Quantifying Multimodal Capabilities: Formal Generalization Guarantees in Pairwise Metric Learning

TL;DR

This paper provides a theoretical analysis of multimodal metric learning, establishing generalization bounds and demonstrating how fine-grained modality features improve model performance and reduce complexity.

Contribution

It introduces a formal framework analyzing the relationship between modality subsets and generalization, offering new bounds and insights for multimodal learning.

Findings

Derived novel generalization error bounds for multimodal metric learning.

Showed that fine-grained modality features reduce hypothesis space complexity.

Demonstrated the impact of modality quantity and granularity on model performance.

Abstract

Multimodal learning leverages the integration of diverse data modalities to enhance performance in complex tasks. Yet, it frequently encounters incomplete or redundant modality data in real-world scenarios. This paper presents a fine-grained theoretical analysis of the generalization properties of multimodal metric learning models, addressing critical gaps in understanding the relationship between modality selection and algorithmic performance. We establish hierarchical relationships between function classes corresponding to different modality subsets and quantify the discrepancy between learned mappings and ground truth. Through rigorous analysis of pairwise complexity within the multimodal learning framework, we derive novel generalization error bounds that reveal the joint impact of modality quantity and granularity on model performance. Our theoretical findings on both upper and lower bounds demonstrate that incorporating fine-grained modality features reduces the complexity of the hypothesis space by enhancing modality complementarity. This work offers both theoretical foundations and practical implications for improving convergence rates and accuracy in multimodal learning systems.