Manifold Contrastive Learning with Variational Lie Group Operators

TL;DR

This paper introduces a novel contrastive learning method that explicitly models data manifolds using Lie group operators with a variational approach, enhancing self-supervised and semi-supervised learning performance.

Contribution

It proposes a Lie group-based contrastive learning framework with a variational model for manifold sampling, enabling explicit manifold modeling and improved data augmentation.

Findings

Improves self-supervised learning benchmarks with manifold feature augmentations.

Enhances semi-supervised classification performance with learned transformations.

Effectively applies manifold-based augmentations with or without a projection head.

Abstract

Self-supervised learning of deep neural networks has become a prevalent paradigm for learning representations that transfer to a variety of downstream tasks. Similar to proposed models of the ventral stream of biological vision, it is observed that these networks lead to a separation of category manifolds in the representations of the penultimate layer. Although this observation matches the manifold hypothesis of representation learning, current self-supervised approaches are limited in their ability to explicitly model this manifold. Indeed, current approaches often only apply augmentations from a pre-specified set of "positive pairs" during learning. In this work, we propose a contrastive learning approach that directly models the latent manifold using Lie group operators parameterized by coefficients with a sparsity-promoting prior. A variational distribution over these coefficients provides a generative model of the manifold, with samples which provide feature augmentations applicable both during contrastive training and downstream tasks. Additionally, learned coefficient distributions provide a quantification of which transformations are most likely at each point on the manifold while preserving identity. We demonstrate benefits in self-supervised benchmarks for image datasets, as well as a downstream semi-supervised task. In the former case, we demonstrate that the proposed methods can effectively apply manifold feature augmentations and improve learning both with and without a projection head. In the latter case, we demonstrate that feature augmentations sampled from learned Lie group operators can improve classification performance when using few labels.