目录
1.写在前面
循环神经网络让神经网络有了记忆, 对于序列话的数据,循环神经网络能达到更好的效果.上次我们提到了用 RNN 的最后一个时间点输出来判断之前看到的图片属于哪一类, 这次我们来真的了, 用 RNN 来及时预测时间序列.
2.训练数据
我们要用到的数据就是这样的一些数据, 我们想要用 sin 的曲线预测出 cos 的曲线.
import torch
from torch import nn
import numpy as np
import matplotlib.pyplot as plt
torch.manual_seed(1) # reproducible
# Hyper Parameters
TIME_STEP = 10 # rnn time step / image height
INPUT_SIZE = 1 # rnn input size / image width
LR = 0.02 # learning rate
DOWNLOAD_MNIST = False # set to True if haven't download the data3.RNN模型
这一次的 RNN, 我们对每一个 r_out 都得放到 Linear 中去计算出预测的 output, 所以我们能用一个 for loop 来循环计算. 这点是 Tensorflow 望尘莫及的! 看看我们的 PyTorch 和 Tensorflow 到底哪家强.
class RNN(nn.Module):
def __init__(self):
super(RNN, self).__init__()
self.rnn = nn.RNN( # 这回一个普通的 RNN 就能胜任
input_size=1,
hidden_size=32, # rnn hidden unit
num_layers=1, # 有几层 RNN layers
batch_first=True, # input & output 会是以 batch size 为第一维度的特征集 e.g. (batch, time_step, input_size)
)
self.out = nn.Linear(32, 1)
def forward(self, x, h_state): # 因为 hidden state 是连续的, 所以我们要一直传递这一个 state
# x (batch, time_step, input_size)
# h_state (n_layers, batch, hidden_size)
# r_out (batch, time_step, output_size)
r_out, h_state = self.rnn(x, h_state) # h_state 也要作为 RNN 的一个输入
outs = [] # 保存所有时间点的预测值
for time_step in range(r_out.size(1)): # 对每一个时间点计算 output
outs.append(self.out(r_out[:, time_step, :]))
return torch.stack(outs, dim=1), h_state
rnn = RNN()
print(rnn)
"""
RNN (
(rnn): RNN(1, 32, batch_first=True)
(out): Linear (32 -> 1)
)
""" 其实熟悉 RNN 的朋友应该知道, forward 过程中的对每个时间点求输出还有一招使得计算量比较小的. 不过上面的内容主要是为了呈现 PyTorch 在动态构图上的优势, 所以我用了一个 for loop 来搭建那套输出系统. 下面介绍一个替换方式. 使用 reshape 的方式整批计算.
def forward(self, x, h_state):
r_out, h_state = self.rnn(x, h_state)
r_out = r_out.view(-1, 32)
outs = self.out(r_out)
return outs.view(-1, 32, TIME_STEP), h_state4.训练
下面的代码就能实现动图的效果啦~开心, 可以看出, 我们使用 x 作为输入的 sin 值, 然后 y 作为想要拟合的输出, cos 值. 因为他们两条曲线是存在某种关系的, 所以我们就能用 sin 来预测 cos. rnn 会理解他们的关系, 并用里面的参数分析出来这个时刻 sin 曲线上的点如何对应上 cos 曲线上的点.
optimizer = torch.optim.Adam(rnn.parameters(), lr=LR) # optimize all rnn parameters
loss_func = nn.MSELoss()
h_state = None # 要使用初始 hidden state, 可以设成 None
for step in range(100):
start, end = step * np.pi, (step+1)*np.pi # time steps
# sin 预测 cos
steps = np.linspace(start, end, 10, dtype=np.float32)
x_np = np.sin(steps) # float32 for converting torch FloatTensor
y_np = np.cos(steps)
x = torch.from_numpy(x_np[np.newaxis, :, np.newaxis]) # shape (batch, time_step, input_size)
y = torch.from_numpy(y_np[np.newaxis, :, np.newaxis])
prediction, h_state = rnn(x, h_state) # rnn 对于每个 step 的 prediction, 还有最后一个 step 的 h_state
# !! 下一步十分重要 !!
h_state = h_state.data # 要把 h_state 重新包装一下才能放入下一个 iteration, 不然会报错
loss = loss_func(prediction, y) # cross entropy loss
optimizer.zero_grad() # clear gradients for this training step
loss.backward() # backpropagation, compute gradients
optimizer.step() # apply gradients
5.完整代码演示
import torch
from torch import nn
import numpy as np
import matplotlib.pyplot as plt
# torch.manual_seed(1) # reproducible
# Hyper Parameters
TIME_STEP = 10 # rnn time step
INPUT_SIZE = 1 # rnn input size
LR = 0.02 # learning rate
# show data
steps = np.linspace(0, np.pi*2, 100, dtype=np.float32) # float32 for converting torch FloatTensor
x_np = np.sin(steps)
y_np = np.cos(steps)
plt.plot(steps, y_np, 'r-', label='target (cos)')
plt.plot(steps, x_np, 'b-', label='input (sin)')
plt.legend(loc='best')
plt.show()
class RNN(nn.Module):
def __init__(self):
super(RNN, self).__init__()
self.rnn = nn.RNN(
input_size=INPUT_SIZE,
hidden_size=32, # rnn hidden unit
num_layers=1, # number of rnn layer
batch_first=True, # input & output will has batch size as 1s dimension. e.g. (batch, time_step, input_size)
)
self.out = nn.Linear(32, 1)
def forward(self, x, h_state):
# x (batch, time_step, input_size)
# h_state (n_layers, batch, hidden_size)
# r_out (batch, time_step, hidden_size)
r_out, h_state = self.rnn(x, h_state)
outs = [] # save all predictions
for time_step in range(r_out.size(1)): # calculate output for each time step
outs.append(self.out(r_out[:, time_step, :]))
return torch.stack(outs, dim=1), h_state
# instead, for simplicity, you can replace above codes by follows
# r_out = r_out.view(-1, 32)
# outs = self.out(r_out)
# outs = outs.view(-1, TIME_STEP, 1)
# return outs, h_state
# or even simpler, since nn.Linear can accept inputs of any dimension
# and returns outputs with same dimension except for the last
# outs = self.out(r_out)
# return outs
rnn = RNN()
print(rnn)
optimizer = torch.optim.Adam(rnn.parameters(), lr=LR) # optimize all cnn parameters
loss_func = nn.MSELoss()
h_state = None # for initial hidden state
plt.figure(1, figsize=(12, 5))
plt.ion() # continuously plot
for step in range(100):
start, end = step * np.pi, (step+1)*np.pi # time range
# use sin predicts cos
steps = np.linspace(start, end, TIME_STEP, dtype=np.float32, endpoint=False) # float32 for converting torch FloatTensor
x_np = np.sin(steps)
y_np = np.cos(steps)
x = torch.from_numpy(x_np[np.newaxis, :, np.newaxis]) # shape (batch, time_step, input_size)
y = torch.from_numpy(y_np[np.newaxis, :, np.newaxis])
prediction, h_state = rnn(x, h_state) # rnn output
# !! next step is important !!
h_state = h_state.data # repack the hidden state, break the connection from last iteration
loss = loss_func(prediction, y) # calculate loss
optimizer.zero_grad() # clear gradients for this training step
loss.backward() # backpropagation, compute gradients
optimizer.step() # apply gradients
# plotting
plt.plot(steps, y_np.flatten(), 'r-')
plt.plot(steps, prediction.data.numpy().flatten(), 'b-')
plt.draw(); plt.pause(0.05)
plt.ioff()
plt.show()