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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

Indonesian

Joint-Embedding Predictive Data Architectures (JEPA) menawarkan pendekatan yang menarik untuk pembelajaran yang diawasi sendiri, tetapi biasanya rentan terhadap runtuhnya representasi. LeJEPA memecahkan ini dengan memperkenalkan objektif distribusi-matching kode yang didasarkan pada teori yang mendorong embedding ke arah Gaussian isotropik. Namun, pendekatan ini secara fundamental terikat dengan asumsi Euclidean, dan tujuannya global tidak mencerminkan prioritas geometris resocacial spesifik domain, seperti penggunaan geometri embedding paradigma non-Euclidean, misalnya, ekuivariant CNNs atau hyperbolic ViTs. Oleh karena itu, kami memperkenalkan LocaLeJEPA, kerangka kerja yang didorong oleh visi reformasi teoritis manifold dari LeJEPA's tasksopy-maximization property, sementara garis

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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