PyTorch: Tensors¶
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.
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() 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')
Total running time of the script: ( 0 minutes 0.000 seconds)
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