Gradient Computation

In our PyTorch implementation of Normalized Cut (NCUT), gradient computation is handled seamlessly by PyTorch autograd, you can backpropagate gradients from the eigenvectors to the input features.

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With Nyström Approximation

This example demonstrates how to compute gradients when using the Nyström approximation. For gradient-sensitive workloads in 3.0.0, enable exact_gradient=True.

from ncut_pytorch import Ncut
import torch

# Initialize features with gradient tracking
features = torch.randn(10000, 768)
features.requires_grad = True

# Compute NCUT with the exact eigensolver path for a stable backward pass
ncut = Ncut(n_eig=50, exact_gradient=True)
eigenvectors = ncut.fit_transform(features)
eigenvalues = ncut.eigval

# Define a loss function (e.g., sum of eigenvectors)
loss = eigenvectors.sum()

# Backpropagate
loss.backward()

# Access gradients
grad = features.grad
print(f"Gradient shape: {grad.shape}")
# Output: torch.Size([10000, 768])