
batch_size, seq_len, input_size, hidden_size = 2, 5, 10, 10
inputs = torch.randn(size=[batch_size, seq_len, input_size])# 设置模型的hidden_size
bih_attr = torch.nn.Parameter(torch.zeros([4 * hidden_size, ]))
paddle_lstm = nn.LSTM(input_size, hidden_size)
paddle_lstm.bias_ih_l0 = bih_attr
paddle_lstm.bias_ih_l1 = bih_attr
paddle_lstm.bias_ih_l2 = bih_attr
paddle_lstm.bias_ih_l3 = bih_attr
paddle_lstm.bias_ih_l4 = bih_attr# 获取paddle_lstm中的参数，并设置相应的paramAttr,用于初始化lstm
print(paddle_lstm.weight_ih_l0.T.shape)
chunked_W = torch.split(paddle_lstm.weight_ih_l0.T, split_size_or_sections=10, dim=-1)
chunked_U = torch.split(paddle_lstm.weight_hh_l0.T, split_size_or_sections=10, dim=-1)
chunked_b = torch.split(paddle_lstm.bias_hh_l0.T, split_size_or_sections=10, dim=-1)
print(chunked_b[0].shape, chunked_b[1].shape, chunked_b[2].shape)
Wi_attr = torch.tensor(chunked_W[0])
Wf_attr = torch.tensor(chunked_W[1])
Wc_attr = torch.tensor(chunked_W[2])
Wo_attr = torch.tensor(chunked_W[3])
Ui_attr = torch.tensor(chunked_U[0])
Uf_attr = torch.tensor(chunked_U[1])
Uc_attr = torch.tensor(chunked_U[2])
Uo_attr = torch.tensor(chunked_U[3])
bi_attr = torch.tensor(chunked_b[0])
bf_attr = torch.tensor(chunked_b[1])
bc_attr = torch.tensor(chunked_b[2])
bo_attr = torch.tensor(chunked_b[3])
self_lstm = LSTM(input_size, hidden_size, Wi_attr=Wi_attr, Wf_attr=Wf_attr, Wo_attr=Wo_attr, Wc_attr=Wc_attr,Ui_attr=Ui_attr, Uf_attr=Uf_attr, Uo_attr=Uo_attr, Uc_attr=Uc_attr,bi_attr=bi_attr, bf_attr=bf_attr, bo_attr=bo_attr, bc_attr=bc_attr)# 进行前向计算，获取隐状态向量，并打印展示
self_hidden_state = self_lstm(inputs)
paddle_outputs, (paddle_hidden_state, _) = paddle_lstm(inputs)
print("paddle SRN:\n", paddle_hidden_state.detach().numpy().squeeze(0))
print("self SRN:\n", self_hidden_state.detach().numpy())

可以看到，两者的输出基本是一致的。另外，还可以进行对比两者在运算速度方面的差异。代码实现如下：

import time# 这里创建一个随机数组作为测试数据，数据shape为batch_size x seq_len x input_size
batch_size, seq_len, input_size = 8, 20, 32
inputs = torch.randn(size=[batch_size, seq_len, input_size])# 设置模型的hidden_size
hidden_size = 32
self_lstm = LSTM(input_size, hidden_size)
paddle_lstm = nn.LSTM(input_size, hidden_size)# 计算自己实现的SRN运算速度
model_time = 0
for i in range(100):strat_time = time.time()hidden_state = self_lstm(inputs)# 预热10次运算，不计入最终速度统计if i < 10:continueend_time = time.time()model_time += (end_time - strat_time)
avg_model_time = model_time / 90
print('self_lstm speed:', avg_model_time, 's')# 计算Paddle内置的SRN运算速度
model_time = 0
for i in range(100):strat_time = time.time()outputs, (hidden_state, cell_state) = paddle_lstm(inputs)# 预热10次运算，不计入最终速度统计if i < 10:continueend_time = time.time()model_time += (end_time - strat_time)
avg_model_time = model_time / 90
print('paddle_lstm speed:', avg_model_time, 's')

