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PyTorch: nn#
Created On: Dec 03, 2020 | Last Updated: Sep 29, 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 uses the nn package from PyTorch to build the network. PyTorch autograd makes it easy to define computational graphs and take gradients, but raw autograd can be a bit too low-level for defining complex neural networks; this is where the nn package can help. The nn package defines a set of Modules, which you can think of as a neural network layer that produces output from input and may have some trainable weights.
99 250.57286071777344
199 171.801025390625
299 118.80036926269531
399 83.10763549804688
499 59.04848098754883
599 42.81584548950195
699 31.85308074951172
799 24.44186782836914
899 19.426502227783203
999 16.02899742126465
1099 13.724963188171387
1199 12.160786628723145
1299 11.097723007202148
1399 10.374421119689941
1499 9.881753921508789
1599 9.54578685760498
1699 9.31641960144043
1799 9.159647941589355
1899 9.052372932434082
1999 8.978883743286133
Result: y = -0.010280085727572441 + 0.8487606644630432 x + 0.0017734861467033625 x^2 + -0.09219527989625931 x^3
import torch
import math
# Create Tensors to hold input and outputs.
x = torch.linspace(-math.pi, math.pi, 2000)
y = torch.sin(x)
# For this example, the output y is a linear function of (x, x^2, x^3), so
# we can consider it as a linear layer neural network. Let's prepare the
# tensor (x, x^2, x^3).
p = torch.tensor([1, 2, 3])
xx = x.unsqueeze(-1).pow(p)
# In the above code, x.unsqueeze(-1) has shape (2000, 1), and p has shape
# (3,), for this case, broadcasting semantics will apply to obtain a tensor
# of shape (2000, 3)
# Use the nn package to define our model as a sequence of layers. nn.Sequential
# is a Module which contains other Modules, and applies them in sequence to
# produce its output. The Linear Module computes output from input using a
# linear function, and holds internal Tensors for its weight and bias.
# The Flatten layer flatens the output of the linear layer to a 1D tensor,
# to match the shape of `y`.
model = torch.nn.Sequential(
torch.nn.Linear(3, 1),
torch.nn.Flatten(0, 1)
)
# The nn package also contains definitions of popular loss functions; in this
# case we will use Mean Squared Error (MSE) as our loss function.
loss_fn = torch.nn.MSELoss(reduction='sum')
learning_rate = 1e-6
for t in range(2000):
# Forward pass: compute predicted y by passing x to the model. Module objects
# override the __call__ operator so you can call them like functions. When
# doing so you pass a Tensor of input data to the Module and it produces
# a Tensor of output data.
y_pred = model(xx)
# Compute and print loss. We pass Tensors containing the predicted and true
# values of y, and the loss function returns a Tensor containing the
# loss.
loss = loss_fn(y_pred, y)
if t % 100 == 99:
print(t, loss.item())
# Zero the gradients before running the backward pass.
model.zero_grad()
# Backward pass: compute gradient of the loss with respect to all the learnable
# parameters of the model. Internally, the parameters of each Module are stored
# in Tensors with requires_grad=True, so this call will compute gradients for
# all learnable parameters in the model.
loss.backward()
# Update the weights using gradient descent. Each parameter is a Tensor, so
# we can access its gradients like we did before.
with torch.no_grad():
for param in model.parameters():
param -= learning_rate * param.grad
# You can access the first layer of `model` like accessing the first item of a list
linear_layer = model[0]
# For linear layer, its parameters are stored as `weight` and `bias`.
print(f'Result: y = {linear_layer.bias.item()} + {linear_layer.weight[:, 0].item()} x + {linear_layer.weight[:, 1].item()} x^2 + {linear_layer.weight[:, 2].item()} x^3')
Total running time of the script: (0 minutes 0.528 seconds)
