PyTorch：张量 与 Autograd

原文：https://pytorch.org/tutorials/beginner/examples_autograd/polynomial_autograd.html#sphx-glr-beginner-examples-autograd-polynomial-autograd-py

校对：DrDavidS

这里我们准备一个三阶多项式，通过最小化平方欧几里得距离来训练，并预测函数 y = sin(x) 在-pi到pi上的值。

此实现使用了 PyTorch 张量(tensor)运算来实现前向传播，并使用 PyTorch Autograd 来计算梯度。

PyTorch 张量表示计算图中的一个节点。 如果x是一个张量，且x.requires_grad=True，则x.grad是另一个张量，它保存了x相对于某个标量值的梯度。

  1. import torch
  2. import math
  4. dtype = torch.float
  5. device = torch.device("cpu")
  6. # device = torch.device("cuda:0")  # Uncomment this to run on GPU
  8. # Create Tensors to hold input and outputs.
  9. # By default, requires_grad=False, which indicates that we do not need to
  10. # compute gradients with respect to these Tensors during the backward pass.
  11. x = torch.linspace(-math.pi, math.pi, 2000, device=device, dtype=dtype)
  12. y = torch.sin(x)
  14. # Create random Tensors for weights. For a third order polynomial, we need
  15. # 4 weights: y = a + b x + c x^2 + d x^3
  16. # Setting requires_grad=True indicates that we want to compute gradients with
  17. # respect to these Tensors during the backward pass.
  18. a = torch.randn((), device=device, dtype=dtype, requires_grad=True)
  19. b = torch.randn((), device=device, dtype=dtype, requires_grad=True)
  20. c = torch.randn((), device=device, dtype=dtype, requires_grad=True)
  21. d = torch.randn((), device=device, dtype=dtype, requires_grad=True)
  23. learning_rate = 1e-6
  24. for t in range(2000):
  25.     # Forward pass: compute predicted y using operations on Tensors.
  26.     y_pred = a + b * x + c * x ** 2 + d * x ** 3
  28.     # Compute and print loss using operations on Tensors.
  29.     # Now loss is a Tensor of shape (1,)
  30.     # loss.item() gets the scalar value held in the loss.
  31.     loss = (y_pred - y).pow(2).sum()
  32.     if t % 100 == 99:
  33.         print(t, loss.item())
  35.     # Use autograd to compute the backward pass. This call will compute the
  36.     # gradient of loss with respect to all Tensors with requires_grad=True.
  37.     # After this call a.grad, b.grad. c.grad and d.grad will be Tensors holding
  38.     # the gradient of the loss with respect to a, b, c, d respectively.
  39.     loss.backward()
  41.     # Manually update weights using gradient descent. Wrap in torch.no_grad()
  42.     # because weights have requires_grad=True, but we don't need to track this
  43.     # in autograd.
  44.     with torch.no_grad():
  45.         a -= learning_rate * a.grad
  46.         b -= learning_rate * b.grad
  47.         c -= learning_rate * c.grad
  48.         d -= learning_rate * d.grad
  50.         # Manually zero the gradients after updating weights
  51.         a.grad = None
  52.         b.grad = None
  53.         c.grad = None
  54.         d.grad = None
  56. print(f'Result: y = {a.item()} + {b.item()} x + {c.item()} x^2 + {d.item()} x^3')

脚本的总运行时间：（0 分钟 0.000 秒）

下载 Python 源码：polynomial_autograd.py

下载 Jupyter 笔记本：polynomial_autograd.ipynb