# Quantifying Multimodal Capabilities: Formal Generalization Guarantees in Pairwise Metric Learning

arXiv: https://arxiv.org/abs/2605.01424 · HTML: https://mlsanity.com/paper/2605.01424/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 52 references that are in the map.
- First posted on arXiv 2 May 2026.

## Builds on (most cited first, 18 of 18)

- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [A Survey on Multimodal Large Language Models for Autonomous Driving](https://mlsanity.com/paper/2311.12320/) (2023)
- [Multimodal Trajectory Predictions for Autonomous Driving using Deep Convolutional Networks](https://mlsanity.com/paper/1809.10732/) (2018)
- [What Makes Multi-modal Learning Better than Single (Provably)](https://mlsanity.com/paper/2106.04538/) (2021)
- [Predicting What You Already Know Helps: Provable Self-Supervised Learning](https://mlsanity.com/paper/2008.01064/) (2020)
- [Contrastive learning, multi-view redundancy, and linear models](https://mlsanity.com/paper/2008.10150/) (2020)
- [Multimodality Helps Unimodality: Cross-Modal Few-Shot Learning with Multimodal Models](https://mlsanity.com/paper/2301.06267/) (2023)
- [CrossCLR: Cross-modal Contrastive Learning For Multi-modal Video Representations](https://mlsanity.com/paper/2109.14910/) (2021)
- [Cross Modal Retrieval with Querybank Normalisation](https://mlsanity.com/paper/2112.12777/) (2021)
- [Polos: Multimodal Metric Learning from Human Feedback for Image Captioning](https://mlsanity.com/paper/2402.18091/) (2024)
- [Global Non-convex Optimization with Discretized Diffusions](https://mlsanity.com/paper/1810.12361/) (2018)
- [Understanding Multimodal Contrastive Learning and Incorporating Unpaired Data](https://mlsanity.com/paper/2302.06232/) (2023)
- [Deep Multi-modal Fusion of Image and Non-image Data in Disease Diagnosis and Prognosis: A Review](https://mlsanity.com/paper/2203.15588/) (2022)
- [A Theory of Multimodal Learning](https://mlsanity.com/paper/2309.12458/) (2023)
- [Learning from Heterogeneity: Generalizing Dynamic Facial Expression Recognition via Distributionally Robust Optimization](https://mlsanity.com/paper/2507.15765/) (2025)
- [Multi-view Metric Learning in Vector-valued Kernel Spaces](https://mlsanity.com/paper/1803.07821/) (2018)
- [Fine-grained Analysis of Stability and Generalization for Stochastic Bilevel Optimization](https://mlsanity.com/paper/2604.04090/) (2026)
- [Generalized Sparse Additive Model with Unknown Link Function](https://mlsanity.com/paper/2410.06012/) (2024)

## Abstract (arXiv)

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.