Matrix Information Theory for Self-Supervised Learning

TL;DR

Matrix-SSL introduces a matrix information theory-based framework for self-supervised learning that improves performance on image and language tasks by incorporating matrix uniformity and alignment losses.

Contribution

The paper proposes Matrix-SSL, a novel self-supervised learning method that unifies and enhances existing approaches through matrix information theory, achieving state-of-the-art results.

Findings

Outperforms SOTA on ImageNet linear evaluation

Achieves up to 3.3% improvement on MS-COCO transfer learning

Improves language model fine-tuning with matrix cross-entropy loss

Abstract

The maximum entropy encoding framework provides a unified perspective for many non-contrastive learning methods like SimSiam, Barlow Twins, and MEC. Inspired by this framework, we introduce Matrix-SSL, a novel approach that leverages matrix information theory to interpret the maximum entropy encoding loss as matrix uniformity loss. Furthermore, Matrix-SSL enhances the maximum entropy encoding method by seamlessly incorporating matrix alignment loss, directly aligning covariance matrices in different branches. Experimental results reveal that Matrix-SSL outperforms state-of-the-art methods on the ImageNet dataset under linear evaluation settings and on MS-COCO for transfer learning tasks. Specifically, when performing transfer learning tasks on MS-COCO, our method outperforms previous SOTA methods such as MoCo v2 and BYOL up to 3.3% with only 400 epochs compared to 800 epochs pre-training. We also try to introduce representation learning into the language modeling regime by fine-tuning a 7B model using matrix cross-entropy loss, with a margin of 3.1% on the GSM8K dataset over the standard cross-entropy loss. Code available at https://github.com/yifanzhang-pro/Matrix-SSL.