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经过训练的三阶多项式,可以通过最小化平方的欧几里得距离来预测y = sin(x)-pipi

此实现使用来自 PyTorch 的nn包来构建网络。

与其像以前那样手动更新模型的权重,不如使用optim包定义一个优化器,该优化器将为我们更新权重。 optim包定义了许多深度学习常用的优化算法,包括 SGD + 动量,RMSProp,Adam 等。

import torch
import math

# Create Tensors to hold input and outputs.
x = torch.linspace(-math.pi, math.pi, 2000)
y = torch.sin(x)

# Prepare the input tensor (x, x^2, x^3).
p = torch.tensor([1, 2, 3])
xx = x.unsqueeze(-1).pow(p)

# Use the nn package to define our model and loss function.
model = torch.nn.Sequential(
    torch.nn.Linear(3, 1),
    torch.nn.Flatten(0, 1)
loss_fn = torch.nn.MSELoss(reduction='sum')

# Use the optim package to define an Optimizer that will update the weights of
# the model for us. Here we will use RMSprop; the optim package contains many other
# optimization algorithms. The first argument to the RMSprop constructor tells the
# optimizer which Tensors it should update.
learning_rate = 1e-3
optimizer = torch.optim.RMSprop(model.parameters(), lr=learning_rate)
for t in range(2000):
    # Forward pass: compute predicted y by passing x to the model.
    y_pred = model(xx)

    # Compute and print loss.
    loss = loss_fn(y_pred, y)
    if t % 100 == 99:
        print(t, loss.item())

    # Before the backward pass, use the optimizer object to zero all of the
    # gradients for the variables it will update (which are the learnable
    # weights of the model). This is because by default, gradients are
    # accumulated in buffers( i.e, not overwritten) whenever .backward()
    # is called. Checkout docs of torch.autograd.backward for more details.

    # Backward pass: compute gradient of the loss with respect to model
    # parameters

    # Calling the step function on an Optimizer makes an update to its
    # parameters

linear_layer = model[0]
print(f'Result: y = {linear_layer.bias.item()} + {linear_layer.weight[:, 0].item()} x + {linear_layer.weight[:, 1].item()} x^2 + {linear_layer.weight[:, 2].item()} x^3')

脚本的总运行时间:(0 分钟 0.000 秒)

下载 Python 源码

下载 Jupyter 笔记本:polynomial_optim.ipynb

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