Matrix Information Theory for Self-Supervised Learning
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, achieving 72.3% on the GSM8K dataset by fine-tuning a 7B model using matrix cross-entropy loss, with a margin of 3.1% over the standard cross-entropy loss. Code available at https://github.com/yifanzhang-pro/Matrix-SSL.
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Datasets
ImageNet
MS COCO
GSM8K
MATH
| Task | Dataset | Model | Metric Name | Metric Value | Global Rank | Benchmark |
|---|---|---|---|---|---|---|
| Contrastive Learning | imagenet-1k | ResNet50 | ImageNet Top-1 Accuracy | 73.6 | # 1 |
