PyTorch: Tensors

Created On: Dec 03, 2020 | Last Updated: Dec 03, 2020 | 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 1634.0506591796875
199 1099.37744140625
299 741.1851806640625
399 501.04583740234375
499 339.92962646484375
599 231.7466278076172
699 159.04660034179688
799 110.15023803710938
899 77.23455810546875
999 55.05645751953125
1099 40.09944534301758
1199 30.002578735351562
1299 23.179832458496094
1399 18.56486701965332
1499 15.440007209777832
1599 13.32192611694336
1699 11.88467025756836
1799 10.908334732055664
1899 10.244379043579102
1999 9.792350769042969
Result: y = -0.023177823051810265 + 0.8350979685783386 x + 0.003998560830950737 x^2 + -0.0902518779039383 x^3

import torch
import math


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(-math.pi, math.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')