[人工智能]【Pytorch】（十二）长短期记忆（LSTM）、门控循环单元（GRU）

LSTM与GRU

长短期记忆（LSTM）

LSTM（Long short-term memory ）是1997年提出的。与普通RNN一样，下面以”序列动，网络不动“的角度画出示意图。

图片来源[1]。$\sigma :\text{sigmoid}$，注意$\text{sigmoid}$的“遗忘”特性

门控循环单元（GRU）

GRU（Gate Recurrent Unit）是2014年提出的，它用了更少的参数实现了与LSTM相当的效果。

说明：目前网上流传的两个版本，一个是(原论文)
$$H_t=H_t^{\prime }\odot (1?Z_t)+H_{t?1}\odot Z_t$$
另一个是：
$$H_t=H_t^{\prime }\odot Z_t+H_{t?1}\odot (1?Z_t)$$

pytorch实现正弦波预测

LSTM

import torch
import torch.nn as nn
import numpy as np
import torch.optim as optim
from matplotlib import pyplot as plt
import matplotlib

torch.manual_seed(1)
np.random.seed(1)
matplotlib.rcParams['font.family'] = 'SimHei'
matplotlib.rcParams['axes.unicode_minus'] = False
plt.rcParams['figure.dpi'] = 150
device = 'cuda' if torch.cuda.is_available() else 'cpu'
print(device)


class RNN(nn.Module):
    def __init__(self, input_size, hidden_size, num_layers, output_size):
        super(RNN, self).__init__()
        self.num_layers = num_layers
        self.hidden_size = hidden_size

        self.rnn = nn.LSTM(
            input_size=input_size,
            hidden_size=hidden_size,
            num_layers=num_layers,
            batch_first=True,
            bidirectional=False,
        )
        self.linear = nn.Linear(hidden_size, output_size)

    def forward(self, inputs, h0, c0):
        # x: [batch_size, seq_len, input_size]
        # h0: [num_layers, batch_size, hidden_size]
        # c0: [num_layers, batch_size, hidden_size]
        outputs, (hn, cn) = self.rnn(inputs, (h0, c0))
        # out: [batch_size, seq_len, hidden_size]
        # hn: [num_layers, batch_size, hidden_size]
        # cn: [num_layers, batch_size, hidden_size]

        # [batch, seq_len, hidden_size] => [batch * seq_len, hidden_size]
        outputs = outputs.view(-1, self.hidden_size)

        # [batch_size * seq_len, hidden_size] => [batch_size * seq_len, output_size]
        outputs = self.linear(outputs)

        # [batch_size * seq_len, output_size] => [batch_size, seq_len, output_size]
        outputs = outputs.view(inputs.size())

        return outputs, hn,cn


def test(model, seq_len, h0, c0):
    input = torch.tensor(0, dtype=torch.float)
    predictions = []
    for _ in range(seq_len):
        input = input.view(1, 1, 1)
        prediction, hn, cn= model(input, h0, c0)
        input = prediction
        h0 = hn
        c0 = cn
        predictions.append(prediction.detach().numpy().ravel()[0])
    # 画图
    time_steps = np.linspace(0, 10, seq_len)
    data = np.sin(time_steps)
    a, = plt.plot(time_steps, data, color='b')
    b = plt.scatter(time_steps[0], 0, color='black', s=10)
    c = plt.scatter(time_steps[1:], predictions[1:], color='red', s=10)
    plt.legend([a, b, c], ['正弦波', '输入', '预测'])
    plt.show()


def train():
    seq_len = 100
    input_size = 1
    hidden_size = 16
    output_size = 1
    num_layers = 1
    lr = 0.01

    model = RNN(input_size, hidden_size, num_layers, output_size)
    loss_function = nn.MSELoss()
    optimizer = optim.Adam(model.parameters(), lr)
    h0 = torch.zeros(num_layers, input_size, hidden_size)
    c0 = torch.zeros(num_layers, input_size, hidden_size)
    for i in range(300):
        # 训练的数据:batch_size=1
        time_steps = np.linspace(0, 10, seq_len + 1)
        data = np.sin(time_steps)
        data = data.reshape(seq_len + 1, 1)
        # 去掉最后一个元素，作为输入
        inputs = torch.tensor(data[:-1]).float().view(1, seq_len, 1)
        # 去掉第一个元素，作为目标值 [batch_size, seq_len, input_size]
        target = torch.tensor(data[1:]).float().view(1, seq_len, 1)

        output, hn,cn = model(inputs, h0, c0)

