polynomial_autograd.py

r"""
PyTorch: Tensors and autograd
-------------------------------

A third order polynomial, trained to predict :math:`y=\sin(x)` from :math:`-\pi`
to :math:`\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.
"""
import torch
import math

# 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(-1, 1, 2000, dtype=dtype)
y = torch.exp(x) # A Taylor expansion would be 1 + x + (1/2) x**2 + (1/3!) x**3 + ...

# 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)

initial_loss = 1.
learning_rate = 1e-5
for t in range(5000):
    # 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()

    # Calculare initial loss, so we can report loss relative to it
    if t==0:
        initial_loss=loss.item()

    if t % 100 == 99:
        print(f'Iteration t = {t:4d}  loss(t)/loss(0) = {round(loss.item()/initial_loss, 6):10.6f}  a = {a.item():10.6f}  b = {b.item():10.6f}  c = {c.item():10.6f}  d = {d.item():10.6f}')

    # 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')