Mushen's version of "Learning Deep Learning by Hands" study notes, recording the learning process, please buy books for detailed content.
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recurrent neural network
Latent variable autoregressive model:
Recurrent neural network structure: In simple terms, the recurrent neural network RNN is to add an item to the MLP so that it can be compared with ht − 1 h_{t-1}
of the previous timeht−1Have a relationship. Timing information is stored in W hh W_{hh}Whh。
Language models using recurrent neural networks:
Definition of perplexity:
The average cross entropy is taken as an index. If the perplexity is k, it means that there are k possibilities for the next word, and 1 is the best case.
Gradient clipping:
RNN needs to calculate T times, and O(T) matrix multiplication will be done during the backpropagation process, resulting in numerical instability. Gradient clipping is a projection operation, and if the gradient length is too large, it is pulled back. || || Made an L2 norm.
RNN-related applications: generation, classification, question answering machine translation, Tag generation.
Summarize
hands-on learning
Recurrent Neural Network Manual Implementation
%matplotlib inline
import math
import torch
from torch import nn
from torch.nn import functional as F
from d2l import torch as d2l
batch_size, num_steps = 32, 35 # 批量大小，长度
train_iter, vocab = d2l.load_data_time_machine(batch_size, num_steps)
F.one_hot(torch.tensor([1, 2]), len(vocab)) # 独热编码
tensor([[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0]])
X = torch.arange(10).reshape((2, 5)) # 小批量数据形状是二维张量:（批量大小，时间步数）
F.one_hot(X.T, 28).shape
torch.Size([5, 2, 28])
def get_params(vocab_size, num_hiddens, device):
'''初始化循环神经网络的模型参数'''
num_inputs = num_outputs = vocab_size # RNN输入、输出的维度都是vocab_size
def normal(shape): # tensor生成辅助函数
return torch.randn(size=shape, device=device) * 0.01
# 隐藏层参数
W_xh = normal((num_inputs, num_hiddens)) # 输入变量映射到隐藏层
W_hh = normal((num_hiddens, num_hiddens))
b_h = torch.zeros(num_hiddens, device=device)
# 输出层参数
W_hq = normal((num_hiddens, num_outputs)) # 隐藏层到输出变量的映射
b_q = torch.zeros(num_outputs, device=device)
# 附加梯度
params = [W_xh, W_hh, b_h, W_hq, b_q]
for param in params:
param.requires_grad_(True)
return params
def init_rnn_state(batch_size, num_hiddens, device):
'''初始化隐藏变量'''
return (torch.zeros((batch_size, num_hiddens), device=device), ) # 临时刻时没有隐藏状态
def rnn(inputs, state, params):
'''rnn计算，类似forward函数'''
# inputs的形状：(时间步数量，批量大小，词表大小) 与MLP区别在于多一个时间步数量
W_xh, W_hh, b_h, W_hq, b_q = params
H, = state
outputs = []
# X的形状：(批量大小，词表大小)
for X in inputs:
H = torch.tanh(torch.mm(X, W_xh) + torch.mm(H, W_hh) + b_h)
Y = torch.mm(H, W_hq) + b_q
outputs.append(Y) # Y：（批量大小*时间长度）*词表大小
return torch.cat(outputs, dim=0), (H,)
class RNNModelScratch: #@save
"""从零开始实现的循环神经网络模型"""
def __init__(self, vocab_size, num_hiddens, device, get_params, init_state, forward_fn):
self.vocab_size, self.num_hiddens = vocab_size, num_hiddens