        # 与上一个批次的计算图分离 https://www.cnblogs.com/catnofishing/p/13287322.html
        hn.detach()

        loss = loss_function(output, target)
        model.zero_grad()
        loss.backward()
        optimizer.step()

        if i % 100 == 0:
            print("迭代次数: {} loss {}".format(i, loss.item()))

    test(model, seq_len, h0, c0)


if __name__ == '__main__':
    train()

GRU

import torch
import torch.nn as nn
import numpy as np
import torch.optim as optim
from matplotlib import pyplot as plt
import matplotlib

torch.manual_seed(1)
np.random.seed(1)
matplotlib.rcParams['font.family'] = 'SimHei'
matplotlib.rcParams['axes.unicode_minus'] = False
plt.rcParams['figure.dpi'] = 150
device = 'cuda' if torch.cuda.is_available() else 'cpu'
print(device)


class RNN(nn.Module):
    def __init__(self, input_size, hidden_size, num_layers, output_size):
        super(RNN, self).__init__()
        self.num_layers = num_layers
        self.hidden_size = hidden_size

        self.rnn = nn.GRU(
            input_size=input_size,
            hidden_size=hidden_size,
            num_layers=num_layers,
            batch_first=True,
            bidirectional=False,
        )
        self.linear = nn.Linear(hidden_size, output_size)

    def forward(self, inputs, h0):
        # x: [batch_size, seq_len, input_size]
        # h0: [num_layers, batch_size, hidden_size]
        outputs, hn = self.rnn(inputs, h0)
        # out: [batch_size, seq_len, hidden_size]
        # hn: [num_layers, batch_size, hidden_size]

        # [batch, seq_len, hidden_size] => [batch * seq_len, hidden_size]
        outputs = outputs.view(-1, self.hidden_size)

        # [batch_size * seq_len, hidden_size] => [batch_size * seq_len, output_size]
        outputs = self.linear(outputs)

        # [batch_size * seq_len, output_size] => [batch_size, seq_len, output_size]
        outputs = outputs.view(inputs.size())

        return outputs, hn


def test(model, seq_len, h0):
    input = torch.tensor(0, dtype=torch.float)
    predictions = []
    for _ in range(seq_len):
        input = input.view(1, 1, 1)
        prediction, hn = model(input, h0)
        input = prediction
        h0 = hn
        predictions.append(prediction.detach().numpy().ravel()[0])
    # 画图
    time_steps = np.linspace(0, 10, seq_len)
    data = np.sin(time_steps)
    a, = plt.plot(time_steps, data, color='b')
    b = plt.scatter(time_steps[0], 0, color='black', s=10)
    c = plt.scatter(time_steps[1:], predictions[1:], color='red', s=10)
    plt.legend([a, b, c], ['正弦波', '输入', '预测'])
    plt.show()


def train():
    seq_len = 100
    input_size = 1
    hidden_size = 16
    output_size = 1
    num_layers = 1
    lr = 0.01

    model = RNN(input_size, hidden_size, num_layers, output_size)
    loss_function = nn.MSELoss()
    optimizer = optim.Adam(model.parameters(), lr)
    h0 = torch.zeros(num_layers, input_size, hidden_size)

    for i in range(300):
        # 训练的数据:batch_size=1
        time_steps = np.linspace(0, 10, seq_len + 1)
        data = np.sin(time_steps)
        data = data.reshape(seq_len + 1, 1)
        # 去掉最后一个元素，作为输入
        inputs = torch.tensor(data[:-1]).float().view(1, seq_len, 1)
        # 去掉第一个元素，作为目标值 [batch_size, seq_len, input_size]
        target = torch.tensor(data[1:]).float().view(1, seq_len, 1)

        output, hn = model(inputs, h0)

        # 与上一个批次的计算图分离 https://www.cnblogs.com/catnofishing/p/13287322.html
        hn.detach()

        loss = loss_function(output, target)
        model.zero_grad()
        loss.backward()
        optimizer.step()

        if i % 100 == 0:
            print("迭代次数: {} loss {}".format(i, loss.item()))

    test(model, seq_len, h0)


if __name__ == '__main__':
    train()

对比（训练迭代300次）

普通RNN	LSTM	GRU

nn.LSTM

CLASStorch.nn.LSTM(*args, **kwargs)

