On the Stepwise Nature of Self-Supervised Learning

2023/03/27 by James B. Simon, Maksis Knutins, Simon, James B. +9 · 2 citations
Computer Science · Physics and Astronomy · #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.2303.15438

openalex publication_date 2023/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a simple picture of the training process of joint embedding self-supervised learning methods. We find that these methods learn their high-dimensional embeddings one dimension at a time in a sequence of discrete, well-separated steps. We arrive at this conclusion via the study of a linearized model of Barlow Twins applicable to the case in which the trained network is infinitely wide. We solve the training dynamics of this model from small initialization, finding that the model learns the top eigenmodes of a certain contrastive kernel in a stepwise fashion, and obtain a closed-form expression for the final learned representations. Remarkably, we then see the same stepwise learning phenomenon when training deep ResNets using the Barlow Twins, SimCLR, and VICReg losses. Our theory suggests that, just as kernel regression can be thought of as a model of supervised learning, kernel PCA may serve as a useful model of self-supervised learning.

Cited by

• Tracing the Representation Geometry of Language Models from Pretraining to Post-training
• Kernel VICReg for Self-Supervised Learning in Reproducing Kernel Hilbert Space

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