The Indra Representation Hypothesis for Multimodal Alignment

TL;DR

This paper introduces the Indra Representation Hypothesis, proposing a relational structure-based representation that improves robustness and alignment across unimodal foundation models in vision, language, and audio.

Contribution

It formalizes the Indra representation using category theory, demonstrating its effectiveness for training-free cross-modal and cross-architecture alignment.

Findings

Indra representations enhance robustness across models and modalities.

The approach is theoretically grounded and improves alignment without additional training.

Experiments show consistent performance gains in diverse scenarios.

Abstract

Recent studies have uncovered an interesting phenomenon: unimodal foundation models tend to learn convergent representations, regardless of differences in architecture, training objectives, or data modalities. However, these representations are essentially internal abstractions of samples that characterize samples independently, leading to limited expressiveness. In this paper, we propose The Indra Representation Hypothesis, inspired by the philosophical metaphor of Indra's Net. We argue that representations from unimodal foundation models are converging to implicitly reflect a shared relational structure underlying reality, akin to the relational ontology of Indra's Net. We formalize this hypothesis using the V-enriched Yoneda embedding from category theory, defining the Indra representation as a relational profile of each sample with respect to others. This formulation is shown to be unique, complete, and structure-preserving under a given cost function. We instantiate the Indra representation using angular distance and evaluate it in cross-model and cross-modal scenarios involving vision, language, and audio. Extensive experiments demonstrate that Indra representations consistently enhance robustness and alignment across architectures and modalities, providing a theoretically grounded and practical framework for training-free alignment of unimodal foundation models. Our code is available at https://github.com/Jianglin954/Indra.