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Anchors Aweigh! Sail for Optimal Unified Multi-Modal Representations

Minoh Jeong, Zae Myung Kim, Min Namgung, Dongyeop Kang, Yao-Yi Chiang, Alfred Hero

TL;DR

The paper analyzes fixed-anchor binding methods for multi-modal representation learning and identifies three core drawbacks: over-reliance on a single anchor, loss of intra-modal cues, and neglect of correlations among non-anchor modalities. It introduces CentroBind, an adaptive anchor binding framework that computes batch-wise centroid anchors from all modalities and aligns each modality via symmetric InfoNCE losses, thereby capturing intra-, inter-, and alignment information. The authors provide a theoretical lower bound showing the CentroBind objective effectively encourages comprehensive cross-modal learning, and they validate the approach on synthetic and real-world datasets, where CentroBind outperforms fixed-anchor methods and strengthens cross-modal retrieval and downstream tasks. Overall, CentroBind offers a scalable, modality-agnostic path to a robust, unified multi-modal representation space with practical impact for cross-modal analytics and retrieval.

Abstract

A unified representation space in multi-modal learning is essential for effectively integrating diverse data sources, such as text, images, and audio, to enhance efficiency and performance across various downstream tasks. Recent binding methods, such as ImageBind, typically rely on a single, fixed anchor modality for aligning multi-modal data. We mathematically analyze these fixed anchor binding methods and uncover significant limitations: (1) over-reliance on the choice of the anchor modality, (2) inadequate capture of intra-modal information, and (3) failure to account for cross-modal correlation among non-anchored modalities. To address these issues, we propose the need for adaptive anchor binding methods, exemplified by our framework CentroBind. The proposed method uses adaptively adjustable centroid-based anchors generated from all available modalities, leading to a balanced and rich representation space. We theoretically demonstrate that our approach captures three critical properties of multi-modal learning -- intra-modal learning, inter-modal learning, and multi-modal alignment -- while constructing a unified representation that spans all modalities. Experiments on both synthetic and real-world datasets show that adaptive anchor methods such as CentroBind consistently outperform fixed anchor binding methods, verifying our analysis.

Anchors Aweigh! Sail for Optimal Unified Multi-Modal Representations

TL;DR

The paper analyzes fixed-anchor binding methods for multi-modal representation learning and identifies three core drawbacks: over-reliance on a single anchor, loss of intra-modal cues, and neglect of correlations among non-anchor modalities. It introduces CentroBind, an adaptive anchor binding framework that computes batch-wise centroid anchors from all modalities and aligns each modality via symmetric InfoNCE losses, thereby capturing intra-, inter-, and alignment information. The authors provide a theoretical lower bound showing the CentroBind objective effectively encourages comprehensive cross-modal learning, and they validate the approach on synthetic and real-world datasets, where CentroBind outperforms fixed-anchor methods and strengthens cross-modal retrieval and downstream tasks. Overall, CentroBind offers a scalable, modality-agnostic path to a robust, unified multi-modal representation space with practical impact for cross-modal analytics and retrieval.

Abstract

A unified representation space in multi-modal learning is essential for effectively integrating diverse data sources, such as text, images, and audio, to enhance efficiency and performance across various downstream tasks. Recent binding methods, such as ImageBind, typically rely on a single, fixed anchor modality for aligning multi-modal data. We mathematically analyze these fixed anchor binding methods and uncover significant limitations: (1) over-reliance on the choice of the anchor modality, (2) inadequate capture of intra-modal information, and (3) failure to account for cross-modal correlation among non-anchored modalities. To address these issues, we propose the need for adaptive anchor binding methods, exemplified by our framework CentroBind. The proposed method uses adaptively adjustable centroid-based anchors generated from all available modalities, leading to a balanced and rich representation space. We theoretically demonstrate that our approach captures three critical properties of multi-modal learning -- intra-modal learning, inter-modal learning, and multi-modal alignment -- while constructing a unified representation that spans all modalities. Experiments on both synthetic and real-world datasets show that adaptive anchor methods such as CentroBind consistently outperform fixed anchor binding methods, verifying our analysis.
Paper Structure (53 sections, 4 theorems, 27 equations, 11 figures, 6 tables, 1 algorithm)

This paper contains 53 sections, 4 theorems, 27 equations, 11 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Issues with fixed anchor binding.
  3. Adaptive anchor alignment.
  4. Problem Formulation
  5. Representation learning framework
  6. Notation.
  7. Binding representation spaces
  8. Analysis of FABind
  9. P1--Over-reliance on a single anchor modality.
  10. P2--Failure to capture intra information.
  11. P3--Absence of shared information among non-anchored modalities.
  12. Alignment using adaptive anchor
  13. CentroBind
  14. Initial encoders.
  15. Anchor embedding.
  16. ...and 38 more sections

Key Result

Proposition 2.2

Let $f_1^{\rm suf}({\bf X}_1)$ be a sufficient embedding of the anchor ${\bf X}_1$, and let ${\bf X}_i,i\in[M],$ be a discrete random variable. Assume that $f_i^{\rm FB},i\in\{2,\cdots,M\}$ are obtained by eq:obj_IB_info with a sufficient anchor encoder $f_1 = f_1^{\rm suf}$, i.e., $I(f_1^{\rm suf}(

Figures (11)

  • Figure 1: Limitations of fixed-anchor binding (FABIND) and remedy via CentroBind (CB). Shapes denote semantic classes (e.g., dog, cat, horse) and colors denote modalities (image, text, audio). P1--Over-reliance on anchor: a poor or poorly chosen anchor yields misalignment across modalities. P2--Loss of intra-modal information: anchoring suppresses modality-specific cues present only in non-anchored views. P3--Loss of shared information among non-anchors: optimizing only anchor $\leftrightarrow$ others ignores correlations between non-anchored modalities. CB addresses all three by computing adaptive, batch-wise anchors (centroids) from the available modalities and aligning each modality to this shared anchor, preserving intra-information and non-anchor shared-information while improving overall alignment.
  • Figure 2: Graphical illustration of adaptive anchor alignment: Adaptive anchors are dynamically generated from current embeddings using an aggregation method for every batch.
  • Figure 3: (a) and (b): Accuracy as a measure of the representation space quality. Abbreviation: ${\bf X}_i$-B or CB: applying FABind with anchor ${\bf X}_i$ or applying CentroBind; acc$({\bf Z}_i)$ or acc(All): accuracy of ${\bf Z}_i$ or of concatenated embeddings $({\bf Z}_1,\cdots,{\bf Z}_M)$; (rnd): if random backbones are used. (c) and (d): Representation visualization via UMAP.
  • Figure 4: Accuracy as a measure of the representation space quality. Abbreviation: ${\bf X}_i$-B or CB: applying FABind with anchor ${\bf X}_i$ or applying CentroBind; acc$({\bf Z}_i)$ or acc(All): accuracy of ${\bf Z}_i$ or of concatenated embeddings $({\bf Z}_1,\cdots,{\bf Z}_M)$; (rnd): if random backbones are used.
  • Figure 5: Representation visualization via t-SNE and UMAP.
  • ...and 6 more figures

Theorems & Definitions (8)

  • Definition 2.1: $\mathcal{Z}_i$-Sufficient embedding of ${\bf X}_i$ for ${\bf X}_l$
  • Proposition 2.2: FABind with sufficient anchor
  • proof
  • Proposition 2.3: FABind with insufficient anchor
  • proof
  • Theorem 3.1
  • proof
  • Lemma B.1: Reverse inequality of the $M$-variable Hölder inequality seo2013generalized