可以看到，由于Paddle框架的LSTM底层采用了C++实现并进行优化，Paddle框架内置的LSTM运行效率远远高于自己实现的LSTM。

6.3.1.2 模型汇总

在本节实验中，我们将使用6.1.2.4的Model_RNN4SeqClass作为预测模型，不同在于在实例化时将传入实例化的LSTM层。

动手联系6.2 在我们手动实现的LSTM算子中，是逐步计算每个时刻的隐状态。请思考如何实现更加高效的LSTM算子。

6.3.2 模型训练

6.3.2.1 训练指定长度的数字预测模型

本节将基于RunnerV3类进行训练，首先定义模型训练的超参数，并保证和简单循环网络的超参数一致. 然后定义一个train函数，其可以通过指定长度的数据集，并进行训练. 在train函数中，首先加载长度为length的数据，然后实例化各项组件并创建对应的Runner，然后训练该Runner。同时在本节将使用4.5.4节定义的准确度（Accuracy）作为评估指标，代码实现如下：

import os
import random
import numpy as np
from nndl4.runner import RunnerV3# 训练轮次
num_epochs = 500
# 学习率
lr = 0.001
# 输入数字的类别数
num_digits = 10
# 将数字映射为向量的维度
input_size = 32
# 隐状态向量的维度
hidden_size = 32
# 预测数字的类别数
num_classes = 19
# 批大小 
batch_size = 8
# 模型保存目录
save_dir = "./checkpoints"from torch.utils.data import Dataset,DataLoader
import torch
class DigitSumDataset(Dataset):def __init__(self, data):self.data = datadef __getitem__(self, idx):example = self.data[idx]seq = torch.tensor(example[0], dtype=torch.int64)label = torch.tensor(example[1], dtype=torch.int64)return seq, labeldef __len__(self):return len(self.data)
class Embedding(nn.Module):def __init__(self, num_embeddings, embedding_dim):super(Embedding, self).__init__()self.W = nn.init.xavier_uniform_(torch.empty(num_embeddings, embedding_dim),gain=1.0)def forward(self, inputs):# 根据索引获取对应词向量embs = self.W[inputs]return embs# emb_layer = Embedding(10, 5)
# inputs = torch.tensor([0, 1, 2, 3])
# emb_layer(inputs)# 基于RNN实现数字预测的模型
class Model_RNN4SeqClass(nn.Module):def __init__(self, model, num_digits, input_size, hidden_size, num_classes):super(Model_RNN4SeqClass, self).__init__()# 传入实例化的RNN层，例如SRNself.rnn_model = model# 词典大小self.num_digits = num_digits# 嵌入向量的维度self.input_size = input_size# 定义Embedding层self.embedding = Embedding(num_digits, input_size)# 定义线性层self.linear = nn.Linear(hidden_size, num_classes)def forward(self, inputs):# 将数字序列映射为相应向量inputs_emb = self.embedding(inputs)# 调用RNN模型hidden_state = self.rnn_model(inputs_emb)# 使用最后一个时刻的状态进行数字预测logits = self.linear(hidden_state)return logits
# 可以设置不同的length进行不同长度数据的预测实验
def train(length):print(f"\n====> Training LSTM with data of length {length}.")np.random.seed(0)random.seed(0)# 加载长度为length的数据data_path = f"./datasets/{length}"train_examples, dev_examples, test_examples = load_data(data_path)train_set, dev_set, test_set = DigitSumDataset(train_examples), DigitSumDataset(dev_examples), DigitSumDataset(test_examples)train_loader = DataLoader(train_set, batch_size=batch_size)dev_loader = DataLoader(dev_set, batch_size=batch_size)test_loader = DataLoader(test_set, batch_size=batch_size)# 实例化模型base_model = LSTM(input_size, hidden_size)model = Model_RNN4SeqClass(base_model, num_digits, input_size, hidden_size, num_classes)# 指定优化器optimizer = torch.optim.Adam(lr=lr, params=model.parameters())# 定义评价指标metric = Accuracy()# 定义损失函数loss_fn = torch.nn.CrossEntropyLoss()# 基于以上组件，实例化Runnerrunner = RunnerV3(model, optimizer, loss_fn, metric)# 进行模型训练model_save_path = os.path.join(save_dir, f"best_lstm_model_{length}.pdparams")runner.train(train_loader, dev_loader, num_epochs=num_epochs, eval_steps=100, log_steps=100, save_path=model_save_path)return runner

