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DeepSuM: Deep Sufficient Modality Learning Framework

Zhe Gao, Jian Huang, Ting Li, Xueqin Wang

TL;DR

DeepSuM tackles the challenge of efficient, interpretable multimodal learning by independently learning modality-specific representations that are sufficient for predicting the target while enforcing independence across modalities. It combines a dependence-based objective (distance covariance) with a density-matching regularizer (f-divergence) to steer each modality into a low-dimensional, Gaussian latent space, then fuses them for downstream tasks. A modality-selection mechanism uses a dependency-based utility to filter out non-informative modalities, reducing computation and avoiding negative transfer. Theoretical results establish convergence of the learned representations and strong selection consistency, while experiments on synthetic data and real-world biomedical datasets (kidney cell classification and BRCA survival) demonstrate improved efficiency and interpretability through informed modality inclusion. The framework provides a scalable blueprint for principled multimodal integration with explicit informativity and cost considerations.

Abstract

Multimodal learning has become a pivotal approach in developing robust learning models with applications spanning multimedia, robotics, large language models, and healthcare. The efficiency of multimodal systems is a critical concern, given the varying costs and resource demands of different modalities. This underscores the necessity for effective modality selection to balance performance gains against resource expenditures. In this study, we propose a novel framework for modality selection that independently learns the representation of each modality. This approach allows for the assessment of each modality's significance within its unique representation space, enabling the development of tailored encoders and facilitating the joint analysis of modalities with distinct characteristics. Our framework aims to enhance the efficiency and effectiveness of multimodal learning by optimizing modality integration and selection.

DeepSuM: Deep Sufficient Modality Learning Framework

TL;DR

DeepSuM tackles the challenge of efficient, interpretable multimodal learning by independently learning modality-specific representations that are sufficient for predicting the target while enforcing independence across modalities. It combines a dependence-based objective (distance covariance) with a density-matching regularizer (f-divergence) to steer each modality into a low-dimensional, Gaussian latent space, then fuses them for downstream tasks. A modality-selection mechanism uses a dependency-based utility to filter out non-informative modalities, reducing computation and avoiding negative transfer. Theoretical results establish convergence of the learned representations and strong selection consistency, while experiments on synthetic data and real-world biomedical datasets (kidney cell classification and BRCA survival) demonstrate improved efficiency and interpretability through informed modality inclusion. The framework provides a scalable blueprint for principled multimodal integration with explicit informativity and cost considerations.

Abstract

Multimodal learning has become a pivotal approach in developing robust learning models with applications spanning multimedia, robotics, large language models, and healthcare. The efficiency of multimodal systems is a critical concern, given the varying costs and resource demands of different modalities. This underscores the necessity for effective modality selection to balance performance gains against resource expenditures. In this study, we propose a novel framework for modality selection that independently learns the representation of each modality. This approach allows for the assessment of each modality's significance within its unique representation space, enabling the development of tailored encoders and facilitating the joint analysis of modalities with distinct characteristics. Our framework aims to enhance the efficiency and effectiveness of multimodal learning by optimizing modality integration and selection.

Paper Structure

This paper contains 15 sections, 6 theorems, 35 equations, 1 figure, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methodology
  3. Notation
  4. The Deep Sufficient Modality Learning Framework
  5. The DeepSuM Algorithm
  6. Modalities selection
  7. Theoretical Properties
  8. Convergence of DeepSuM Algorithm
  9. Modality Selection Properties
  10. Linear Case
  11. Numerical Studies
  12. Real Data Analysis
  13. Kidney cortex cells classification
  14. Breast invasive carcinoma survival status analysis
  15. Conclusion and Discussion

Key Result

Lemma 1

Suppose that $f$ is differentiable, proper, convex and lower-semicontinuous on its domain. Then, where $f^*$ is the Fenchel conjugate. In addition, the maximum is attained at $D(\mathbf{z})=f^{\prime}\left(\frac{\mathrm{d} \mu}{\mathrm{d} \gamma}(\mathbf{z})\right)$.

Figures (1)

  • Figure 1: Distance correlation in cell classification

Theorems & Definitions (7)

  • Definition 1
  • Lemma 1
  • Theorem 1
  • Theorem 2
  • Theorem 3: Strong selection consistency
  • Theorem 4
  • Theorem 5