- 6.3 LSTM的记忆能力实验
- - 6.3.1 模型构建
  - - 6.3.1.1 LSTM层
    - 6.3.1.2 模型汇总
  - 6.3.2 模型训练
  - - 6.3.2.1 训练指定长度的数字预测模型
    - 6.3.2.2 多组训练
    - 6.3.2.3 损失曲线展示
  - 6.3.3 模型评价
  - - 6.3.3.1 在测试集上进行模型评价
    - 6.3.3.2 模型在不同长度的数据集上的准确率变化图
    - 6.3.3.3 LSTM模型门状态和单元状态的变化
思考题
- 【思考题1】LSTM与SRN实验结果对比，谈谈看法。
- 【思考题2】LSTM与SRN在不同长度数据集上的准确度对比，谈谈看法。
- 【思考题3】分析LSTM中单元状态和门数值的变化图，并用自己的话解释该图。
- 总结：

6.3 LSTM的记忆能力实验

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） $\in \mathbb{R}^D$ 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

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.nn.functional as F
import torch
import torch.nn as 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_size
        self.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_size
        batch_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_size
        if 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_size
            step_input = inputs[:, step, :]
            # 计算输入门, 遗忘门和输出门, 其shape为：batch_size x hidden_size
            I_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_size
            C_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_size
            cell_state = F_gate * cell_state + I_gate * C_tilde
            # 计算隐状态向量，其shape为：batch_size x hidden_size
            hidden_state = O_gate * F.tanh(cell_state)

        return hidden_state

Wi_attr = [[0.1, 0.2], [0.1, 0.2]]
Wf_attr = [[0.1, 0.2], [0.1, 0.2]]
Wo_attr = [[0.1, 0.2], [0.1, 0.2]]
Wc_attr = [[0.1, 0.2], [0.1, 0.2]]
Ui_attr = [[0.0, 0.1], [0.1, 0.0]]
Uf_attr = [[0.0, 0.1], [0.1, 0.0]]
Uo_attr = [[0.0, 0.1], [0.1, 0.0]]
Uc_attr = [[0.0, 0.1], [0.1, 0.0]]
bi_attr = [[0.1, 0.1]]
bf_attr = [[0.1, 0.1]]
bo_attr = [[0.1, 0.1]]
bc_attr = [[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.as_tensor([[[1, 0]]], dtype=torch.float32)
hidden_state = lstm(inputs)
print(hidden_state)

运行结果：

tensor([[0.0594, 0.0952]], grad_fn=<MulBackward0>)

这里我们可以将自己实现的SRN和pytorch框架内置的SRN返回的结果进行打印展示，nn.LSTM，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)

运行结果：

self_lstm hidden_state:  torch.Size([8, 32])
torch_lstm outpus: torch.Size([8, 20, 32])
torch_lstm hidden_state: torch.Size([1, 20, 32])
torch_lstm cell_state: torch.Size([1, 20, 32])

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].

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pytorch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。代码实现如下：


import torch
torch.seed()

# 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([batch_size, seq_len, input_size])

# 设置模型的hidden_size
torch_lstm = nn.LSTM(input_size, hidden_size, bias=True)

# 获取torch_lstm中的参数，并设置相应的paramAttr,用于初始化lstm
print(torch_lstm.weight_ih_l0.T.shape)
chunked_W = torch.split(torch_lstm.weight_ih_l0.T, split_size_or_sections=10, dim=-1)
chunked_U = torch.split(torch_lstm.weight_hh_l0.T, split_size_or_sections=10, dim=-1)
chunked_b = torch.split(torch_lstm.bias_hh_l0.T, split_size_or_sections=10, dim=-1)

Wi_attr = chunked_W[0]
Wf_attr = chunked_W[1]
Wc_attr = chunked_W[2]
Wo_attr = chunked_W[3]
Ui_attr = chunked_U[0]
Uf_attr = chunked_U[1]
Uc_attr = chunked_U[2]
Uo_attr = chunked_U[3]
bi_attr = chunked_b[0]
bf_attr = chunked_b[1]
bc_attr = chunked_b[2]
bo_attr = 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)
torch_outputs, (torch_hidden_state, _) = torch_lstm(inputs)
print("torch SRN:\n", torch_hidden_state.detach().numpy().squeeze(0))
print("self SRN:\n", self_hidden_state.detach().numpy())

