GLL: A Differentiable Graph Learning Layer for Neural Networks

TL;DR

This paper introduces a differentiable graph learning layer that integrates similarity graph construction and label propagation into neural networks, enhancing classification performance and robustness.

Contribution

It derives backpropagation equations for end-to-end training of graph learning layers within neural networks, enabling precise integration of graph-based label propagation.

Findings

Improved generalization over standard softmax models

Enhanced robustness to adversarial attacks

Smoother label transitions across data

Abstract

Standard deep learning architectures used for classification generate label predictions with a projection head and softmax activation function. Although successful, these methods fail to leverage the relational information between samples for generating label predictions. In recent works, graph-based learning techniques, namely Laplace learning, have been heuristically combined with neural networks for both supervised and semi-supervised learning (SSL) tasks. However, prior works approximate the gradient of the loss function with respect to the graph learning algorithm or decouple the processes; end-to-end integration with neural networks is not achieved. In this work, we derive backpropagation equations, via the adjoint method, for inclusion of a general family of graph learning layers into a neural network. The resulting method, distinct from graph neural networks, allows us to precisely integrate similarity graph construction and graph Laplacian-based label propagation into a neural network layer, replacing a projection head and softmax activation function for general classification task. Our experimental results demonstrate smooth label transitions across data, improved generalization and robustness to adversarial attacks, and improved training dynamics compared to a standard softmax-based approach.