SheafAlign: A Sheaf-theoretic Framework for Decentralized Multimodal Alignment

TL;DR

SheafAlign introduces a sheaf-theoretic, decentralized framework for multimodal alignment that handles non-redundant modalities, improving robustness and reducing communication costs in real-world scenarios.

Contribution

It presents a novel sheaf-theoretic approach for decentralized multimodal alignment that does not rely on mutual redundancy among all modalities.

Findings

Superior zero-shot generalization and cross-modal alignment

Robustness to missing modalities

50% lower communication cost than baselines

Abstract

Conventional multimodal alignment methods assume mutual redundancy across all modalities, an assumption that fails in real-world distributed scenarios. We propose SheafAlign, a sheaf-theoretic framework for decentralized multimodal alignment that replaces single-space alignment with multiple comparison spaces. This approach models pairwise modality relations through sheaf structures and leverages decentralized contrastive learning-based objectives for training. SheafAlign overcomes the limitations of prior methods by not requiring mutual redundancy among all modalities, preserving both shared and unique information. Experiments on multimodal sensing datasets show superior zero-shot generalization, cross-modal alignment, and robustness to missing modalities, with 50\% lower communication cost than state-of-the-art baselines.