运行结果：

torch SRN:
 [[ 0.18889587  0.22909477 -0.09446836  0.12350862 -0.10332021  0.1447071
  -0.09885797  0.21804206  0.24330382 -0.01940097]
 [ 0.0015913  -0.04910816 -0.20106004  0.05199507  0.0731848  -0.11231253
  -0.16018324  0.02682209  0.05274585 -0.05101069]
 [-0.28802228  0.01322857  0.05574065  0.03401611  0.07091789  0.05456219
  -0.07439326  0.23246141  0.09514102  0.1679858 ]
 [ 0.06339199 -0.17604417 -0.25506425  0.13275442 -0.01235366 -0.01637743
  -0.05622694 -0.02631905 -0.06070121 -0.02347214]
 [-0.16658303 -0.23682319 -0.17211306  0.09990654  0.12816645 -0.22735865
  -0.23990081  0.03094203 -0.05261126  0.03364622]]
self SRN:
 [[-0.02027875 -0.16522248 -0.27700496  0.22390729 -0.16141854 -0.11002751
  -0.26292458 -0.00784523 -0.28317857 -0.00937643]
 [-0.07514299  0.14097507 -0.1628691   0.18740548  0.22439012 -0.11031323
  -0.03122664  0.2146629  -0.05938914 -0.09684459]]

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([batch_size, seq_len, input_size])

# 设置模型的hidden_size
hidden_size = 32
self_lstm = LSTM(input_size, hidden_size)
torch_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:
        continue
    end_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torch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) = torch_lstm(inputs)
    # 预热10次运算，不计入最终速度统计
    if i < 10:
        continue
    end_time = time.time()
    model_time += (end_time - strat_time)
avg_model_time = model_time / 90
print('torch_lstm speed:', avg_model_time, 's')

运行结果：

self_lstm speed: 0.005891463491651747 s
torch_lstm speed: 0.001395318243238661 s

可以看到，由于pytorch框架的LSTM底层采用了C++实现并进行优化，pytorch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 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Runner
    runner = 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

上面涉及到的代码(放在上面代码的前面)：


from torch.utils.data import Dataset,DataLoader
import torch
class DigitSumDataset(Dataset):
    def __init__(self, data):
        self.data = data

    def __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, label

    def __len__(self):
        return len(self.data)

import os
# 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label
            items = 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label
            items = 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label
            items = 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

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SRN
        self.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

class RunnerV3(object):
    def __init__(self, model, optimizer, loss_fn, metric, **kwargs):
        self.model = model
        self.optimizer = optimizer
        self.loss_fn = loss_fn
        self.metric = metric  # 只用于计算评价指标

        # 记录训练过程中的评价指标变化情况
        self.dev_scores = []

        # 记录训练过程中的损失函数变化情况
        self.train_epoch_losses = []  # 一个epoch记录一次loss
        self.train_step_losses = []  # 一个step记录一次loss
        self.dev_losses = []

        # 记录全局最优指标
        self.best_score = 0

    def train(self, train_loader, dev_loader=None, **kwargs):
        # 将模型切换为训练模式
        self.model.train()

        # 传入训练轮数，如果没有传入值则默认为0
        num_epochs = kwargs.get("num_epochs", 0)
        # 传入log打印频率，如果没有传入值则默认为100
        log_steps = kwargs.get("log_steps", 100)
        # 评价频率
        eval_steps = kwargs.get("eval_steps", 0)

        # 传入模型保存路径，如果没有传入值则默认为"best_model.pdparams"
        save_path = kwargs.get("save_path", "best_model.pdparams")

        custom_print_log = kwargs.get("custom_print_log", None)

        # 训练总的步数
        num_training_steps = num_epochs * len(train_loader)

        if eval_steps:
            if self.metric is None:
                raise RuntimeError('Error: Metric can not be None!')
            if dev_loader is None:
                raise RuntimeError('Error: dev_loader can not be None!')

