mlsanityData to 7 Oct 2026

Submodularity In Machine Learning and Artificial Intelligence

arXiv 2202.00132 ↗First posted 31 Jan 2022cs.LG cs.AIcited by 37

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Abstract (arXiv)

In this manuscript, we offer a gentle review of submodularity and supermodularity and their properties. We offer a plethora of submodular definitions; a full description of a number of example submodular functions and their generalizations; example discrete constraints; a discussion of basic algorithms for maximization, minimization, and other operations; a brief overview of continuous submodular extensions; and some historical applications. We then turn to how submodularity is useful in machine learning and artificial intelligence. This includes summarization, and we offer a complete account of the differences between and commonalities amongst sketching, coresets, extractive and abstractive summarization in NLP, data distillation and condensation, and data subset selection and feature selection. We discuss a variety of ways to produce a submodular function useful for machine learning, including heuristic hand-crafting, learning or approximately learning a submodular function or aspects thereof, and some advantages of the use of a submodular function as a coreset producer. We discuss submodular combinatorial information functions, and how submodularity is useful for clustering, data partitioning, parallel machine learning, active and semi-supervised learning, probabilistic modeling, and structured norms and loss functions.

Key facts. Cited by 37 papers in the map (data through 7 Oct 2026). Builds on 67 of its 261 references that are in the map. First posted on arXiv 31 Jan 2022.

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67 of 261 references.

References · 67

  1. 2015Distilling the Knowledge in a Neural Networkcited by 10,076
  2. 2017A Unified Approach to Interpreting Model Predictionscited by 6,488
  3. 2019Deep Leakage from Gradientscited by 1,004
  4. 2019Adversarial Examples Are Not Bugs, They Are Featurescited by 950
  5. 2020On Faithfulness and Factuality in Abstractive Summarizationcited by 895
  6. 2019Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Boundscited by 602
  7. 2019Evaluating the Factual Consistency of Abstractive Text Summarizationcited by 578
  8. 2020Dataset Condensation with Gradient Matchingcited by 510
  9. 2013Do Deep Nets Really Need to be Deep?cited by 466
  10. 2019BatchBALD: Efficient and Diverse Batch Acquisition for Deep Bayesian Active Learningcited by 428
  11. 2019Dreaming to Distill: Data-free Knowledge Transfer via DeepInversioncited by 419
  12. 2018Generating Wikipedia by Summarizing Long Sequencescited by 333
38 more
  1. 2020FEQA: A Question Answering Evaluation Framework for Faithfulness Assessment in Abstractive Summarizationcited by 292
  2. 2021Dataset Condensation with Differentiable Siamese Augmentationcited by 290
  3. 2014Sketching as a Tool for Numerical Linear Algebracited by 285
  4. 2020Dataset Meta-Learning from Kernel Ridge-Regressioncited by 230
  5. 2020GLISTER: Generalization based Data Subset Selection for Efficient and Robust Learningcited by 224
  6. 2021Dataset Distillation with Infinitely Wide Convolutional Networkscited by 215
  7. 2021Evaluating Gradient Inversion Attacks and Defenses in Federated Learningcited by 196
  8. 2020Coresets via Bilevel Optimization for Continual Learning and Streamingcited by 191
  9. 2018Bottom-Up Abstractive Summarizationcited by 177
  10. 2019Soft-Label Dataset Distillation and Text Dataset Distillationcited by 106
  11. 2019Generative Teaching Networks: Accelerating Neural Architecture Search by Learning to Generate Synthetic Training Datacited by 103
  12. 2020Flexible Dataset Distillation: Learn Labels Instead of Imagescited by 91
  13. 2020Submodular Combinatorial Information Measures with Applications in Machine Learningcited by 88
  14. 2019On Extractive and Abstractive Neural Document Summarization with Transformer Language Modelscited by 83
  15. 2020What Have We Achieved on Text Summarization?cited by 65
  16. 2019Learning From Less Data: A Unified Data Subset Selection and Active Learning Framework for Computer Visioncited by 64
  17. 2015A Faster Cutting Plane Method and its Implications for Combinatorial and Convex Optimizationcited by 50
  18. 2021PRISM: A Rich Class of Parameterized Submodular Information Measures for Guided Subset Selectioncited by 50
  19. 2018Stochastic Conditional Gradient Methods: From Convex Minimization to Submodular Maximizationcited by 47
  20. 2018A Unified Model for Extractive and Abstractive Summarization using Inconsistency Losscited by 47
  21. 2020Introduction to Core-sets: an Updated Surveycited by 45
  22. 2017Query-Focused Video Summarization: Dataset, Evaluation, and A Memory Network Based Approachcited by 42
  23. 2013Submodular Optimization with Submodular Cover and Submodular Knapsack Constraintscited by 40
  24. 2016Query-Focused Extractive Video Summarizationcited by 26
  25. 2015Submodular Functions: from Discrete to Continous Domainscited by 24
  26. 2017Continuous DR-submodular Maximization: Structure and Algorithmscited by 24
  27. 2017Query-adaptive Video Summarization via Quality-aware Relevance Estimationcited by 22
  28. 2014Distributed Submodular Maximizationcited by 20
  29. 2018Determinantal Point Processes for Coresetscited by 18
  30. 2019Introduction to Coresets: Accurate Coresetscited by 17
  31. 2014Algorithms for Approximate Minimization of the Difference Between Submodular Functions, with Applicationscited by 16
  32. 2015The Limitations of Optimization from Samplescited by 13
  33. 2019The FAST Algorithm for Submodular Maximizationcited by 13
  34. 2013Curvature and Optimal Algorithms for Learning and Minimizing Submodular Functionscited by 12
  35. 2017Deep Submodular Functionscited by 11
  36. 2019Near-optimal Approximate Discrete and Continuous Submodular Function Minimizationcited by 11
  37. 2015Robust Monotone Submodular Function Maximizationcited by 10
  38. 2015Deterministic Algorithms for Submodular Maximization Problemscited by 10

