TOWARDS A UNIFIED THEORETICAL UNDERSTAND-ING OF NON-CONTRASTIVE LEARNING VIA RANK DIFFERENTIAL MECHANISM

Abstract

Recently, a variety of methods under the name of non-contrastive learning (like BYOL, SimSiam, SwAV, DINO) show that when equipped with some asymmetric architectural designs, aligning positive pairs alone is sufficient to attain good performance in self-supervised visual learning. Despite some understandings of some specific modules (like the predictor in BYOL), there is yet no unified theoretical understanding of how these seemingly different asymmetric designs can all avoid feature collapse, particularly considering methods that also work without the predictor (like DINO). In this work, we propose a unified theoretical understanding for existing variants of non-contrastive learning. Our theory named Rank Differential Mechanism (RDM) shows that all these asymmetric designs create a consistent rank difference in their dual-branch output features. This rank difference will provably lead to an improvement of effective dimensionality and alleviate either complete or dimensional feature collapse. Different from previous theories, our RDM theory is applicable to different asymmetric designs (with and without the predictor), and thus can serve as a unified understanding of existing non-contrastive learning methods. Besides, our RDM theory also provides practical guidelines for designing many new non-contrastive variants. We show that these variants indeed achieve comparable performance to existing methods on benchmark datasets, and some of them even outperform the baselines.

1. INTRODUCTION

Self-supervised learning of visual representations has undergone rapid progress in recent years, particularly due to the rise of contrastive learning (CL) (Oord et al., 2018; Wang et al., 2021) . Canonical contrastive learning methods like SimCLR (Chen et al., 2020) and MoCo (He et al., 2020) utilize both positive samples (for feature alignment) and negative samples (for feature uniformity). Surprisingly, researchers notice that CL can also work well by only aligning positive samples, which is referred to as non-contrastive learning. Without the help of negative samples, various techniques are proposed to prevent feature collapse, for example, stop-gradient, momentum encoder, predictor (BYOL (Grill et al., 2020) , SimSiam (Chen & He, 2021)), Sinkhorn iterations (SwAV (Caron et al., 2020)), feature centering and sharpening (DINO (Caron et al., 2021) ). These above designs all create a certain of asymmetry between the online branch (with gradient) and the target branch (without gradient) (Wang et al., 2022a) . Empirically, these tricks can successfully alleviate feature collapse and obtain comparable or even superior performance than canonical contrastive learning. Despite this progress, it is still not clear why these different heuristics can reach the same goal. Some existing works are proposed to understand some specific non-contrastive techniques, mostly focusing on the predictor head proposed by BYOL (Grill et al., 2020) . From an empirical side, Chen & He (2021) think that the predictor helps approximate the expectation over augmentations, and Zhang et al. (2022a) take a center-residual decomposition of representations for analyzing the collapse. From a theoretical perspective, Tian et al. (2021) analyze the dynamics of predictor weights

availability

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