        # 运行的step数目
        global_step = 0

        # 进行num_epochs轮训练
        for epoch in range(num_epochs):
            # 用于统计训练集的损失
            total_loss = 0
            for step, data in enumerate(train_loader):
                X, y = data
                # 获取模型预测
                logits = self.model(X)
                loss = self.loss_fn(logits, y.long())  # 默认求mean
                total_loss += loss

                # 训练过程中，每个step的loss进行保存
                self.train_step_losses.append((global_step, loss.item()))

                if log_steps and global_step % log_steps == 0:
                    print(
                        f"[Train] epoch: {epoch}/{num_epochs}, step: {global_step}/{num_training_steps}, loss: {loss.item():.5f}")

                # 梯度反向传播，计算每个参数的梯度值
                loss.backward()

                if custom_print_log:
                    custom_print_log(self)

                # 小批量梯度下降进行参数更新
                self.optimizer.step()
                # 梯度归零
                self.optimizer.zero_grad()

                # 判断是否需要评价
                if eval_steps > 0 and global_step > 0 and \
                        (global_step % eval_steps == 0 or global_step == (num_training_steps - 1)):

                    dev_score, dev_loss = self.evaluate(dev_loader, global_step=global_step)
                    print(f"[Evaluate]  dev score: {dev_score:.5f}, dev loss: {dev_loss:.5f}")

                    # 将模型切换为训练模式
                    self.model.train()

                    # 如果当前指标为最优指标，保存该模型
                    if dev_score > self.best_score:
                        self.save_model(save_path)
                        print(
                            f"[Evaluate] best accuracy performence has been updated: {self.best_score:.5f} --> {dev_score:.5f}")
                        self.best_score = dev_score

                global_step += 1

            # 当前epoch 训练loss累计值
            trn_loss = (total_loss / len(train_loader)).item()
            # epoch粒度的训练loss保存
            self.train_epoch_losses.append(trn_loss)

        print("[Train] Training done!")

    # 模型评估阶段，使用'torch.no_grad()'控制不计算和存储梯度
    @torch.no_grad()
    def evaluate(self, dev_loader, **kwargs):
        assert self.metric is not None

        # 将模型设置为评估模式
        self.model.eval()

        global_step = kwargs.get("global_step", -1)

        # 用于统计训练集的损失
        total_loss = 0

        # 重置评价
        self.metric.reset()

        # 遍历验证集每个批次
        for batch_id, data in enumerate(dev_loader):
            X, y = data

            # 计算模型输出
            logits = self.model(X)

            # 计算损失函数
            loss = self.loss_fn(logits, y.long()).item()
            # 累积损失
            total_loss += loss

            # 累积评价
            self.metric.update(logits, y)

        dev_loss = (total_loss / len(dev_loader))
        dev_score = self.metric.accumulate()

        # 记录验证集loss
        if global_step != -1:
            self.dev_losses.append((global_step, dev_loss))
            self.dev_scores.append(dev_score)

        return dev_score, dev_loss

    # 模型评估阶段，使用'torch.no_grad()'控制不计算和存储梯度
    @torch.no_grad()
    def predict(self, x, **kwargs):
        # 将模型设置为评估模式
        self.model.eval()
        # 运行模型前向计算，得到预测值
        logits = self.model(x)
        return logits

    def save_model(self, save_path):
        torch.save(self.model.state_dict(), save_path)

    def load_model(self, model_path):
        state_dict = torch.load(model_path)
        self.model.load_state_dict(state_dict)

class Accuracy():
    def __init__(self, is_logist=True):
        # 用于统计正确的样本个数
        self.num_correct = 0
        # 用于统计样本的总数
        self.num_count = 0

        self.is_logist = is_logist

    def update(self, outputs, labels):

        # 判断是二分类任务还是多分类任务，shape[1]=1时为二分类任务，shape[1]>1时为多分类任务
        if outputs.shape[1] == 1:  # 二分类
            outputs = torch.squeeze(outputs, dim=-1)
            if self.is_logist:
                # logist判断是否大于0
                preds = torch.tensor((outputs >= 0), dtype=torch.float32)
            else:
                # 如果不是logist，判断每个概率值是否大于0.5，当大于0.5时，类别为1，否则类别为0
                preds = torch.tensor((outputs >= 0.5), dtype=torch.float32)
        else:
            # 多分类时，使用'torch.argmax'计算最大元素索引作为类别
            preds = torch.argmax(outputs, dim=1)

