# Hinge-Loss Markov Random Fields and Probabilistic Soft Logic

arXiv: https://arxiv.org/abs/1505.04406 · HTML: https://mlsanity.com/paper/1505.04406/

## Key facts

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

## Built on by (most cited first, 30 of 63)

- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [ESC: Exploration with Soft Commonsense Constraints for Zero-shot Object Navigation](https://mlsanity.com/paper/2301.13166/) (2023)
- [MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networks](https://mlsanity.com/paper/2111.01564/) (2021)
- [Modular Design Patterns for Hybrid Learning and Reasoning Systems: a taxonomy, patterns and use cases](https://mlsanity.com/paper/2102.11965/) (2021)
- [A Survey on Neural-symbolic Learning Systems](https://mlsanity.com/paper/2111.08164/) (2021)
- [Towards LogiGLUE: A Brief Survey and A Benchmark for Analyzing Logical Reasoning Capabilities of Language Models](https://mlsanity.com/paper/2310.00836/) (2023)
- [NeuPSL: Neural Probabilistic Soft Logic](https://mlsanity.com/paper/2205.14268/) (2022)
- [Identifying Morality Frames in Political Tweets using Relational Learning](https://mlsanity.com/paper/2109.04535/) (2021)
- [Probabilistic Box Embeddings for Uncertain Knowledge Graph Reasoning](https://mlsanity.com/paper/2104.04597/) (2021)
- [Zero-shot Object Navigation with Vision-Language Models Reasoning](https://mlsanity.com/paper/2410.18570/) (2024)
- [Classifying Argumentative Relations Using Logical Mechanisms and Argumentation Schemes](https://mlsanity.com/paper/2105.07571/) (2021)
- [More than Classification: A Unified Framework for Event Temporal Relation Extraction](https://mlsanity.com/paper/2305.17607/) (2023)
- [Advances in Embodied Navigation Using Large Language Models: A Survey](https://mlsanity.com/paper/2311.00530/) (2023)
- [DomiKnowS: A Library for Integration of Symbolic Domain Knowledge in Deep Learning](https://mlsanity.com/paper/2108.12370/) (2021)
- [Semantic Strengthening of Neuro-Symbolic Learning](https://mlsanity.com/paper/2302.14207/) (2023)
- [LNN-EL: A Neuro-Symbolic Approach to Short-text Entity Linking](https://mlsanity.com/paper/2106.09795/) (2021)
- [Learning with Logical Constraints but without Shortcut Satisfaction](https://mlsanity.com/paper/2403.00329/) (2024)
- [GLUECons: A Generic Benchmark for Learning Under Constraints](https://mlsanity.com/paper/2302.10914/) (2023)
- [Data Cleaning and Machine Learning: A Systematic Literature Review](https://mlsanity.com/paper/2310.01765/) (2023)
- [Evaluating Relaxations of Logic for Neural Networks: A Comprehensive Study](https://mlsanity.com/paper/2107.13646/) (2021)
- [Logical Entity Representation in Knowledge-Graphs for Differentiable Rule Learning](https://mlsanity.com/paper/2305.12738/) (2023)
- [Extensions to Generalized Annotated Logic and an Equivalent Neural Architecture](https://mlsanity.com/paper/2302.12195/) (2023)
- [Using Domain Knowledge to Guide Dialog Structure Induction via Neural Probabilistic Soft Logic](https://mlsanity.com/paper/2403.17853/) (2024)
- [Randomized Deep Structured Prediction for Discourse-Level Processing](https://mlsanity.com/paper/2101.10435/) (2021)
- [Relational Reasoning Networks](https://mlsanity.com/paper/2106.00393/) (2021)
- [Principled and Efficient Motif Finding for Structure Learning of Lifted Graphical Models](https://mlsanity.com/paper/2302.04599/) (2023)
- [DeepPSL: End-to-end perception and reasoning](https://mlsanity.com/paper/2109.13662/) (2021)
- [Knowledge Enhanced Neural Networks for relational domains](https://mlsanity.com/paper/2205.15762/) (2022)
- [LogicMP: A Neuro-symbolic Approach for Encoding First-order Logic Constraints](https://mlsanity.com/paper/2309.15458/) (2023)
- [Learning from Noisy Crowd Labels with Logics](https://mlsanity.com/paper/2302.06337/) (2023)

## 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.