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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

Spanish

Las Arquitecturas Predictivas Conjunto-Embedding de Datos Ordinarios (JEPA) ofrecen un enfoque atractivo para el aprendizaje auto-supervisado, pero suelen ser propensos al colapso de la representación. LeJEPA resuelve esto mediante la introducción de un objetivo de codificación de distribución teóricamente fundamentado que impulsa la incorporación hacia un Gaussiano isotrópico. Sin embargo, este enfoque está fundamentalmente ligado a las suposiciones de Euclides, y su objetivo global no refleja las propiedades geométricas previas de la resocación de tareas específicas de LeJEPA, como el uso de geometrías de incorporación de paradigmas no euclidianos, por ejemplo, el equivalente a CNNs o a ViTs hiperbólicos. Por lo

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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