        # 获取本批数据中预测正确的样本个数
        labels = torch.squeeze(labels, dim=-1)
        batch_correct = torch.sum(torch.tensor(preds == labels, dtype=torch.float32)).cpu().numpy()
        batch_count = len(labels)

        # 更新num_correct 和 num_count
        self.num_correct += batch_correct
        self.num_count += batch_count

    def accumulate(self):
        # 使用累计的数据，计算总的指标
        if self.num_count == 0:
            return 0
        return self.num_correct / self.num_count

    def reset(self):
        # 重置正确的数目和总数
        self.num_correct = 0
        self.num_count = 0

    def name(self):
        return "Accuracy"

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。

lstm_runners = {}

lengths = [10, 15, 20, 25, 30, 35]
for length in lengths:
    runner = train(length)
    lstm_runners[length] = runner

运行结果(部分展示)：

[Evaluate]  dev score: 0.88000, dev loss: 0.65520
[Evaluate] best accuracy performence has been updated: 0.87000 --> 0.88000
[Train] epoch: 471/500, step: 17900/19000, loss: 0.00103
[Evaluate]  dev score: 0.88000, dev loss: 0.65717
[Train] epoch: 473/500, step: 18000/19000, loss: 0.00156
[Evaluate]  dev score: 0.88000, dev loss: 0.66018
[Train] epoch: 476/500, step: 18100/19000, loss: 0.00158
[Evaluate]  dev score: 0.88000, dev loss: 0.66119
[Train] epoch: 478/500, step: 18200/19000, loss: 0.00255
[Evaluate]  dev score: 0.88000, dev loss: 0.66236
[Train] epoch: 481/500, step: 18300/19000, loss: 0.00080
[Evaluate]  dev score: 0.88000, dev loss: 0.66521
[Train] epoch: 484/500, step: 18400/19000, loss: 0.00103
[Evaluate]  dev score: 0.88000, dev loss: 0.66682
[Train] epoch: 486/500, step: 18500/19000, loss: 0.00131
[Evaluate]  dev score: 0.88000, dev loss: 0.66822
[Train] epoch: 489/500, step: 18600/19000, loss: 0.00166
[Evaluate]  dev score: 0.88000, dev loss: 0.67098
[Train] epoch: 492/500, step: 18700/19000, loss: 0.00124
[Evaluate]  dev score: 0.88000, dev loss: 0.67337
[Train] epoch: 494/500, step: 18800/19000, loss: 0.00105
[Evaluate]  dev score: 0.88000, dev loss: 0.67340
[Train] epoch: 497/500, step: 18900/19000, loss: 0.00069
[Evaluate]  dev score: 0.88000, dev loss: 0.67506
[Evaluate]  dev score: 0.88000, dev loss: 0.67903
[Train] Training done!