6.3.2.2 多组训练

接下来，分别进行数据长度为10, 15, 20, 25, 30, 35的数字预测模型训练实验，训练后的runner保存至runners字典中。

import os
import random
import torch
import numpy as np# 训练轮次
num_epochs = 500
# 学习率
lr = 0.001
# 输入数字的类别数
num_digits = 10
# 将数字映射为向量的维度
input_size = 32
# 隐状态向量的维度
hidden_size = 32
# 预测数字的类别数
num_classes = 19
# 批大小 
batch_size = 8
# 模型保存目录
save_dir = "./checkpoints"# 可以设置不同的length进行不同长度数据的预测实验
def train(length):print(f"\n====> Training LSTM with data of length {length}.")np.random.seed(0)random.seed(0)# 加载长度为length的数据data_path = f"./datasets/{length}"train_examples, dev_examples, test_examples = load_data(data_path)train_set, dev_set, test_set = DigitSumDataset(train_examples), DigitSumDataset(dev_examples), DigitSumDataset(test_examples)train_loader = DataLoader(train_set, batch_size=batch_size)dev_loader = DataLoader(dev_set, batch_size=batch_size)test_loader = DataLoader(test_set, batch_size=batch_size)# 实例化模型base_model = LSTM(input_size, hidden_size)model = Model_RNN4SeqClass(base_model, num_digits, input_size, hidden_size, num_classes) # 指定优化器optimizer = torch.optim.Adam(lr=lr, params=model.parameters())# 定义评价指标metric = Accuracy()# 定义损失函数loss_fn = torch.nn.CrossEntropyLoss()# 基于以上组件，实例化Runnerrunner = RunnerV3(model, optimizer, loss_fn, metric)# 进行模型训练model_save_path = os.path.join(save_dir, f"best_lstm_model_{length}.pdparams")runner.train(train_loader, dev_loader, num_epochs=num_epochs, eval_steps=100, log_steps=100, save_path=model_save_path)return runner

其中 load_data(data_path) 函数与之前的函数有差别，修改后为

# 加载数据
def load_data(data_path):# 加载训练集train_examples = []train_path = os.path.join(data_path, "train.txt")with open(train_path, "r", encoding="utf-8") as f:for line in f.readlines():# 解析一行数据，将其处理为数字序列seq和标签labelitems = line.strip().split("\t")seq = [int(i) for i in items[0].split(" ")]label = int(items[1])train_examples.append((seq, label))# 加载验证集dev_examples = []dev_path = os.path.join(data_path, "dev.txt")with open(dev_path, "r", encoding="utf-8") as f:for line in f.readlines():# 解析一行数据，将其处理为数字序列seq和标签labelitems = line.strip().split("\t")seq = [int(i) for i in items[0].split(" ")]label = int(items[1])dev_examples.append((seq, label))# 加载测试集test_examples = []test_path = os.path.join(data_path, "test.txt")with open(test_path, "r", encoding="utf-8") as f:for line in f.readlines():# 解析一行数据，将其处理为数字序列seq和标签labelitems = line.strip().split("\t")seq = [int(i) for i in items[0].split(" ")]label = int(items[1])test_examples.append((seq, label))return train_examples, dev_examples, test_examples

6.3.2.3 损失曲线展示

分别画出基于LSTM的各个长度的数字预测模型训练过程中，在训练集和验证集上的损失曲线，代码实现如下：

# 画出训练过程中的损失图
for length in lengths:runner = lstm_runners[length]fig_name = f"./images/6.11_{length}.pdf"plot_training_loss(runner, fig_name, sample_step=100)

同SRN模型一样，随着序列长度的增加，训练集上的损失逐渐不稳定，验证集上的损失整体趋向于变大，这说明当序列长度增加时，保持长期依赖的能力同样在逐渐变弱. 同RNN的图相比，LSTM模型在序列长度增加时，收敛情况比SRN模型更好。

6.3.3 模型评价

6.3.3.1 在测试集上进行模型评价

使用测试数据对在训练过程中保存的最好模型进行评价，观察模型在测试集上的准确率. 同时获取模型在训练过程中在验证集上最好的准确率，实现代码如下:

lstm_dev_scores = []
lstm_test_scores = []
for length in lengths:print(f"Evaluate LSTM with data length {length}.")runner = lstm_runners[length]# 加载训练过程中效果最好的模型model_path = os.path.join(save_dir, f"best_lstm_model_{length}.pdparams")runner.load_model(model_path)# 加载长度为length的数据data_path = f"./datasets/{length}"train_examples, dev_examples, test_examples = load_data(data_path)test_set = DigitSumDataset(test_examples)test_loader = DataLoader(test_set, batch_size=batch_size)# 使用测试集评价模型，获取测试集上的预测准确率score, _ = runner.evaluate(test_loader)lstm_test_scores.append(score)lstm_dev_scores.append(max(runner.dev_scores))for length, dev_score, test_score in zip(lengths, lstm_dev_scores, lstm_test_scores):print(f"[LSTM] length:{length}, dev_score: {dev_score}, test_score: {test_score: .5f}")