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Citing papers per year: 2022: 6; 2023: 8; 2024: 10; 2025: 6; 2026: 7.

37 papers.

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  1. 2023MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Modelscited by 724
  2. 2023Data Distillation: A Surveycited by 86
  3. 2024CultureLLM: Incorporating Cultural Differences into Large Language Modelscited by 49
  4. 2025Weight Ensembling Improves Reasoning in Language Modelscited by 36
  5. 2023A Formal Perspective on Byte-Pair Encodingcited by 35
  6. 2024CulturePark: Boosting Cross-cultural Understanding in Large Language Modelscited by 24
  7. 2023Submodular Reinforcement Learningcited by 23
  8. 2022Infinite Recommendation Networks: A Data-Centric Approachcited by 20
  9. 2024Global Reinforcement Learning: Beyond Linear and Convex Rewards via Submodular Semi-gradient Methodscited by 15
  10. 2022Neural Set Function Extensions: Learning with Discrete Functions in High Dimensionscited by 14
  11. 2026COMI: Coarse-to-fine Context Compression via Marginal Information Gaincited by 13
  12. 2022Near-Optimal Multi-Agent Learning for Safe Coverage Controlcited by 11
25 more
  1. 2022Sequential Attention for Feature Selectioncited by 9
  2. 2023Accelerating Batch Active Learning Using Continual Learning Techniquescited by 8
  3. 2023Cluster-aware Semi-supervised Learning: Relational Knowledge Distillation Provably Learns Clusteringcited by 7
  4. 2024Measuring Diversity: Axioms and Challengescited by 6
  5. 2022Online Submodular Coordination with Bounded Tracking Regret: Theory, Algorithm, and Applications to Multi-Robot Coordinationcited by 5
  6. 2025Looking Beyond the Known: Towards a Data Discovery Guided Open-World Object Detectioncited by 4
  7. 2023Farzi Data: Autoregressive Data Distillationcited by 3
  8. 2023Exploration with Principles for Diverse AI Supervisioncited by 2
  9. 2024FedCore: Straggler-Free Federated Learning with Distributed Coresetscited by 2
  10. 2024Communication- and Computation-Efficient Distributed Submodular Optimization in Robot Mesh Networkscited by 2
  11. 2024COBRA: COmBinatorial Retrieval Augmentation for Few-Shot Adaptationcited by 2
  12. 2025Prompting Test-Time Scaling Is A Strong LLM Reasoning Data Augmentationcited by 2
  13. 2026Classroom AI: Large Language Models as Grade-Specific Teacherscited by 2
  14. 2024Theoretical Analysis of Submodular Information Measures for Targeted Data Subset Selectioncited by 1
  15. 2024STONE: A Submodular Optimization Framework for Active 3D Object Detectioncited by 1
  16. 2024MentalArena: Self-play Training of Language Models for Diagnosis and Treatment of Mental Health Disorderscited by 1
  17. 2025Unifying and Optimizing Data Values for Selection via Sequential Decision-Makingcited by 1
  18. 2026SHaSaM: Submodular Hard Sample Mining for Fair Facial Attribute Recognitioncited by 1
  19. 2026SMA: Submodular Modality Aligner For Data Efficient Multimodal Learningcited by 1
  20. 2022Online Subset Selection using α-Core with no Augmented Regretcited by 0
  21. 2025Discrete and Continuous Difference of Submodular Minimizationcited by 0
  22. 2025DiRe: Diversity-promoting Regularization for Dataset Condensationcited by 0
  23. 2026Learnability-Driven Submodular Optimization for Active Roadside 3D Detectioncited by 0
  24. 2026Accelerated Relax-and-Round for Concave Coverage Problemscited by 0
  25. 2026Complement Submodular Information Measures for Balanced and Robust Data Selectioncited by 0