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Submodular Information Measures Clarified for Representation Learning.

Rishabh Iyer, Truong Pham, Anay Majee· July 31, 2026 View original

Key takeaways

  • SIMs are powerful for representation learning but their properties were unclear.
  • Total Information (TI) objectives characterize intra-class structure (variance).
  • Mutual Information (MI) objectives capture inter-class structure (separation).
  • The research provides principled guidance for selecting SIM-based objectives.

Who benefits

AI/ML ResearchData ScienceComputer VisionNatural Language ProcessingHealthcare

Summary

This work provides a unified theoretical framework connecting Submodular Information Measures (SIMs) to classical concepts in representation learning, showing how different SIMs characterize intra-class structure (variance) and inter-class structure (separation). It offers principled guidance for selecting SIM-based objectives through theoretical characterizations and synthetic experiments.

Submodular Information Measures (SIMs) have recently gained prominence as effective objectives for representation learning, particularly in frameworks like SCORE for supervised contrastive learning. Despite their empirical success, the underlying geometric and statistical properties induced by various SIMs have remained largely unclear. This research develops a comprehensive theoretical framework that links SIMs to established concepts in representation learning and statistical pattern recognition. It demonstrates that Total Information (TI) objectives primarily characterize intra-class structure. For instance, Graph Cut TI relates to within-class variance, LogDet TI to generalized variance, and Facility Location TI to imbalance-aware separation, especially for rare classes. Conversely, Mutual Information (MI) objectives are shown to capture inter-class structure. Graph Cut MI connects to centroid separation, LogDet MI to Mahalanobis distance-based separation, and Facility Location MI to measuring representational overlap between nearest modes. These theoretical insights were validated through controlled synthetic experiments that systematically varied factors like variance, covariance, class imbalance, and separation, with empirical results closely matching the proposed theory. This work provides crucial guidance for designing and selecting SIM-based objectives.

Why it matters

AI researchers and engineers can use this deeper understanding of SIMs to make more informed decisions when designing representation learning objectives, leading to more effective and robust models, especially in complex or imbalanced datasets.

How to implement this in your domain

  1. 1Review current representation learning objectives in use and identify areas for improvement, especially with imbalanced data.
  2. 2Experiment with different Submodular Information Measures (SIMs) as loss functions in contrastive learning setups.
  3. 3Utilize the theoretical insights to select the most appropriate SIM (e.g., Graph Cut TI for variance, LogDet MI for covariance-aware separation) for specific data characteristics.
  4. 4Develop custom SIM-based objectives tailored to unique challenges in multimodal or imbalanced datasets.

Original post by Rishabh Iyer, Truong Pham, Anay Majee

"arXiv:2607.27660v1 Announce Type: new Abstract: Submodular Information Measures (SIMs) have recently emerged as a powerful framework for representation learning and multimodal learning. In particular, the SCORE framework~\cite{majee2024score} demonstrated that SIMs can serve as e…"

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Originally posted by Rishabh Iyer, Truong Pham, Anay Majee on X · view source

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