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SheafAlign: A Sheaf-theoretic Framework for Decentralized Multimodal Alignment

graph-neural-networks › graph-learning

📄 Abstract

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.

Authors (4)

Abdulmomen Ghalkha

Zhuojun Tian

Chaouki Ben Issaid

Mehdi Bennis

Submitted

October 23, 2025

arXiv Category

cs.LG

arXiv PDF

Key Contributions

SheafAlign is a novel sheaf-theoretic framework for decentralized multimodal alignment that replaces single-space alignment with multiple comparison spaces. It models pairwise modality relations using sheaf structures and employs decentralized contrastive learning. This approach overcomes the limitation of requiring mutual redundancy across all modalities, preserves both shared and unique information, and achieves superior zero-shot generalization and robustness to missing modalities with significantly lower communication costs.

Business Value

Enables more efficient and robust multimodal data fusion in decentralized systems, such as sensor networks or collaborative robotics. This is crucial for applications where data is distributed and modalities may be incomplete or unreliable.

Paper Metadata

Innovation Type

Algorithmic / Theoretical Framework

Deployment Feasibility

Moderate to high, requires understanding of sheaf theory and decentralized learning architectures.

Limitations Addressed

Assumption of mutual redundancy across all modalities in conventional methods,Inability to handle real-world distributed scenarios effectively,High communication overhead in centralized alignment,Loss of modality-specific information

Performance Gains

50% lower communication cost than state-of-the-art baselines.

Technical Tags

Sheaf TheoryDecentralized Multimodal AlignmentContrastive LearningModality RelationsZero-Shot GeneralizationCross-Modal AlignmentMissing ModalitiesCommunication CostSheaf StructuresPairwise Modality Relations

Research Topics

Multimodal LearningDecentralized LearningRepresentation LearningInformation TheoryRobustness in AI

Methods & Architectures

Sheaf-theoretic frameworkDecentralized contrastive learningPairwise modality relation modeling Sheaf structures

Applications & Tasks

Multimodal Sensing Robotics Autonomous Systems Data Fusion Assumption of mutual redundancy across all modalitiesLimitations in real-world distributed scenariosHigh communication costs in centralized alignmentLoss of shared and unique information Decentralized multimodal alignmentAligning modalities without mutual redundancyImproving zero-shot generalization and cross-modal alignmentReducing communication costs

Datasets & Benchmarks

Datasets

Multimodal sensing datasets

Zero-shot generalizationCross-modal alignmentRobustness to missing modalitiesCommunication cost

Related Fields

Machine LearningMultimodal AIGraph TheoryInformation TheoryDistributed Systems

Keywords

Multimodal AlignmentDecentralized LearningSheaf TheoryContrastive LearningModalityZero-ShotRobustnessCommunication CostData FusionSheafAlign

Academic Context

#Multimodal Learning#Decentralized Learning#Representation Learning#Information Theory#Robustness in AI

Commercial Potential

Potential Products

Decentralized multimodal AI platformsTools for robust sensor fusion in distributed systems

Target Industries

RoboticsAutonomous VehiclesInternet of Things (IoT)AerospaceDefense

Use Case Examples

Aligning sensor data from multiple robots in a swarmFusing visual, auditory, and tactile information in a robotEnabling robust perception in environments with sensor failures

Competitive Edge

Offers a novel theoretical framework (sheaf theory) for decentralized multimodal alignment, addressing limitations of centralized methods and providing significant communication cost savings.

Market Opportunity

Growing market for decentralized AI and robust multimodal systems.

Revenue Models

Licensing the SheafAlign frameworkoffering specialized multimodal AI solutions.

Resource Requirements

Compute Needs

Moderate, depending on the number of modalities and the complexity of the sheaf structures.

Data Requirements

Multimodal datasets, potentially with missing modalities.

Deployment Constraints

Requires a decentralized architecture and careful definition of sheaf structures for specific modalities.

Scalability

Scales well in decentralized settings and reduces communication bottlenecks.

Regulatory Considerations

Data privacy and security in decentralized systems.

Production Readiness

Maturity Level

Research

Time to Market

2-4 years for integration into complex distributed AI systems.

Patent Potential

Moderate to high, for the sheaf-theoretic framework and its application in multimodal alignment.

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