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LocaLeJEPA: Maximum Entropy Representations under Geometric Priors

Kartik Tandon, Alessio Borgi, Pavel Snopov, Inés García‐Redondo, Davide D’Ascenzo, Sebastiano Cultrera di Montesano, Fabrizio Silvestri, Pietro Liò, Francesca Dominici, Randall Balestriero, Claudio Battiloro · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28458 · cited by 0 works (OpenAlex) · open-access PDF

Russian

Joint-Embedding Predictive Data Architectures (JEPA) предлагают привлекательный подход к самонаблюдаемому обучению, но, как правило, склонны к срыву представления. LeJEPA решает это путем введения теоретически заложенного объектива распределения-совпадения кода, который приводит встраивание в сторону изотропического Gaussian. Тем не менее, этот подход в основном связан с эвклидовыми предположениями, а его глобальная цель не отражает доменно-специфические геометрические преоры, такие как использование не-евклидовых парадигм встраивания геометрий, например, эквивалентный CNNs или гиперболический ViTs. Таким образом, мы вводим LocaLeJEPA, рамки, мотивированные множественным

Machine translation (Meta M2M100); the English original follows.

Abstract

Joint-Embedding Predictive Architectures (JEPA) offer an appealing approach to self-supervised learning, but are typically prone to representation collapse. LeJEPA resolves this by introducing a theoretically grounded distribution-matching objective that drives the embedding towards an isotropic Gaussian. However, this approach is fundamentally tied to Euclidean assumptions, and its global target does not reflect domain-specific geometric priors, such as the use of non-Euclidean embedding geometries, e.g., equivariant CNNs or hyperbolic ViTs. We thus introduce LocaLeJEPA, a framework motivated by a manifold-theoretic reformulation of LeJEPA's entropy-maximization property. The accompanying LocaLeReg, a novel locally Euclidean distribution-matching regularizer, enables a stable and scalable implementation of the LocaLeJEPA framework. We then perform extensive experiments in the vision setting on models trained on ImageNet-1K. LocaLeJEPA significantly outperforms LeJEPA when paired with hyperbolic ViT-S/8 and equivariant ResNet-50 backbones, and also with ordinary Euclidean ViT-S/8 and ViT-L/14 backbones. This holds both in terms of linear and k-NN classification performance on ImageNet and on a series of downstream tasks tested. We view the LocaLeJEPA formalism as a principled approach to the JEPA paradigm that better respects intrinsic data geometry while also accommodating generalizations to exotic embedding geometries. Code available at https://github.com/alessioborgi/LocaLeJEPA.

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Topics: Embedding, Euclidean geometry, Equivariant map, Mathematics, Invariant (physics), Entropy (arrow of time)

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