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Learning Optimal Multimodal Information Bottleneck Representations

Qilong Wu, Yiyang Shao, Jun Wang, Xiaobo Sun

TL;DR

This work tackles the problem of learning truly optimal multimodal information bottleneck representations by addressing two core issues in prior MIB methods: ad hoc regularization and imbalanced task-relevant information across modalities. The authors introduce Optimal Multimodal Information Bottleneck (OMIB), a framework that combines task relevance branches with an optimal multimodal fusion block using cross-attention, trained under a variational objective that enforces sufficiency while minimizing redundancy. A key theoretical contribution is the derivation of a beta bound $M_u$ (and extensions to multiple modalities) that guarantees achievability of the optimal MIB, together with a dynamic per-modality weight $r$ to handle information imbalance; mutual information estimates are obtained via MINE and a variational upper bound is employed for tractable optimization. Empirically, OMIB outperforms state-of-the-art MIB methods across synthetic data and real-world tasks including emotion recognition (CREMA-D), multimodal sentiment analysis (CMU-MOSI), and anomalous tissue detection (8x 10x datasets), while ablation studies confirm the importance of warm-up, cross-attention fusion, and the dynamic weighting strategy. The work provides a solid information-theoretic foundation for principled multimodal fusion and demonstrates practical gains in diverse downstream tasks.

Abstract

Leveraging high-quality joint representations from multimodal data can greatly enhance model performance in various machine-learning based applications. Recent multimodal learning methods, based on the multimodal information bottleneck (MIB) principle, aim to generate optimal MIB with maximal task-relevant information and minimal superfluous information via regularization. However, these methods often set ad hoc regularization weights and overlook imbalanced task-relevant information across modalities, limiting their ability to achieve optimal MIB. To address this gap, we propose a novel multimodal learning framework, Optimal Multimodal Information Bottleneck (OMIB), whose optimization objective guarantees the achievability of optimal MIB by setting the regularization weight within a theoretically derived bound. OMIB further addresses imbalanced task-relevant information by dynamically adjusting regularization weights per modality, promoting the inclusion of all task-relevant information. Moreover, we establish a solid information-theoretical foundation for OMIB's optimization and implement it under the variational approximation framework for computational efficiency. Finally, we empirically validate the OMIB's theoretical properties on synthetic data and demonstrate its superiority over the state-of-the-art benchmark methods in various downstream tasks.

Learning Optimal Multimodal Information Bottleneck Representations

TL;DR

This work tackles the problem of learning truly optimal multimodal information bottleneck representations by addressing two core issues in prior MIB methods: ad hoc regularization and imbalanced task-relevant information across modalities. The authors introduce Optimal Multimodal Information Bottleneck (OMIB), a framework that combines task relevance branches with an optimal multimodal fusion block using cross-attention, trained under a variational objective that enforces sufficiency while minimizing redundancy. A key theoretical contribution is the derivation of a beta bound (and extensions to multiple modalities) that guarantees achievability of the optimal MIB, together with a dynamic per-modality weight to handle information imbalance; mutual information estimates are obtained via MINE and a variational upper bound is employed for tractable optimization. Empirically, OMIB outperforms state-of-the-art MIB methods across synthetic data and real-world tasks including emotion recognition (CREMA-D), multimodal sentiment analysis (CMU-MOSI), and anomalous tissue detection (8x 10x datasets), while ablation studies confirm the importance of warm-up, cross-attention fusion, and the dynamic weighting strategy. The work provides a solid information-theoretic foundation for principled multimodal fusion and demonstrates practical gains in diverse downstream tasks.

Abstract

Leveraging high-quality joint representations from multimodal data can greatly enhance model performance in various machine-learning based applications. Recent multimodal learning methods, based on the multimodal information bottleneck (MIB) principle, aim to generate optimal MIB with maximal task-relevant information and minimal superfluous information via regularization. However, these methods often set ad hoc regularization weights and overlook imbalanced task-relevant information across modalities, limiting their ability to achieve optimal MIB. To address this gap, we propose a novel multimodal learning framework, Optimal Multimodal Information Bottleneck (OMIB), whose optimization objective guarantees the achievability of optimal MIB by setting the regularization weight within a theoretically derived bound. OMIB further addresses imbalanced task-relevant information by dynamically adjusting regularization weights per modality, promoting the inclusion of all task-relevant information. Moreover, we establish a solid information-theoretical foundation for OMIB's optimization and implement it under the variational approximation framework for computational efficiency. Finally, we empirically validate the OMIB's theoretical properties on synthetic data and demonstrate its superiority over the state-of-the-art benchmark methods in various downstream tasks.

Paper Structure

This paper contains 48 sections, 14 theorems, 146 equations, 6 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Multimodal Fusion
  4. Multimodal Information Bottleneck
  5. Notations
  6. Method
  7. Warm-up training.
  8. Main Training.
  9. Inference.
  10. Theoretical Foundation
  11. Optimal Information Bottleneck for Multimodal Data with Imbalanced Task-Relevant Information
  12. Achievability of Optimal Multimodal Information Bottleneck
  13. Experiment
  14. Datasets
  15. Empirical Analysis of OMIB Performance Using Synthetic Data
  16. ...and 33 more sections

Key Result

Proposition 5.1

The loss function $L_{OMF}$ in equ:IB loss imp provides a variational upper bound for optimizing the objective function in equ:IB alter and can be explicitly calculated during training.

Figures (6)

  • Figure 1: a) Venn diagrams for two data modalities ($v_1$ and $v_2$). The gridded area represents consistent information, while the non-gridded area denotes modality-specific information. Task-relevant information is highlighted in green, whereas superfluous information is shown in blue. b) An optimal MIB should exclusively contain task-relevant, non-superfluous information (i.e., $a_0, a_1$ and $a_2$) to be utilized in downstream tasks for enhanced performance.
  • Figure 2: OMIB Framework. Here, 'C' represents the concatenation operation. For the definitions of other notations, refer to the \ref{['sec:method']} and \ref{['tab:notation']}.
  • Figure 3: The impact of $\beta$ values on classification accuracy on synthetic data. $v_1$ and $v_2$ represent sample vectors of two modalities, respectively. $F_{\text{rel}}(\cdot)$ denotes task-relevant information. "$a$" sub-vectors denote task-relevant information, while "$b$" superfluous information. $d_{11}$ and $d_{21}$ denote the dimensions of modality-specific $a_1$ and $a_2$. $M_u$ is the computed $\beta$ upper bound.
  • Figure 4: Runtime per epoch during warm-up and main training phase on synthetic data.
  • Figure 5: Venn diagrams for three data modalities ($v_1$, $v_2$, and $v_3$). The gridded area represents consistent information, while the non-gridded area denotes modality-specific information. Task-relevant information is highlighted in green, whereas superfluous information is shown in blue.
  • ...and 1 more figures

Theorems & Definitions (32)

  • Proposition 5.1: Variational upper bound of OMIB's objective function
  • proof
  • Proposition 5.2: Explicit formula for $r$
  • proof
  • Definition 5.4: Optimal multimodal information bottleneck
  • Lemma 5.5: Inclusiveness of task-relevant information
  • proof
  • Lemma 5.6: Exclusiveness of superfluous information
  • proof
  • Proposition 5.7: Achievability of optimal MIB
  • ...and 22 more