6.3.3.2 模型在不同长度的数据集上的准确率变化图

接下来，将SRN和LSTM在不同长度的验证集和测试集数据上的准确率绘制成图片，以方面观察。

import matplotlib.pyplot as plt
plt.plot(lengths, lstm_dev_scores, '-o', color='#e8609b',  label="LSTM Dev Accuracy")
plt.plot(lengths, lstm_test_scores,'-o', color='#000000', label="LSTM Test Accuracy")#绘制坐标轴和图例
plt.ylabel("accuracy", fontsize='large')
plt.xlabel("sequence length", fontsize='large')
plt.legend(loc='lower left', fontsize='x-large')fig_name = "./images/6.12.pdf"
plt.savefig(fig_name)
plt.show()

展示了LSTM模型与SRN模型在不同长度数据集上的准确度对比。随着数据集长度的增加，LSTM模型在验证集和测试集上的准确率整体也趋向于降低；同时LSTM模型的准确率显著高于SRN模型，表明LSTM模型保持长期依赖的能力要优于SRN模型.

6.3.3.3 LSTM模型门状态和单元状态的变化

LSTM模型通过门控机制控制信息的单元状态的更新，这里可以观察当LSTM在处理一条数字序列的时候，相应门和单元状态是如何变化的。首先需要对以上LSTM模型实现代码中，定义相应列表进行存储这些门和单元状态在每个时刻的向量。

# 声明LSTM和相关参数
class LSTM(nn.Module):def __init__(self, input_size, hidden_size, Wi_attr=None, Wf_attr=None, Wo_attr=None, Wc_attr=None,Ui_attr=None, Uf_attr=None, Uo_attr=None, Uc_attr=None, bi_attr=None, bf_attr=None,bo_attr=None, bc_attr=None):super(LSTM, self).__init__()self.input_size = input_sizeself.hidden_size = hidden_size# 初始化模型参数if Wi_attr==None:Wi=torch.zeros(size=[input_size, hidden_size], dtype=torch.float32)else:Wi = torch.tensor(Wi_attr, dtype=torch.float32)self.W_i = torch.nn.Parameter(Wi)if Wf_attr==None:Wf=torch.zeros(size=[input_size, hidden_size], dtype=torch.float32)else:Wf = torch.tensor(Wf_attr, dtype=torch.float32)self.W_f = torch.nn.Parameter(Wf)if Wo_attr==None:Wo=torch.zeros(size=[input_size, hidden_size], dtype=torch.float32)else:Wo = torch.tensor(Wo_attr, dtype=torch.float32)self.W_o =torch.nn.Parameter(Wo)if Wc_attr==None:Wc=torch.zeros(size=[input_size, hidden_size], dtype=torch.float32)else:Wc = torch.tensor(Wc_attr, dtype=torch.float32)self.W_c = torch.nn.Parameter(Wc)if Ui_attr==None:Ui = torch.zeros(size=[hidden_size, hidden_size], dtype=torch.float32)else:Ui = torch.tensor(Ui_attr, dtype=torch.float32)self.U_i = torch.nn.Parameter(Ui)if Uf_attr == None:Uf = torch.zeros(size=[hidden_size, hidden_size], dtype=torch.float32)else:Uf = torch.tensor(Uf_attr, dtype=torch.float32)self.U_f = torch.nn.Parameter(Uf)if Uo_attr == None:Uo = torch.zeros(size=[hidden_size, hidden_size], dtype=torch.float32)else:Uo = torch.tensor(Uo_attr, dtype=torch.float32)self.U_o = torch.nn.Parameter(Uo)if Uc_attr == None:Uc = torch.zeros(size=[hidden_size, hidden_size], dtype=torch.float32)else:Uc = torch.tensor(Uc_attr, dtype=torch.float32)self.U_c = torch.nn.Parameter(Uc)if bi_attr == None:bi = torch.zeros(size=[1,hidden_size], dtype=torch.float32)else:bi = torch.tensor(bi_attr, dtype=torch.float32)self.b_i = torch.nn.Parameter(bi)if bf_attr == None:bf = torch.zeros(size=[1,hidden_size], dtype=torch.float32)else:bf = torch.tensor(bf_attr, dtype=torch.float32)self.b_f = torch.nn.Parameter(bf)if bo_attr == None:bo = torch.zeros(size=[1,hidden_size], dtype=torch.float32)else:bo = torch.tensor(bo_attr, dtype=torch.float32)self.b_o = torch.nn.Parameter(bo)if bc_attr == None:bc = torch.zeros(size=[1,hidden_size], dtype=torch.float32)else:bc = torch.tensor(bc_attr, dtype=torch.float32)self.b_c = torch.nn.Parameter(bc)# 初始化状态向量和隐状态向量def init_state(self, batch_size):hidden_state = torch.zeros(size=[batch_size, self.hidden_size], dtype=torch.float32)cell_state = torch.zeros(size=[batch_size, self.hidden_size], dtype=torch.float32)return hidden_state, cell_state# 定义前向计算def forward(self, inputs, states=None):# inputs: 输入数据，其shape为batch_size x seq_len x input_sizebatch_size, seq_len, input_size = inputs.shape# 初始化起始的单元状态和隐状态向量，其shape为batch_size x hidden_sizeif states is None:states = self.init_state(batch_size)hidden_state, cell_state = states# 定义相应的门状态和单元状态向量列表self.Is = []self.Fs = []self.Os = []self.Cs = []# 初始化状态向量和隐状态向量cell_state = torch.zeros(size=[batch_size, self.hidden_size], dtype=torch.float32)hidden_state = torch.zeros(size=[batch_size, self.hidden_size], dtype=torch.float32)# 执行LSTM计算，包括：隐藏门、输入门、遗忘门、候选状态向量、状态向量和隐状态向量for step in range(seq_len):input_step = inputs[:, step, :]I_gate = F.sigmoid(torch.matmul(input_step, self.W_i) + torch.matmul(hidden_state, self.U_i) + self.b_i)F_gate = F.sigmoid(torch.matmul(input_step, self.W_f) + torch.matmul(hidden_state, self.U_f) + self.b_f)O_gate = F.sigmoid(torch.matmul(input_step, self.W_o) + torch.matmul(hidden_state, self.U_o) + self.b_o)C_tilde = F.tanh(torch.matmul(input_step, self.W_c) + torch.matmul(hidden_state, self.U_c) + self.b_c)cell_state = F_gate * cell_state + I_gate * C_tildehidden_state = O_gate * F.tanh(cell_state)# 存储门状态向量和单元状态向量self.Is.append(I_gate.detach().numpy().copy())self.Fs.append(F_gate.detach().numpy().copy())self.Os.append(O_gate.detach().numpy().copy())self.Cs.append(cell_state.detach().numpy().copy())return hidden_state

