$\lambda$-JEPA Spectral Anti-Collapse Regularization for Self-Supervised Learning

arXiv:2609.35288v2 Announce Type: new Abstract: Joint-embedding self-supervised learning typically combines an invariance objective across augmented views with additional mechanisms to prevent representational collapse. These objectives are often applied after a projection head, while downstream tasks use the backbone representation before the projector. We find that this mismatch does not necessarily prevent dimensional collapse in the backbone, which can retain low effective rank and potentially limit downstream transfer. To address this, we introduce SACReg, a spectral anti-collapse regularizer motivated by an analysis of $\lambda$-balance, which captures the relative scale of weight matrices across layers. In a two-layer linear network, we show that (i) $\lambda$-balance prevents collapse, and (ii) our regularizer applied to the backbone induces $\lambda$-balance. In the nonlinear case, this regularizer leads to anti-collapse as well and, in realistic architectures on ImageNet100, it empirically increases the representations' ranks. We apply SACReg to JEPA and propose $\lambda$-JEPA, which improves over LeJEPA and VISReg on ImageNet-1k classification and in average linear-probe transfer performance across eight downstream image datasets. On video self-supervised learning, $\lambda$-JEPA improves over LeVJEPA and V-JEPA 2 on the Something-Something-v2 and Kinetics-400 benchmarks. Code is available at https://github.com/berkerdemirel/lambda-jepa.