NNDL 实验七 循环神经网络(3) LSTM的记忆能力实验
目录
LSTM的记忆能力实验
模型构建
LSTM层
模型训练
训练指定长度的数字预测模型
多组训练
损失曲线显示
思考
模型评价
在测试集上进行模型评价
模型在不同长度的数据集上的准确率变化图
思考
LSTM模型门状态和单元状态的变化
思考
全面总结RNN（必做）
参考
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）
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.
使用LSTM模型重新进行数字求和实验，验证LSTM模型的长程依赖能力。
LSTM 模型在第 t 步时，循环单元的内部结构如下图所示．
模型构建
使用第6.1.2.4中定义Model_RNN4SeqClass模型，并构建 LSTM 算子．只需要实例化 LSTM ，并传入Model_RNN4SeqClass模型，就可以用 LSTM 进行数字求和实验。
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 as nn
import torch.nn.functional as F
# 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)
输出结果：
tensor([[0.0594, 0.0952]], grad_fn=
)
将实现的结果进行打印显示：
# 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)输出结果：
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].
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，这里首先根据Paddle内置的LSTM实例化模型（为了进行对比，在实例化时只保留一个偏置，将偏置
设置为0），然后提取该模型对应的参数，进行参数分割后，使用相应参数去初始化自己实现的LSTM，从而保证两者在参数初始化时是一致的。
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。代码实现如下：
torch.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([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())输出结果：
torch.Size([10, 40])
torch SRN:
[[ 0.05112649 0.00698039 -0.03931072 0.08884124 0.1154766 -0.13408035
0.16033086 0.00135596 -0.063761 -0.2974773 ]
[ 0.11241535 0.07274596 0.36305282 -0.0627713 0.01287347 -0.15761302
0.22385654 0.01972566 -0.35233897 -0.20609131]
[ 0.13069035 -0.03020173 -0.0636995 0.13535675 0.34181932 -0.11440605
0.10832828 0.04234035 0.08991404 -0.15160468]
[ 0.0727646 0.15715009 0.06807105 0.07414025 0.36294693 -0.06236503
-0.11784356 0.00420525 -0.1500205 0.08434849]
[ 0.07962178 0.01809997 -0.02799227 -0.09783129 -0.08596174 -0.13848482
0.06129256 0.15295173 -0.14451739 -0.11927365]]
self SRN:
[[ 0.0940564 -0.14659543 -0.14954016 0.20936163 -0.12826967 0.14749622
0.00946941 0.1993472 -0.06859784 -0.2767597 ]
[ 0.17217153 0.16705877 -0.05719084 0.14882174 0.10330292 -0.20432511
0.13150844 0.03508793 -0.07331903 -0.06966008]]
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')输出结果：
self_lstm speed: 0.00374555852678087 s
torch_lstm speed: 0.0007863892449273003 s
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。
模型训练
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 random
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其中所使用到的函数代码：
RunnerV3类函数：
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)准确率Accuracy函数：
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"DigitSumDataset()函数：
from torch.utils.data import Dataset, DataLoader
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)load_data()函数：
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_examplesEmbedding()类：
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)Model_RNN4SeqClass()类：
# 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训练结果：
[Train] epoch: 0/500, step: 0/19000, loss: 2.96668
[Train] epoch: 2/500, step: 100/19000, loss: 2.76372[Evaluate] dev score: 0.90000, dev loss: 2.87625
......
[Train] epoch: 490/500, step: 18600/19000, loss: 0.00154
[Evaluate] dev score: 0.90000, dev loss: 0.53487
[Train] epoch: 492/500, step: 18700/19000, loss: 0.00142
[Evaluate] dev score: 0.90000, dev loss: 0.52435
[Train] epoch: 495/500, step: 18800/19000, loss: 0.00108
[Evaluate] dev score: 0.90000, dev loss: 0.50064
[Train] epoch: 497/500, step: 18900/19000, loss: 0.00104
[Evaluate] dev score: 0.90000, dev loss: 0.48256
[Evaluate] dev score: 0.90000, dev loss: 0.47586
[Train] Training done！
损失曲线显示
# 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)
上图展示了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。
思考
LSTM与SRN实验结果对比，谈谈看法。（选做）
LSTM：
L=10[Evaluate] best accuracy performence has been updated: 0.93000 --> 0.94000
L=15[Evaluate] best accuracy performence has been updated: 0.95000 --> 0.96000
L=20[Evaluate] best accuracy performence has been updated: 0.88000 --> 0.89000
L=25[Evaluate] best accuracy performence has been updated: 0.93000 --> 0.94000
L=30[Evaluate] best accuracy performence has been updated: 0.87000 --> 0.88000
L=35:[Evaluate] best accuracy performence has been updated: 0.90000 --> 0.91000
SRN：
L=10[Evaluate] best accuracy performence has been updated: 0.74000 --> 0.78000
L=15[Evaluate] best accuracy performence has been updated: 0.71000 --> 0.73000
L=20[Evaluate] best accuracy performence has been updated: 0.53000 --> 0.55000
L=25[Evaluate] best accuracy performence has been updated: 0.26000 --> 0.28000
L=30[Evaluate] best accuracy performence has been updated: 0.28000 --> 0.29000
L=35:[Evaluate] best accuracy performence has been updated: 0.08000 --> 0.12000
从实验结果可以很清楚的发现，LSTM随着数据集序列长度的增加,准确率并没有下降，而SRN随着序列的增加，在序列长度为20左右的时候准确率急速下降。
由梯度消失引起的短期记忆问题是RNN的痛点.
模型评价
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}")
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: 0.94, test_score: 0.90000
[LSTM] length: 15, dev_score: 0.95, test_score: 0.96000
[LSTM] length: 20, dev_score: 0.93, test_score: 0.92000
[LSTM] length: 25, dev_score: 0.94, test_score: 0.89000
[LSTM] length: 30, dev_score: 0.96, test_score: 0.93000
[LSTM] length: 35, dev_score: 0.95, test_score: 0.93000
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()
LSTM：
RNN：
上图展示了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.
思考
LSTM与SRN在不同长度数据集上的准确度对比，谈谈看法。（选做）
从实验的结果可以看到，RNN的准确率在数据较多的时候会不断下降，应该是因为他对于刚开始数据信息的遗忘损失造成的；而LSTM的准确率一直都还不错，这说明使用LSTM可以解决长度较大数据集的问题。
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)
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.
思考
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0时，保持了数值大小基本不变，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.
全面总结RNN（必做）
参考
NNDL 实验6（上） - HBU_DAVID - 博客园 (cnblogs.com)
NNDL 实验七 循环神经网络（3）LSTM的记忆能力实验
循环神经网络 — 动手学深度学习 2.0.0-beta1 documentation (d2l.ai)