接下来，需要使用新的LSTM模型，重新实例化一个runner，本节使用序列长度为10的模型进行此项实验，因此需要加载序列长度为10的模型。

# 实例化模型
base_model = LSTM(input_size, hidden_size)
model = Model_RNN4SeqClass(base_model, num_digits, input_size, hidden_size, num_classes) 
# 指定优化器
optimizer = torch.optim.Adam(lr=lr, params=model.parameters())
# 定义评价指标
metric = Accuracy()
# 定义损失函数
loss_fn = torch.nn.CrossEntropyLoss()
# 基于以上组件，重新实例化Runner
runner = RunnerV3(model, optimizer, loss_fn, metric)length = 10
# 加载训练过程中效果最好的模型
model_path = os.path.join(save_dir, f"best_lstm_model_{length}.pdparams")
runner.load_model(model_path)

接下来，给定一条数字序列，并使用数字预测模型进行数字预测，这样便会将相应的门状态和单元状态向量保存至模型中. 然后分别从模型中取出这些向量，并将这些向量进行绘制展示。代码实现如下：


import seaborn as sns
import matplotlib.pyplot as plt
def plot_tensor(inputs, tensor,  save_path, vmin=0, vmax=1):tensor = np.stack(tensor, axis=0)tensor = np.squeeze(tensor, 1).Tplt.figure(figsize=(16,6))# vmin, vmax定义了色彩图的上下界ax = sns.heatmap(tensor, vmin=vmin, vmax=vmax) ax.set_xticklabels(inputs)ax.figure.savefig(save_path)# 定义模型输入
inputs = [6, 7, 0, 0, 1, 0, 0, 0, 0, 0]
X = torch.as_tensor(inputs.copy())
X = X.unsqueeze(0)
# 进行模型预测，并获取相应的预测结果
logits = runner.predict(X)
predict_label = torch.argmax(logits, dim=-1)
print(f"predict result: {predict_label.numpy()[0]}")# 输入门
Is = runner.model.rnn_model.Is
plot_tensor(inputs, Is, save_path="./images/6.13_I.pdf")
# 遗忘门
Fs = runner.model.rnn_model.Fs
plot_tensor(inputs, Fs, save_path="./images/6.13_F.pdf")
# 输出门
Os = runner.model.rnn_model.Os
plot_tensor(inputs, Os, save_path="./images/6.13_O.pdf")
# 单元状态
Cs = runner.model.rnn_model.Cs
plot_tensor(inputs, Cs, save_path="./images/6.13_C.pdf", vmin=-5, vmax=5)