What Structure Does Predictive Self-Supervised Learning Recover?

par Michael N. Arbel (Inria Grenoble - Rhône-Alpes, Equipe THOTH)

mardi 13 oct. 2026, 11:15 → 12:15 Europe/Paris

Salle Huron (1R1, 106)

Self-supervised learning (SSL) can produce highly informative representations without labeled data, yet what structure these representations capture and how training dynamics select them remain poorly understood. This is particularly true for successful non-contrastive methods such as SimSiam, BYOL, I-JEPA, and DINO, which rely on asymmetric teacher–student or self-distillation dynamics that typically do not correspond to minimizing a fixed explicit 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.