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Towards the Causal Complete Cause of Multi-Modal Representation Learning

Jingyao Wang, Siyu Zhao, Wenwen Qiang, Jiangmeng Li, Changwen Zheng, Fuchun Sun, Hui Xiong

TL;DR

The paper tackles the challenge of learning robust multi-modal representations by reframing MML through causal sufficiency and necessity. It defines the Causal Complete Cause ($C^3$) and develops identifiability results that hold without assuming exogeneity or monotonicity, leveraging an instrumental variable and a twin-network to measure $C^3$ via $C^3$ risk. The proposed Causal Complete Cause Regularization ($C^3$R) is a plug-and-play framework that enforces causal completeness by jointly optimizing an empirical $C^3$ risk, instrumental-variable guidance, and counterfactual regularization. The authors provide theoretical guarantees and demonstrate through extensive experiments across diverse datasets that $C^3$R improves average and worst-case performance, particularly under missing modalities and in the presence of spurious correlations. This work advances MML by delivering practical identifiability tools and regularization principles that promote representations grounded in causal content rather than confounded associations.

Abstract

Multi-Modal Learning (MML) aims to learn effective representations across modalities for accurate predictions. Existing methods typically focus on modality consistency and specificity to learn effective representations. However, from a causal perspective, they may lead to representations that contain insufficient and unnecessary information. To address this, we propose that effective MML representations should be causally sufficient and necessary. Considering practical issues like spurious correlations and modality conflicts, we relax the exogeneity and monotonicity assumptions prevalent in prior works and explore the concepts specific to MML, i.e., Causal Complete Cause $C^3$. We begin by defining $C^3$, which quantifies the probability of representations being causally sufficient and necessary. We then discuss the identifiability of $C^3$ and introduce an instrumental variable to support identifying $C^3$ with non-exogeneity and non-monotonicity. Building on this, we conduct the $C^3$ measurement, i.e., \(C^3\) risk. We propose a twin network to estimate it through (i) the real-world branch: utilizing the instrumental variable for sufficiency, and (ii) the hypothetical-world branch: applying gradient-based counterfactual modeling for necessity. Theoretical analyses confirm its reliability. Based on these results, we propose $C^3$ Regularization, a plug-and-play method that enforces the causal completeness of the learned representations by minimizing $C^3$ risk. Extensive experiments demonstrate its effectiveness.

Towards the Causal Complete Cause of Multi-Modal Representation Learning

TL;DR

The paper tackles the challenge of learning robust multi-modal representations by reframing MML through causal sufficiency and necessity. It defines the Causal Complete Cause () and develops identifiability results that hold without assuming exogeneity or monotonicity, leveraging an instrumental variable and a twin-network to measure via risk. The proposed Causal Complete Cause Regularization (R) is a plug-and-play framework that enforces causal completeness by jointly optimizing an empirical risk, instrumental-variable guidance, and counterfactual regularization. The authors provide theoretical guarantees and demonstrate through extensive experiments across diverse datasets that R improves average and worst-case performance, particularly under missing modalities and in the presence of spurious correlations. This work advances MML by delivering practical identifiability tools and regularization principles that promote representations grounded in causal content rather than confounded associations.

Abstract

Multi-Modal Learning (MML) aims to learn effective representations across modalities for accurate predictions. Existing methods typically focus on modality consistency and specificity to learn effective representations. However, from a causal perspective, they may lead to representations that contain insufficient and unnecessary information. To address this, we propose that effective MML representations should be causally sufficient and necessary. Considering practical issues like spurious correlations and modality conflicts, we relax the exogeneity and monotonicity assumptions prevalent in prior works and explore the concepts specific to MML, i.e., Causal Complete Cause . We begin by defining , which quantifies the probability of representations being causally sufficient and necessary. We then discuss the identifiability of and introduce an instrumental variable to support identifying with non-exogeneity and non-monotonicity. Building on this, we conduct the measurement, i.e., risk. We propose a twin network to estimate it through (i) the real-world branch: utilizing the instrumental variable for sufficiency, and (ii) the hypothetical-world branch: applying gradient-based counterfactual modeling for necessity. Theoretical analyses confirm its reliability. Based on these results, we propose Regularization, a plug-and-play method that enforces the causal completeness of the learned representations by minimizing risk. Extensive experiments demonstrate its effectiveness.
Paper Structure (54 sections, 7 theorems, 80 equations, 11 figures, 9 tables)

This paper contains 54 sections, 7 theorems, 80 equations, 11 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Problem Analysis
  3. Problem Settings
  4. Example of Causal Sufficiency and Necessity
  5. Causal Analysis of MML
  6. Causal Complete Cause
  7. Definition of $C^3$
  8. Causal Identifiability of $C^3$
  9. Measurement of $C^3$
  10. Performance Guarantee with $C^3$ Risk
  11. Learning Causal Complete Representations
  12. Experiments
  13. Experimental Settings
  14. Results
  15. Related Work
  16. ...and 39 more sections

Key Result

Theorem 3.2

Given the MML model $f_\theta$, where the label variable $\text{Y}$ is influenced by the causal factors $\text{F}_{c}$ and non-causal factors $\text{F}_{s}$. Assume $f_\theta$ satisfy the Positive Markovian assumption tian2002general, the probabilities of $C^3$ ($P(\text{Y}_{do(\text{Z} = c)} = y, \ where $Y$ is monotonic relative to $\text{Z}$ with $\text{Y}_{do(\text{Z}=c)}=\bar{y} \wedge \text{

Figures (11)

  • Figure 1: Example of causal sufficiency and necessity in "duck" classification task (See \ref{['sec:3']} for more analyses).
  • Figure 2: Structural Causal Model (SCM) for MML. Left: causal generating mechanism, Right: the learning process.
  • Figure 3: Evaluation for the property of learned representations (SNC, SC, NC, and SP). See Appendix \ref{['sec:app_F']} for details.
  • Figure 4: Ablation study of $C^3$R (performance when removing different regular terms). See Appendix \ref{['sec:app_F']} for details.
  • Figure 5: Twin Network for $C^3$ estimation in MML.
  • ...and 6 more figures

Theorems & Definitions (10)

  • Definition 3.1: Probability of Causal Complete Cause ($C^3$)
  • Theorem 3.2: Causal Identifiability under Non-Exogeneity
  • Theorem 3.3: Causal Identifiability under Non-Monotonicity and Non-Exogeneity
  • Theorem 3.4: Instrumental Variable $V$ in MML
  • Theorem 3.5: $C^3$ Risk
  • Theorem 4.1: Performance Guarantee via $C^3$
  • Definition 4.1: Exogeneity
  • Definition 4.2: Monotonicity
  • Proposition 4.3: Local Invertibility
  • Proposition 4.4: Markov Identifiability