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This paper introduces Sheaf-based Federated Representation Learning (SFRL), a framework that aligns heterogeneous local representations via learnable sheaf restriction maps and a quadratic gluing regularizer, without assuming a shared global latent space. A decentralized algorithm (Sheaf-FRL) with convergence guarantees is proposed and shown to outperform baselines in cooperative classification under data and model heterogeneity.
This paper introduces a categorical framework for constructing verifiable, local truth-preserving foundation models using composable foundries, implemented in the Odyssey system, and scheduled for a tutorial at ICML 2026.
This paper develops a finite sheaf-theoretic framework for detecting scientific theory shift in AI agents by measuring transport and obstruction across representational contexts, and evaluates it on a benchmark designed to separate deformation within a source language from extension of that language.