mlsanityData to 14 Oct 2026

Hinge-Loss Markov Random Fields and Probabilistic Soft Logic

arXiv 1505.04406 ↗First posted 17 May 2015cs.LG cs.AI stat.MLcited by 63

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Abstract (arXiv)

A fundamental challenge in developing high-impact machine learning technologies is balancing the need to model rich, structured domains with the ability to scale to big data. Many important problem areas are both richly structured and large scale, from social and biological networks, to knowledge graphs and the Web, to images, video, and natural language. In this paper, we introduce two new formalisms for modeling structured data, and show that they can both capture rich structure and scale to big data. The first, hinge-loss Markov random fields (HL-MRFs), is a new kind of probabilistic graphical model that generalizes different approaches to convex inference. We unite three approaches from the randomized algorithms, probabilistic graphical models, and fuzzy logic communities, showing that all three lead to the same inference objective. We then define HL-MRFs by generalizing this unified objective. The second new formalism, probabilistic soft logic (PSL), is a probabilistic programming language that makes HL-MRFs easy to define using a syntax based on first-order logic. We introduce an algorithm for inferring most-probable variable assignments (MAP inference) that is much more scalable than general-purpose convex optimization methods, because it uses message passing to take advantage of sparse dependency structures. We then show how to learn the parameters of HL-MRFs. The learned HL-MRFs are as accurate as analogous discrete models, but much more scalable. Together, these algorithms enable HL-MRFs and PSL to model rich, structured data at scales not previously possible.

Key facts. Cited by 63 papers in the map (data through 14 Oct 2026). First posted on arXiv 17 May 2015.

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Citing papers per year: 2021: 14; 2022: 7; 2023: 20; 2024: 9; 2025: 8; 2026: 5.

63 papers.

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  1. 2023Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoningcited by 391
  2. 2023ESC: Exploration with Soft Commonsense Constraints for Zero-shot Object Navigationcited by 127
  3. 2021MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networkscited by 44
  4. 2021Modular Design Patterns for Hybrid Learning and Reasoning Systems: a taxonomy, patterns and use casescited by 39
  5. 2021A Survey on Neural-symbolic Learning Systemscited by 39
  6. 2023Towards LogiGLUE: A Brief Survey and A Benchmark for Analyzing Logical Reasoning Capabilities of Language Modelscited by 35
  7. 2022NeuPSL: Neural Probabilistic Soft Logiccited by 34
  8. 2021Identifying Morality Frames in Political Tweets using Relational Learningcited by 26
  9. 2021Probabilistic Box Embeddings for Uncertain Knowledge Graph Reasoningcited by 22
  10. 2024Zero-shot Object Navigation with Vision-Language Models Reasoningcited by 19
  11. 2021Classifying Argumentative Relations Using Logical Mechanisms and Argumentation Schemescited by 18
  12. 2023More than Classification: A Unified Framework for Event Temporal Relation Extractioncited by 15
38 more
  1. 2023Advances in Embodied Navigation Using Large Language Models: A Surveycited by 14
  2. 2021DomiKnowS: A Library for Integration of Symbolic Domain Knowledge in Deep Learningcited by 12
  3. 2023Semantic Strengthening of Neuro-Symbolic Learningcited by 12
  4. 2021LNN-EL: A Neuro-Symbolic Approach to Short-text Entity Linkingcited by 11
  5. 2024Learning with Logical Constraints but without Shortcut Satisfactioncited by 10
  6. 2023GLUECons: A Generic Benchmark for Learning Under Constraintscited by 9
  7. 2023Data Cleaning and Machine Learning: A Systematic Literature Reviewcited by 9
  8. 2021Evaluating Relaxations of Logic for Neural Networks: A Comprehensive Studycited by 8
  9. 2023Logical Entity Representation in Knowledge-Graphs for Differentiable Rule Learningcited by 8
  10. 2023Extensions to Generalized Annotated Logic and an Equivalent Neural Architecturecited by 6
  11. 2024Using Domain Knowledge to Guide Dialog Structure Induction via Neural Probabilistic Soft Logiccited by 5
  12. 2021Randomized Deep Structured Prediction for Discourse-Level Processingcited by 4
  13. 2021Relational Reasoning Networkscited by 4
  14. 2023Principled and Efficient Motif Finding for Structure Learning of Lifted Graphical Modelscited by 4
  15. 2021DeepPSL: End-to-end perception and reasoningcited by 3
  16. 2022Knowledge Enhanced Neural Networks for relational domainscited by 3
  17. 2023LogicMP: A Neuro-symbolic Approach for Encoding First-order Logic Constraintscited by 3
  18. 2023Learning from Noisy Crowd Labels with Logicscited by 2
  19. 2023Consumer-side Fairness in Recommender Systems: A Systematic Survey of Methods and Evaluationcited by 2
  20. 2023Parallel Neurosymbolic Integration with Concordiacited by 2
  21. 2023A Survey on Interpretable Cross-modal Reasoningcited by 2
  22. 2023Distantly-Supervised Joint Extraction with Noise-Robust Learningcited by 2
  23. 2024Framing in the Presence of Supporting Data: A Case Study in U.S. Economic Newscited by 2
  24. 2024DECIDER: A Dual-System Rule-Controllable Decoding Framework for Language Generationcited by 2
  25. 2022Constraint Guided Gradient Descent: Guided Training with Inequality Constraintscited by 1
  26. 2022Differentiable Fuzzy ALC: A Neural-Symbolic Representation Language for Symbol Groundingcited by 1
  27. 2023A Novel Neural-symbolic System under Statistical Relational Learningcited by 1
  28. 2023Spatial Knowledge-Infused Hierarchical Learning: An Application in Flood Mapping on Earth Imagerycited by 1
  29. 2024Convex and Bilevel Optimization for Neuro-Symbolic Inference and Learningcited by 1
  30. 2024Faithful Differentiable Reasoning with Reshuffled Region-based Embeddingscited by 1
  31. 2024Efficiently Learning Probabilistic Logical Models by Cheaply Ranking Mined Rulescited by 1
  32. 2025GLRD: Global-Local Collaborative Reason and Debate with PSL for 3D Open-Vocabulary Detectioncited by 1
  33. 2021Human Schema Curation via Causal Association Rule Miningcited by 0
  34. 2021Effective Eigendecomposition based Graph Adaptation for Heterophilic Networkscited by 0
  35. 2022Emotion Recognition in Conversation using Probabilistic Soft Logiccited by 0
  36. 2022Scalable Regularization of Scene Graph Generation Models using Symbolic Theoriescited by 0
  37. 2022Deep Explainable Learning with Graph Based Data Assessing and Rule Reasoningcited by 0
  38. 2023Meta-Path-based Probabilistic Soft Logic for Drug-Target Interaction Predictioncited by 0

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