[Train] epoch: 376/500, step: 14300/19000, loss: 0.03295
[Evaluate]  dev score: 0.86000, dev loss: 0.77074
[Evaluate] best accuracy performence has been updated: 0.85000 --> 0.86000
[Train] epoch: 378/500, step: 14400/19000, loss: 0.02419
[Evaluate]  dev score: 0.86000, dev loss: 0.76510
[Train] epoch: 381/500, step: 14500/19000, loss: 0.02038
[Evaluate]  dev score: 0.86000, dev loss: 0.75816
[Train] epoch: 384/500, step: 14600/19000, loss: 0.03184
[Evaluate]  dev score: 0.86000, dev loss: 0.75432
[Train] epoch: 386/500, step: 14700/19000, loss: 0.01263
[Evaluate]  dev score: 0.85000, dev loss: 0.75332
[Train] epoch: 389/500, step: 14800/19000, loss: 0.01752
[Evaluate]  dev score: 0.85000, dev loss: 0.75455
[Train] epoch: 392/500, step: 14900/19000, loss: 0.02649
[Evaluate]  dev score: 0.85000, dev loss: 0.75574
[Train] epoch: 394/500, step: 15000/19000, loss: 0.01463
[Evaluate]  dev score: 0.85000, dev loss: 0.75772
[Train] epoch: 397/500, step: 15100/19000, loss: 0.01591
[Evaluate]  dev score: 0.85000, dev loss: 0.76009
[Train] epoch: 400/500, step: 15200/19000, loss: 0.02183
[Evaluate]  dev score: 0.85000, dev loss: 0.76348
[Train] epoch: 402/500, step: 15300/19000, loss: 0.00849
[Evaluate]  dev score: 0.85000, dev loss: 0.76631
[Train] epoch: 405/500, step: 15400/19000, loss: 0.01774
[Evaluate]  dev score: 0.85000, dev loss: 0.76891
[Train] epoch: 407/500, step: 15500/19000, loss: 0.01031
[Evaluate]  dev score: 0.85000, dev loss: 0.77206
[Train] epoch: 410/500, step: 15600/19000, loss: 0.00540
[Evaluate]  dev score: 0.85000, dev loss: 0.77642
[Train] epoch: 413/500, step: 15700/19000, loss: 0.00560
[Evaluate]  dev score: 0.85000, dev loss: 0.78110
[Train] epoch: 415/500, step: 15800/19000, loss: 0.00747
[Evaluate]  dev score: 0.85000, dev loss: 0.78641
[Train] epoch: 418/500, step: 15900/19000, loss: 0.00736
[Evaluate]  dev score: 0.85000, dev loss: 0.79182
[Train] epoch: 421/500, step: 16000/19000, loss: 0.02328
[Evaluate]  dev score: 0.85000, dev loss: 0.79689
[Train] epoch: 423/500, step: 16100/19000, loss: 0.00671
[Evaluate]  dev score: 0.83000, dev loss: 0.80291
[Train] epoch: 426/500, step: 16200/19000, loss: 0.01137
[Evaluate]  dev score: 0.83000, dev loss: 0.80719
[Train] epoch: 428/500, step: 16300/19000, loss: 0.00901
[Evaluate]  dev score: 0.83000, dev loss: 0.81101
[Train] epoch: 431/500, step: 16400/19000, loss: 0.00662
[Evaluate]  dev score: 0.83000, dev loss: 0.81447
[Train] epoch: 434/500, step: 16500/19000, loss: 0.01120
[Evaluate]  dev score: 0.83000, dev loss: 0.81732
[Train] epoch: 436/500, step: 16600/19000, loss: 0.00577
[Evaluate]  dev score: 0.83000, dev loss: 0.81990
[Train] epoch: 439/500, step: 16700/19000, loss: 0.00676
[Evaluate]  dev score: 0.83000, dev loss: 0.82178
[Train] epoch: 442/500, step: 16800/19000, loss: 0.01297
[Evaluate]  dev score: 0.83000, dev loss: 0.82374
[Train] epoch: 444/500, step: 16900/19000, loss: 0.00452
[Evaluate]  dev score: 0.83000, dev loss: 0.82601
[Train] epoch: 447/500, step: 17000/19000, loss: 0.00556
[Evaluate]  dev score: 0.83000, dev loss: 0.82745
[Train] epoch: 450/500, step: 17100/19000, loss: 0.01203
[Evaluate]  dev score: 0.83000, dev loss: 0.82950
[Train] epoch: 452/500, step: 17200/19000, loss: 0.00360
[Evaluate]  dev score: 0.83000, dev loss: 0.83090
[Train] epoch: 455/500, step: 17300/19000, loss: 0.00699
[Evaluate]  dev score: 0.83000, dev loss: 0.83299
[Train] epoch: 457/500, step: 17400/19000, loss: 0.00435
[Evaluate]  dev score: 0.83000, dev loss: 0.83533
[Train] epoch: 460/500, step: 17500/19000, loss: 0.00223
[Evaluate]  dev score: 0.83000, dev loss: 0.83608
[Train] epoch: 463/500, step: 17600/19000, loss: 0.00262
[Evaluate]  dev score: 0.83000, dev loss: 0.83843
[Train] epoch: 465/500, step: 17700/19000, loss: 0.00462
[Evaluate]  dev score: 0.83000, dev loss: 0.84042
[Train] epoch: 468/500, step: 17800/19000, loss: 0.00352
[Evaluate]  dev score: 0.83000, dev loss: 0.84169
[Train] epoch: 471/500, step: 17900/19000, loss: 0.01054
[Evaluate]  dev score: 0.83000, dev loss: 0.84364
[Train] epoch: 473/500, step: 18000/19000, loss: 0.00397
[Evaluate]  dev score: 0.83000, dev loss: 0.84550
[Train] epoch: 476/500, step: 18100/19000, loss: 0.00419
[Evaluate]  dev score: 0.83000, dev loss: 0.84744
[Train] epoch: 478/500, step: 18200/19000, loss: 0.00464
[Evaluate]  dev score: 0.83000, dev loss: 0.85005
[Train] epoch: 481/500, step: 18300/19000, loss: 0.00312
[Evaluate]  dev score: 0.83000, dev loss: 0.84981
[Train] epoch: 484/500, step: 18400/19000, loss: 0.00503
[Evaluate]  dev score: 0.83000, dev loss: 0.85256
[Train] epoch: 486/500, step: 18500/19000, loss: 0.00275
[Evaluate]  dev score: 0.83000, dev loss: 0.85765
[Train] epoch: 489/500, step: 18600/19000, loss: 0.00316
[Evaluate]  dev score: 0.83000, dev loss: 0.85330
[Train] epoch: 492/500, step: 18700/19000, loss: 0.00663
[Evaluate]  dev score: 0.83000, dev loss: 0.85381
[Train] epoch: 494/500, step: 18800/19000, loss: 0.00211
[Evaluate]  dev score: 0.83000, dev loss: 0.85953
[Train] epoch: 497/500, step: 18900/19000, loss: 0.00231
[Evaluate]  dev score: 0.83000, dev loss: 0.85619
[Evaluate]  dev score: 0.83000, dev loss: 0.86070
[Train] Training done!

