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.

翻译：最大熵编码框架为SimSiam、Barlow Twins和MEC等多种非对比学习方法提供了统一视角。受此框架启发，我们提出了Matrix-SSL这一新方法，它利用矩阵信息论将最大熵编码损失解释为矩阵均匀性损失。此外，Matrix-SSL通过无缝整合矩阵对齐损失来增强最大熵编码方法，直接对齐不同分支的协方差矩阵。实验结果表明，在线性评估设置下的ImageNet数据集以及迁移学习任务中的MS-COCO数据集上，Matrix-SSL均优于现有最先进方法。具体而言，在MS-COCO上进行迁移学习任务时，我们的方法仅需400轮预训练（相比800轮），其性能就比MoCo v2和BYOL等先前SOTA方法高出3.3%。我们还尝试通过使用矩阵交叉熵损失微调7B模型，将表示学习引入语言建模领域，在GSM8K数据集上相比标准交叉熵损失获得了3.1%的性能提升。代码发布于https://github.com/yifanzhang-pro/Matrix-SSL。