# SheafAlign: A Sheaf-theoretic Framework for Decentralized Multimodal Alignment

arXiv: https://arxiv.org/abs/2510.20540 · HTML: https://mlsanity.com/paper/2510.20540/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 11 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Builds on (most cited first, 10 of 10)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [ImageBind: One Embedding Space To Bind Them All](https://mlsanity.com/paper/2305.05665/) (2023)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [AudioCLIP: Extending CLIP to Image, Text and Audio](https://mlsanity.com/paper/2106.13043/) (2021)
- [Factorized Contrastive Learning: Going Beyond Multi-view Redundancy](https://mlsanity.com/paper/2306.05268/) (2023)
- [Tackling Feature and Sample Heterogeneity in Decentralized Multi-Task Learning: A Sheaf-Theoretic Approach](https://mlsanity.com/paper/2502.01145/) (2025)
- [Proactively Predicting Dynamic 6G Link Blockages Using LiDAR and In-Band Signatures](https://mlsanity.com/paper/2211.09535/) (2022)
- [Probabilistic Semantic Communication over Wireless Networks with Rate Splitting](https://mlsanity.com/paper/2403.00434/) (2024)
- [Sheaf-Based Decentralized Multimodal Learning for Next-Generation Wireless Communication Systems](https://mlsanity.com/paper/2506.22374/) (2025)

## Built on by (most cited first, 2 of 2)

- [Semantic-based Distributed Learning for Diverse and Discriminative Representations](https://mlsanity.com/paper/2604.18237/) (2026)
- [Sheaf-Based Federated Representation Learning](https://mlsanity.com/paper/2608.10016/) (2026)

## Abstract (arXiv)

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.