[Train] epoch: 481/500, step: 18300/19000, loss: 0.10370
[Evaluate]  dev score: 0.82000, dev loss: 0.79325
[Train] epoch: 484/500, step: 18400/19000, loss: 0.41272
[Evaluate]  dev score: 0.83000, dev loss: 0.81523
[Evaluate] best accuracy performence has been updated: 0.82000 --> 0.83000
[Train] epoch: 486/500, step: 18500/19000, loss: 0.21549
[Evaluate]  dev score: 0.84000, dev loss: 0.80410
[Evaluate] best accuracy performence has been updated: 0.83000 --> 0.84000
[Train] epoch: 489/500, step: 18600/19000, loss: 0.12459
[Evaluate]  dev score: 0.83000, dev loss: 0.78478
[Train] epoch: 492/500, step: 18700/19000, loss: 0.21927
[Evaluate]  dev score: 0.83000, dev loss: 0.77985
[Train] epoch: 494/500, step: 18800/19000, loss: 0.22846
[Evaluate]  dev score: 0.84000, dev loss: 0.78622
[Train] epoch: 497/500, step: 18900/19000, loss: 0.03285
[Evaluate]  dev score: 0.84000, dev loss: 0.77512
[Evaluate]  dev score: 0.84000, dev loss: 0.77360
[Train] Training done!

[Train] epoch: 473/500, step: 18000/19000, loss: 0.35202
[Evaluate]  dev score: 0.87000, dev loss: 0.46193
[Train] epoch: 476/500, step: 18100/19000, loss: 0.09771
[Evaluate]  dev score: 0.91000, dev loss: 0.38287
[Evaluate] best accuracy performence has been updated: 0.90000 --> 0.91000
[Train] epoch: 478/500, step: 18200/19000, loss: 0.02467
[Evaluate]  dev score: 0.89000, dev loss: 0.42026
[Train] epoch: 481/500, step: 18300/19000, loss: 0.01818
[Evaluate]  dev score: 0.89000, dev loss: 0.42676
[Train] epoch: 484/500, step: 18400/19000, loss: 0.04383
[Evaluate]  dev score: 0.89000, dev loss: 0.42994
[Train] epoch: 486/500, step: 18500/19000, loss: 0.02579
[Evaluate]  dev score: 0.89000, dev loss: 0.43919
[Train] epoch: 489/500, step: 18600/19000, loss: 0.02788
[Evaluate]  dev score: 0.88000, dev loss: 0.44569
[Train] epoch: 492/500, step: 18700/19000, loss: 0.05951
[Evaluate]  dev score: 0.88000, dev loss: 0.43005
[Train] epoch: 494/500, step: 18800/19000, loss: 0.02288
[Evaluate]  dev score: 0.88000, dev loss: 0.44650
[Train] epoch: 497/500, step: 18900/19000, loss: 0.02292
[Evaluate]  dev score: 0.88000, dev loss: 0.45742
[Evaluate]  dev score: 0.88000, dev loss: 0.44346
[Train] Training done!

