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PyTorch: Tensors and autograd#

Created On: Dec 03, 2020 | Last Updated: May 19, 2025 | Last Verified: Nov 05, 2024

A third order polynomial, trained to predict \(y=\sin(x)\) from \(-\pi\) to \(\pi\) by minimizing squared Euclidean distance.

This implementation computes the forward pass using operations on PyTorch Tensors, and uses PyTorch autograd to compute gradients.

A PyTorch Tensor represents a node in a computational graph. If x is a Tensor that has x.requires_grad=True then x.grad is another Tensor holding the gradient of x with respect to some scalar value.

importtorch
importmath
# We want to be able to train our model on an `accelerator <https://pytorch.org/docs/stable/torch.html#accelerators>`__
# such as CUDA, MPS, MTIA, or XPU. If the current accelerator is available, we will use it. Otherwise, we use the CPU.
dtype = torch.float
device = torch.accelerator.current_accelerator ().type if torch.accelerator.is_available () else "cpu"
print(f"Using {device} device")
torch.set_default_device (device)
# Create Tensors to hold input and outputs.
# By default, requires_grad=False, which indicates that we do not need to
# compute gradients with respect to these Tensors during the backward pass.
x = torch.linspace (-math.pi, math.pi, 2000, dtype=dtype)
y = torch.sin (x)
# Create random Tensors for weights. For a third order polynomial, we need
# 4 weights: y = a + b x + c x^2 + d x^3
# Setting requires_grad=True indicates that we want to compute gradients with
# respect to these Tensors during the backward pass.
a = torch.randn ((), dtype=dtype, requires_grad=True)
b = torch.randn ((), dtype=dtype, requires_grad=True)
c = torch.randn ((), dtype=dtype, requires_grad=True)
d = torch.randn ((), dtype=dtype, requires_grad=True)
learning_rate = 1e-6
for t in range(2000):
 # Forward pass: compute predicted y using operations on Tensors.
 y_pred = a + b * x + c * x ** 2 + d * x ** 3
 # Compute and print loss using operations on Tensors.
 # Now loss is a Tensor of shape (1,)
 # loss.item() gets the scalar value held in the loss.
 loss = (y_pred - y).pow(2).sum()
 if t % 100 == 99:
 print(t, loss.item())
 # Use autograd to compute the backward pass. This call will compute the
 # gradient of loss with respect to all Tensors with requires_grad=True.
 # After this call a.grad, b.grad. c.grad and d.grad will be Tensors holding
 # the gradient of the loss with respect to a, b, c, d respectively.
 loss.backward()
 # Manually update weights using gradient descent. Wrap in torch.no_grad()
 # because weights have requires_grad=True, but we don't need to track this
 # in autograd.
 with torch.no_grad ():
 a -= learning_rate * a.grad
 b -= learning_rate * b.grad
 c -= learning_rate * c.grad
 d -= learning_rate * d.grad
 # Manually zero the gradients after updating weights
 a.grad = None
 b.grad = None
 c.grad = None
 d.grad = None
print(f'Result: y = {a.item()} + {b.item()} x + {c.item()} x^2 + {d.item()} x^3')