# Understanding Submodular Information Measure Based Objectives for Representation Learning: A Variance and Separation Perspective

arXiv: https://arxiv.org/abs/2607.27660 · HTML: https://mlsanity.com/paper/2607.27660/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 36 references that are in the map.
- First posted on arXiv 30 Jul 2026.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [Deep Metric Learning via Lifted Structured Feature Embedding](https://mlsanity.com/paper/1511.06452/) (2015)
- [Analyzing and Improving Representations with the Soft Nearest Neighbor Loss](https://mlsanity.com/paper/1902.01889/) (2019)
- [SIMILAR: Submodular Information Measures Based Active Learning In Realistic Scenarios](https://mlsanity.com/paper/2107.00717/) (2021)
- [Learning From Less Data: A Unified Data Subset Selection and Active Learning Framework for Computer Vision](https://mlsanity.com/paper/1901.01151/) (2019)
- [PRISM: A Rich Class of Parameterized Submodular Information Measures for Guided Subset Selection](https://mlsanity.com/paper/2103.00128/) (2021)
- [TALISMAN: Targeted Active Learning for Object Detection with Rare Classes and Slices using Submodular Mutual Information](https://mlsanity.com/paper/2112.00166/) (2021)
- [Demystifying Multi-Faceted Video Summarization: Tradeoff Between Diversity,Representation, Coverage and Importance](https://mlsanity.com/paper/1901.01153/) (2019)
- [SMILe: Leveraging Submodular Mutual Information For Robust Few-Shot Object Detection](https://mlsanity.com/paper/2407.02665/) (2024)
- [SCoRe: Submodular Combinatorial Representation Learning](https://mlsanity.com/paper/2310.00165/) (2023)
- [Looking Beyond the Known: Towards a Data Discovery Guided Open-World Object Detection](https://mlsanity.com/paper/2510.00303/) (2025)
- [SMA: Submodular Modality Aligner For Data Efficient Multimodal Learning](https://mlsanity.com/paper/2605.12872/) (2026)

## Abstract (arXiv)

Submodular Information Measures (SIMs) have recently emerged as a powerful framework for representation learning and multimodal learning. In particular, the SCORE framework~citemajee2024score demonstrated that SIMs can serve as effective objectives for supervised contrastive learning. Despite their empirical success, however, the geometric and statistical properties induced by different submodular information measures remain poorly understood. In this work, we develop a unified theoretical framework connecting SIMs to classical concepts in representation learning and statistical pattern recognition. We show that Total Information (TI) objectives characterize intra-class structure: Graph Cut TI recovers within-class variance, LogDet TI recovers generalized variance and covariance volume, and Facility Location TI induces imbalance-aware separation that emphasizes rare and confusable classes. We further show that Mutual Information (MI) objectives capture complementary notions of inter-class structure: Graph Cut MI is closely related to centroid separation and Fisher-style discrimination, LogDet MI captures covariance-aware separation through Mahalanobis distance, and Facility Location MI measures nearest-mode representational overlap. We validate these theoretical characterizations using controlled synthetic experiments that independently vary variance, covariance, class imbalance, class separation, and multimodal overlap. Across all settings, the empirical behavior closely matches the proposed theory. Our results provide the first unified geometric and statistical understanding of submodular information measures and offer principled guidance for selecting and designing SIM-based objectives for representation learning.