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)

plot_training_loss：

import matplotlib.pyplot as plt
def plot_training_loss(runner, fig_name, sample_step):
    plt.figure()
    train_items = runner.train_step_losses[::sample_step]
    train_steps = [x[0] for x in train_items]
    train_losses = [x[1] for x in train_items]
    plt.plot(train_steps, train_losses, color='#e4007f', label="Train loss")

    dev_steps = [x[0] for x in runner.dev_losses]
    dev_losses = [x[1] for x in runner.dev_losses]
    plt.plot(dev_steps, dev_losses, color='#f19ec2', linestyle='--', label="Dev loss")

    # 绘制坐标轴和图例
    plt.ylabel("loss", fontsize='large')
    plt.xlabel("step", fontsize='large')
    plt.legend(loc='upper right', fontsize='x-large')

    plt.savefig(fig_name)
    plt.show()

图6.11展示了LSTM模型在不同长度数据集上进行训练后的损失变化，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. 同图6.5相比，LSTM模型在序列长度增加时，收敛情况比SRN模型更好。

图6.11 LSTM在不同长度数据集训练损失变化图

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}")

运行结果：

Evaluate LSTM with data length 15.
Evaluate LSTM with data length 20.
Evaluate LSTM with data length 25.
Evaluate LSTM with data length 30.
Evaluate LSTM with data length 35.
[LSTM] length:10, dev_score: 0.92, test_score:  0.84000
[LSTM] length:15, dev_score: 0.87, test_score:  0.92000
[LSTM] length:20, dev_score: 0.75, test_score:  0.74000
[LSTM] length:25, dev_score: 0.77, test_score:  0.82000
[LSTM] length:30, dev_score: 0.61, test_score:  0.54000
[LSTM] length:35, dev_score: 0.29, test_score:  0.19000

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()

图6.12 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.

图6.12 LSTM与SRN网络在不同长度数据集上的准确度对比图

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_size
        self.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_size
        batch_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_size
        if 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_tilde
            hidden_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).T

    plt.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)

图6.13 当LSTM处理序列数据[6, 7, 0, 0, 1, 0, 0, 0, 0, 0]的过程中单元状态和门数值的变化图，其中横坐标为输入数字，纵坐标为相应门或单元状态向量的维度，颜色的深浅代表数值的大小。可以看到，当输入门遇到不同位置的数字0时，保持了相对一致的数值大小，表明对于0元素保持相同的门控过滤机制，避免输入信息的变化给当前模型带来困扰；当遗忘门遇到数字1后，遗忘门数值在一些维度上变小，表明对某些信息进行了遗忘；随着序列的输入，输出门和单元状态在某些维度上数值变小，在某些维度上数值变大，表明输出门在根据信息的重要性选择信息进行输出，同时单元状态也在保持着对文本预测重要的一些信息.

图6.13 LSTM中单元状态和门数值的变化图

思考题

【思考题1】LSTM与SRN实验结果对比，谈谈看法。

LSTM模型在序列长度增加时，收敛情况比SRN模型更好。因为本身LSTM的设计就是通过门控机制来解决SRN的长程依赖问题。

【思考题2】LSTM与SRN在不同长度数据集上的准确度对比，谈谈看法。

对比来看，LSTM模型的准确率显著高于SRN模型。但是综合来看，他们在随数据集长度的增加，准确率都在降低。

【思考题3】分析LSTM中单元状态和门数值的变化图，并用自己的话解释该图。

横坐标为输入数字，纵坐标为相应门或单元状态向量的维度，颜色的深浅代表数值的大小。可以看到，当输入门遇到不同位置的数字0时，保持了相对一致的数值大小，表明对于0元素保持相同的门控过滤机制，避免输入信息的变化给当前模型带来困扰；当遗忘门遇到数字1后，遗忘门数值在一些维度上变小，表明对某些信息进行了遗忘；随着序列的输入，输出门和单元状态在某些维度上数值变小，在某些维度上数值变大，表明输出门在根据信息的重要性选择信息进行输出，同时单元状态也在保持着对文本预测重要的一些信息.