self.params = get_params(vocab_size, num_hiddens, device)
self.init_state, self.forward_fn = init_state, forward_fn
def __call__(self, X, state):
X = F.one_hot(X.T, self.vocab_size).type(torch.float32)
return self.forward_fn(X, state, self.params)
def begin_state(self, batch_size, device):
return self.init_state(batch_size, self.num_hiddens, device)
# 检查输出是否具有正确的形状
num_hiddens = 512
net = RNNModelScratch(len(vocab), num_hiddens, d2l.try_gpu(), get_params, init_rnn_state, rnn)
state = net.begin_state(X.shape[0], d2l.try_gpu())
Y, new_state = net(X.to(d2l.try_gpu()), state)
Y.shape, len(new_state), new_state[0].shape # 28个词，10-批量*时间步，批量*num_hiddens
(torch.Size([10, 28]), 1, torch.Size([2, 512]))
# 预测
def predict_ch8(prefix, num_preds, net, vocab, device): #@save
"""在prefix后面生成新字符"""
state = net.begin_state(batch_size=1, device=device)
outputs = [vocab[prefix[0]]] # outputs最开始长度为1
get_input = lambda: torch.tensor([outputs[-1]], device=device).reshape((1, 1))
for y in prefix[1:]: # 预热期
_, state = net(get_input(), state)
outputs.append(vocab[y])
for _ in range(num_preds): # 预测num_preds步
y, state = net(get_input(), state)
outputs.append(int(y.argmax(dim=1).reshape(1)))
return ''.join([vocab.idx_to_token[i] for i in outputs])
predict_ch8('time traveller ', 10, net, vocab, d2l.try_gpu())
'time traveller yurlgamfuz'
Gradient clipping
The time step is 35, which is equivalent to a 35-layer MLP, which is prone to gradient explosion.
g ← min ( 1 , θ ∥ g ∥ ) gg \gets min(1,\frac{\theta }{\left \| g \right \| } )gg←min(1,∥g∥i)g
def grad_clipping(net, theta): #@save
"""裁剪梯度"""
if isinstance(net, nn.Module):
params = [p for p in net.parameters() if p.requires_grad]
else:
params = net.params # 所有层的参数
norm = torch.sqrt(sum(torch.sum((p.grad ** 2)) for p in params))
if norm > theta:
for param in params:
param.grad[:] *= theta / norm # 预防梯度变大
#@save
def train_epoch_ch8(net, train_iter, loss, updater, device, use_random_iter):
"""训练网络一个迭代周期（定义见第8章）"""
state, timer = None, d2l.Timer()
metric = d2l.Accumulator(2) # 训练损失之和,词元数量
for X, Y in train_iter:
if state is None or use_random_iter:
# 在第一次迭代或使用随机抽样时初始化state
state = net.begin_state(batch_size=X.shape[0], device=device)
else:
if isinstance(net, nn.Module) and not isinstance(state, tuple):
# state对于nn.GRU是个张量
state.detach_() # 初始化时只关心现在开始后的计算图，之前的计算图丢掉
else:
# state对于nn.LSTM或对于我们从零开始实现的模型是个张量
for s in state:
s.detach_()
y = Y.T.reshape(-1) # 拉长，因为任务本质上就是一个多分类
X, y = X.to(device), y.to(device)
y_hat, state = net(X, state)
l = loss(y_hat, y.long()).mean()
if isinstance(updater, torch.optim.Optimizer):
updater.zero_grad()
l.backward()
grad_clipping(net, 1)
updater.step()
else:
l.backward()
grad_clipping(net, 1)
# 因为已经调用了mean函数
updater(batch_size=1)
metric.add(l * y.numel(), y.numel())
return math.exp(metric[0] / metric[1]), metric[1] / timer.stop()
#@save
def train_ch8(net, train_iter, vocab, lr, num_epochs, device,
use_random_iter=False):
"""训练模型（定义见第8章）"""
loss = nn.CrossEntropyLoss()
animator = d2l.Animator(xlabel='epoch', ylabel='perplexity',
