PEIRA: Learning Predictive Encoders through Inter-View Regressor Alignment

TL;DR

PEIRA is a novel self-supervised learning method that explicitly optimizes for canonical correlation subspaces, demonstrating stability and effectiveness comparable to existing methods on standard datasets.

Contribution

The paper introduces PEIRA, a new SSL approach with an explicit objective based on inter-view regressors, and provides a theoretical analysis of its stability and equilibrium properties.

Findings

PEIRA's stable equilibria align with canonical correlation subspaces.

PEIRA achieves competitive performance on ImageNet-1K and CIFAR-10.

Theoretical analysis explains stability and collapse phenomena in SSL models.

Abstract

Non-contrastive self-supervised learning (SSL) is an effective framework for predictive representation learning, but popular (and in practice effective) methods such as SimSiam, BYOL, I-JEPA or DINO, which rely on a form of self-distillation to train a teacher-student network, remain poorly understood as they typically do not minimize a well-defined objective. We analyze the dynamics of a variant of the Joint Embedding Predictive Architecture (JEPA) using a regularized linear regressor to predict the learned representations of two views of the data from one another, and fully characterize its stability: non-collapsed stable equilibria align with leading nonlinear canonical correlation subspaces, while collapsed equilibria may also be stable attractors. Motivated by this result, we introduce PEIRA, a non-contrastive SSL method with an explicit objective defined through the trace of the optimal linear regressor. We show that its only stable equilibria are nontrivial global minimizers and recover the same canonical correlation subspaces, with regularization selecting the effective dimension. Experiments on ImageNet-1K and CIFAR-10 show PEIRA is competitive with VICReg and LeJEPA baselines, and qualitative empirical results support the theory.