参数说明：

• input_size：输入序列单元$x_t$的维度。
• hidden_size：隐藏层神经元个数，或者也叫输出的维度
• num_layers：网络的层数，默认为1
• bias：是否使用偏置
• batch_first：输入数据的形式，默认是 False，形式为(seq, batch, feature)，也就是将序列长度放在第一位，batch 放在第二位。如果为True，则为(batch, seq, feature)
• dropout：dropout率, 默认为0，即不使用。如若使用将其设置成一个0-1的数字即可。
• birdirectional：是否使用两层的双向的 rnn，默认是 False
• proj_size ： 默认值：0 https://arxiv.org/abs/1402.1128

记：

$$\begin{array}{rl}N& =\text{batch?size}\\ L& =\text{?sequence?length?}\\ D& =2\text{?if?bidirectional=True?otherwise?}1\\ H_{\text{in}}& =\text{?input\_size?}\\ H_{cell}& =\text{?hidden\_size?}\\ H_{out}& =\text{proj\_size},如果\text{proj\_size}>0;否则=\text{?hidden\_size?}\end{array}$$

输入：input, (h_0, c_0)

(1) input(输入序列)

非批量：$(L,H_{in})$

批量：如果batch_first=False，$（L,N,H_{in})$；如果batch_first=True，$（N,L,H_{in})$

(2) h_0（每一层网络的初始状态。如果未提供，则默认为零。）

非批量：$(D\times \text{num\_layers},H_{out})$

批量：$(D\times \text{num\_layers},N,H_{out})$

(3) c_0（默认为零。）

非批量：$(D\times \text{num\_layers},H_{cell})$

批量：$(D\times \text{num\_layers},N,H_{cell})$

输出，output, (h_n, c_n)

（1）output:

非批量：$(L,D\times H_{out})$

批量：如果batch_first=False，$（L,N,H_{out})$；如果batch_first=True，$（N,L,H_{out})$

（2）h_n:

非批量：$(D\times \text{num\_layers},H_{out})$

批量：$(D\times \text{num\_layers},N,H_{out})$

（3）c_n

非批量：$(D\times \text{num\_layers},H_{cell})$

批量：$(D\times \text{num\_layers},N,H_{cell})$

权重和偏置初始化：

从均匀分布$U(?\sqrt{k},\sqrt{k})$采样，其中$k=\frac{1}{\text{hidden\_size}}$

nn.GRU

CLASS torch.nn.GRU(*args, **kwargs)

参数说明：

• input_size：输入序列单元$x_t$的维度。
• hidden_size：隐藏层神经元个数，或者也叫输出的维度
• num_layers：网络的层数，默认为1
• nonlinearity：激活函数，默认为tanh
• bias：是否使用偏置
• batch_first：输入数据的形式，默认是 False，形式为(seq, batch, feature)，也就是将序列长度放在第一位，batch 放在第二位。如果为True，则为(batch, seq, feature)
• dropout：dropout率, 默认为0，即不使用。如若使用将其设置成一个0-1的数字即可。
• birdirectional：是否使用两层的双向的 rnn，默认是 False
  记：
  $$\begin{array}{rl}N& =\text{batch?size}\\ L& =\text{?sequence?length?}\\ D& =2\text{?if?bidirectional=True?otherwise?}1\\ H_{\text{in}}& =\text{?input\_size?}\\ H_{out}& =\text{?hidden\_size?}\end{array}$$

输入：input, h_0

（1）input(输入序列)

非批量：$(L,H_{in})$

批量：如果batch_first=False，$（L,N,H_{in})$；如果batch_first=True，$（N,L,H_{in})$

（2） h_0（每一层网络的初始状态。如果未提供，则默认为零。）

非批量：$(D\times \text{num\_layers},H_{out})$

批量：$(D\times \text{num\_layers},N,H_{out})$

输出，output，hn：

（1）output:

非批量：$(L,D\times H_{out})$

批量：如果batch_first=False，$（L,N,H_{out})$；如果batch_first=True，$（N,L,H_{out})$

（2）h_n:状态

非批量：$(D\times \text{num\_layers},H_{out})$

批量：$(D\times \text{num\_layers},N,H_{out})$

权重和偏置初始化：

从均匀分布$U(?\sqrt{k},\sqrt{k})$采样，其中$k=\frac{1}{hidden\_size}$

[1] https://www.zjujournals.com/eng/article/2019/1008-973X/G181044wanghongxia-1.jpg.html

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