legend=['train'], xlim=[10, num_epochs])
# 初始化
if isinstance(net, nn.Module):
updater = torch.optim.SGD(net.parameters(), lr)
else:
updater = lambda batch_size: d2l.sgd(net.params, lr, batch_size)
predict = lambda prefix: predict_ch8(prefix, 50, net, vocab, device)
# 训练和预测
for epoch in range(num_epochs):
ppl, speed = train_epoch_ch8(
net, train_iter, loss, updater, device, use_random_iter)
if (epoch + 1) % 10 == 0:
print(predict('time traveller'))
animator.add(epoch + 1, [ppl])
print(f'困惑度 {
ppl:.1f}, {
speed:.1f} 词元/秒 {
str(device)}')
print(predict('time traveller'))
print(predict('traveller'))
num_epochs, lr = 500, 1
train_ch8(net, train_iter, vocab, lr, num_epochs, d2l.try_gpu())
# 以字符为vocab来训练，字符靠谱，但放在一块不靠谱了，基本将整本书记住了
net = RNNModelScratch(len(vocab), num_hiddens, d2l.try_gpu(), get_params,
init_rnn_state, rnn)
train_ch8(net, train_iter, vocab, lr, num_epochs, d2l.try_gpu(),
use_random_iter=True)
Simple Implementation of Recurrent Neural Network
import torch
from torch import nn
from torch.nn import functional as F
from d2l import torch as d2l
batch_size, num_steps = 32, 35
train_iter, vocab = d2l.load_data_time_machine(batch_size, num_steps)
# 定义模型
num_hiddens = 256
rnn_layer = nn.RNN(len(vocab), num_hiddens)
# 使用张量来初始化隐状态，它的形状是（隐藏层数，批量大小，隐藏单元数）
state = torch.zeros((1, batch_size, num_hiddens))
state.shape
# 通过一个隐状态和一个输入，我们就可以用更新后的隐状态计算输出。
X = torch.rand(size=(num_steps, batch_size, len(vocab)))
Y, state_new = rnn_layer(X, state)
Y.shape, state_new.shape
(torch.Size([35, 32, 256]), torch.Size([1, 32, 256]))
#@save
class RNNModel(nn.Module):
"""循环神经网络模型"""
def __init__(self, rnn_layer, vocab_size, **kwargs):
super(RNNModel, self).__init__(**kwargs)
self.rnn = rnn_layer
self.vocab_size = vocab_size
self.num_hiddens = self.rnn.hidden_size
# 如果RNN是双向的（之后将介绍），num_directions应该是2，否则应该是1
if not self.rnn.bidirectional:
self.num_directions = 1
self.linear = nn.Linear(self.num_hiddens, self.vocab_size)
else:
self.num_directions = 2
self.linear = nn.Linear(self.num_hiddens * 2, self.vocab_size)
def forward(self, inputs, state):
X = F.one_hot(inputs.T.long(), self.vocab_size)
X = X.to(torch.float32)
Y, state = self.rnn(X, state)
# 全连接层首先将Y的形状改为(时间步数*批量大小,隐藏单元数)
# 它的输出形状是(时间步数*批量大小,词表大小)。
output = self.linear(Y.reshape((-1, Y.shape[-1])))
return output, state
def begin_state(self, device, batch_size=1):
if not isinstance(self.rnn, nn.LSTM):
# nn.GRU以张量作为隐状态
return torch.zeros((self.num_directions * self.rnn.num_layers,
batch_size, self.num_hiddens),
device=device)
else:
# nn.LSTM以元组作为隐状态
return (torch.zeros((
self.num_directions * self.rnn.num_layers,
batch_size, self.num_hiddens), device=device),
torch.zeros((
self.num_directions * self.rnn.num_layers,
batch_size, self.num_hiddens), device=device))
device = d2l.try_gpu()
net = RNNModel(rnn_layer, vocab_size=len(vocab))
net = net.to(device)
d2l.predict_ch8('time traveller', 10, net, vocab, device)
'time travellercccccccccc'
num_epochs, lr = 500, 1
d2l.train_ch8(net, train_iter, vocab, lr, num_epochs, device)
