Self-supervised learning (SSL) learns useful representations from unlabelled data by training networks to be invariant to pairs of augmented versions of the same input. Non-contrastive methods avoid collapse either by directly regularizing the covariance matrix of network outputs or through asymmetric loss architectures, two seemingly unrelated approaches. Here, by building on DirectPred, we lay out a theoretical framework that reconciles these two views. We derive analytical expressions for the representational learning dynamics in linear networks. By expressing them in the eigenspace of the embedding covariance matrix, where the solutions decouple, we reveal the mechanism and conditions that provide implicit variance regularization. These insights allow us to formulate a new isotropic loss function that equalizes eigenvalue contribution and renders learning more robust. Finally, we show empirically that our findings translate to nonlinear networks trained on CIFAR-10 and STL-10.

本论文研究了自监督学习的非对比方法，通过构建 DirectPred 理论框架，分析了线性网络的表示学习动态，并通过共轭积的方法提供了一个显式的方差规则机制，提出了一种新的各向同性损失函数，并在 CIFAR-10 和 STL-10 数据集上证明了理论发现的正确性。

通过预测网络和停梯度方法，实现BYOL/SimSiam的隐式方差正则化