beginner/examples_tensor/polynomial_tensor

Run in Google Colab

Colab

Download Notebook

Notebook

View on GitHub

GitHub

PyTorch: Tensors

Created On: Dec 03, 2020 | Last Updated: May 08, 2026 | 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 uses PyTorch tensors to manually compute the forward pass, loss, and backward pass.

A PyTorch Tensor is basically the same as a numpy array: it does not know anything about deep learning or computational graphs or gradients, and is just a generic n-dimensional array to be used for arbitrary numeric computation.

The biggest difference between a numpy array and a PyTorch Tensor is that a PyTorch Tensor can run on either CPU or GPU. To run operations on the GPU, just cast the Tensor to a cuda datatype.

99 1188.946533203125
199 802.8765258789062
299 543.5830688476562
399 369.2912292480469
499 252.03514099121094
599 173.0804901123047
699 119.86717224121094
799 83.96935272216797
899 59.72889709472656
999 43.344032287597656
1099 32.2576904296875
1199 24.748628616333008
1299 19.65715980529785
1399 16.2011775970459
1499 13.852736473083496
1599 12.255090713500977
1699 11.167035102844238
1799 10.425189971923828
1899 9.918811798095703
1999 9.57275390625
Result: y = -0.02153015322983265 + 0.8387677073478699 x + 0.003714310936629772 x^2 + -0.09077386558055878 x^3

import torch

dtype = torch.float
device = torch.device("cpu")
# device = torch.device("cuda:0") # Uncomment this to run on GPU

# Create random input and output data
x = torch.linspace(-torch.pi, torch.pi, 2000, device=device, dtype=dtype)
y = torch.sin(x)

# Randomly initialize weights
a = torch.randn((), device=device, dtype=dtype)
b = torch.randn((), device=device, dtype=dtype)
c = torch.randn((), device=device, dtype=dtype)
d = torch.randn((), device=device, dtype=dtype)

learning_rate = 1e-6
for t in range(2000):
    # Forward pass: compute predicted y
    y_pred = a + b * x + c * x ** 2 + d * x ** 3

    # Compute and print loss
    loss = (y_pred - y).pow(2).sum().item()
    if t % 100 == 99:
        print(t, loss)

    # Backprop to compute gradients of a, b, c, d with respect to loss
    grad_y_pred = 2.0 * (y_pred - y)
    grad_a = grad_y_pred.sum()
    grad_b = (grad_y_pred * x).sum()
    grad_c = (grad_y_pred * x ** 2).sum()
    grad_d = (grad_y_pred * x ** 3).sum()

    # Update weights using gradient descent
    a -= learning_rate * grad_a
    b -= learning_rate * grad_b
    c -= learning_rate * grad_c
    d -= learning_rate * grad_d


print(f'Result: y = {a.item()} + {b.item()} x + {c.item()} x^2 + {d.item()} x^3')