一、RNN特性

权重共享

word_i · weight + bais

持久记忆单元

word_i · weight_word + bais_word + h_i · weight_h + bais_h

二、公式化表达

h_{t</sub = f(ht - 1, xt)
ht = tanh(Whhht - 1 + Wxhxt)
yt = Whyht}

三、RNN网络正弦波波形预测

环境准备

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

# 时间轴采样数
num_time_steps = 50
input_size = 1
hidden_size = 16
output_size = 1
lr = 0.01

RNN类

class Net(nn.Module):
    def __init__(self,):
        super(Net, self).__init__()
        self.rnn = nn.RNN(
            input_size = input_size, 
            hidden_size = hidden_size, 
            num_layers = 1,
            # 格式为[batch, seq, feature]
            batch_first = True
        )
        for p in self.rnn.parameters():
            nn.init.normal_(p,mean=0.0, std=0.001)
        self.linear = nn.Linear(hidden_size, output_size)

    def forward(self, x, hidden_prev):
        out, hidden_prev = self.rnn(x, hidden_prev)
        # [1, seq, h] => [seq, h]
        out = out.view(-1,hidden_size)
        # [seq, h] => [seq, 1]
        out = self.linear(out)
        # [seq, 1] => [1, seq, 1], 需要和y做均方差
        out = out.unsqueeze(dim=0)
        return out, hidden_prev.clone()

正弦数据构建函数

def create_image():
    start = np.random.randint(3, size=1)[0]
    time_steps = np.linspace(start, start + 10, num_time_steps)
    data = np.sin(time_steps)
    data = data.reshape(num_time_steps, 1)
    x = torch.tensor(data[:-1]).float().view(1, num_time_steps - 1, 1)
    y = torch.tensor(data[1:]).float().view(1, num_time_steps - 1, 1)
    return time_steps,x, y

训练模型

model = Net()
criterion = nn.MSELoss()
optimizer = optim.Adam(model.parameters(), lr)

hidden_prev = torch.zeros(1,1, hidden_size)
for iter in range(6000):
    time_steps,x, y = create_image()
    output, hidden_prev = model(x, hidden_prev)
    hidden_prev = hidden_prev.detach()

    loss = criterion(output,y)
    model.zero_grad()
    loss.backward()
    for p in model.parameters():
        torch.nn.utils.clip_grad_norm_(p,10)
    optimizer.step()

    if iter % 1000 == 0:
        plt.plot(time_steps[:-1], x.ravel(), c = 'b')
        plt.plot(time_steps[:-1], y.ravel(), c= 'r')
        plt.plot(time_steps[:-1], output.detach().numpy().ravel(), c= 'g')
        plt.show()
        print('Iteration:{} loss {}'.format(iter, loss.item()))

可以看到第二次绘制图像的时候，输出曲线基本拟合了目标曲线

图像预测

time_steps,x, y = create_image()

predictions = []
# input = x[:, 0, :]
for i in range(x.shape[1]):
    input = x[:, i, :].view(1, 1, 1)
    (pred, hiden_prev) = model(input, hidden_prev)
    input = pred
    predictions.append(pred.detach().numpy().ravel()[0])

x = x.data.numpy().ravel()

y = y.data.numpy()
plt.scatter(time_steps[:-1], x.ravel(), s=90)
plt.plot(time_steps[:-1], x.ravel())

plt.scatter(time_steps[1:],predictions)
plt.show()
    

输出的预测曲线基本与目标曲线相同