# NeuPSL: Neural Probabilistic Soft Logic

arXiv: https://arxiv.org/abs/2205.14268 · HTML: https://mlsanity.com/paper/2205.14268/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 27 of its 83 references that are in the map.
- First posted on arXiv 27 May 2022.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 27 of 27)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Conditional Random Fields as Recurrent Neural Networks](https://mlsanity.com/paper/1502.03240/) (2015)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning](https://mlsanity.com/paper/1905.06088/) (2019)
- [Harnessing Deep Neural Networks with Logic Rules](https://mlsanity.com/paper/1603.06318/) (2016)
- [Neural Symbolic Machines: Learning Semantic Parsers on Freebase with Weak Supervision](https://mlsanity.com/paper/1611.00020/) (2016)
- [Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective](https://mlsanity.com/paper/2003.00330/) (2020)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [Hinge-Loss Markov Random Fields and Probabilistic Soft Logic](https://mlsanity.com/paper/1505.04406/) (2015)
- [From Statistical Relational to Neuro-Symbolic Artificial Intelligence](https://mlsanity.com/paper/2003.08316/) (2020)
- [DeepStochLog: Neural Stochastic Logic Programming](https://mlsanity.com/paper/2106.12574/) (2021)
- [Programming with a Differentiable Forth Interpreter](https://mlsanity.com/paper/1605.06640/) (2016)
- [Towards Semi-Supervised Learning for Deep Semantic Role Labeling](https://mlsanity.com/paper/1808.09543/) (2018)
- [Deep Adaptive Semantic Logic (DASL): Compiling Declarative Knowledge into Deep Neural Networks](https://mlsanity.com/paper/2003.07344/) (2020)
- [HyperFair: A Soft Approach to Integrating Fairness Criteria](https://mlsanity.com/paper/2009.08952/) (2020)

## Built on by (most cited first, 30 of 34)

- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcuts](https://mlsanity.com/paper/2305.19951/) (2023)
- [A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inference](https://mlsanity.com/paper/2212.12393/) (2022)
- [BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcuts](https://mlsanity.com/paper/2402.12240/) (2024)
- [HardNet: Hard-Constrained Neural Networks with Universal Approximation Guarantees](https://mlsanity.com/paper/2410.10807/) (2024)
- [Towards Cognitive AI Systems: a Survey and Prospective on Neuro-Symbolic AI](https://mlsanity.com/paper/2401.01040/) (2024)
- [A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcuts](https://mlsanity.com/paper/2406.10368/) (2024)
- [On the Independence Assumption in Neurosymbolic Learning](https://mlsanity.com/paper/2404.08458/) (2024)
- [Beyond the convexity assumption: Realistic tabular data generation under quantifier-free real linear constraints](https://mlsanity.com/paper/2502.18237/) (2025)
- [Softened Symbol Grounding for Neuro-symbolic Systems](https://mlsanity.com/paper/2403.00323/) (2024)
- [Semantic Strengthening of Neuro-Symbolic Learning](https://mlsanity.com/paper/2302.14207/) (2023)
- [The Role of Foundation Models in Neuro-Symbolic Learning and Reasoning](https://mlsanity.com/paper/2402.01889/) (2024)
- [ULLER: A Unified Language for Learning and Reasoning](https://mlsanity.com/paper/2405.00532/) (2024)
- [Logical Entity Representation in Knowledge-Graphs for Differentiable Rule Learning](https://mlsanity.com/paper/2305.12738/) (2023)
- [Defining neurosymbolic AI](https://mlsanity.com/paper/2507.11127/) (2025)
- [Towards Efficient Neuro-Symbolic AI: From Workload Characterization to Hardware Architecture](https://mlsanity.com/paper/2409.13153/) (2024)
- [Using Domain Knowledge to Guide Dialog Structure Induction via Neural Probabilistic Soft Logic](https://mlsanity.com/paper/2403.17853/) (2024)
- [The DeepLog Neurosymbolic Machine](https://mlsanity.com/paper/2508.13697/) (2025)
- [DeonticBench: A Benchmark for Reasoning over Rules](https://mlsanity.com/paper/2604.04443/) (2026)
- [On the use of neurosymbolic AI for defending against cyber attacks](https://mlsanity.com/paper/2408.04996/) (2024)
- [ABS: Enforcing Constraint Satisfaction On Generated Sequences Via Automata-Guided Beam Search](https://mlsanity.com/paper/2506.09701/) (2025)
- [Teaching Transformers to Solve Combinatorial Problems through Efficient Trial & Error](https://mlsanity.com/paper/2509.22023/) (2025)
- [Right for the Right Reasons: Avoiding Reasoning Shortcuts via Prototypical Neurosymbolic AI](https://mlsanity.com/paper/2510.25497/) (2025)
- [NeuroSymActive: Differentiable Neural-Symbolic Reasoning with Active Exploration for Knowledge Graph Question Answering](https://mlsanity.com/paper/2602.15353/) (2026)
- [A Neuro-Symbolic Approach for Probabilistic Reasoning on Graph Data](https://mlsanity.com/paper/2507.21873/) (2025)
- [A Novel Neural-symbolic System under Statistical Relational Learning](https://mlsanity.com/paper/2309.08931/) (2023)
- [Convex and Bilevel Optimization for Neuro-Symbolic Inference and Learning](https://mlsanity.com/paper/2401.09651/) (2024)
- [Understanding and Improving Adversarial Robustness of Neural Probabilistic Circuits](https://mlsanity.com/paper/2509.20549/) (2025)
- [Constraint-Aware Neurosymbolic Uncertainty Quantification with Bayesian Deep Learning for Scientific Discovery](https://mlsanity.com/paper/2601.12442/) (2026)
- [Improved Bug Localization with AI Agents Leveraging Hypothesis and Dynamic Cognition](https://mlsanity.com/paper/2601.12522/) (2026)

## Abstract (arXiv)

In this paper, we introduce Neural Probabilistic Soft Logic (NeuPSL), a novel neuro-symbolic (NeSy) framework that unites state-of-the-art symbolic reasoning with the low-level perception of deep neural networks. To model the boundary between neural and symbolic representations, we propose a family of energy-based models, NeSy Energy-Based Models, and show that they are general enough to include NeuPSL and many other NeSy approaches. Using this framework, we show how to seamlessly integrate neural and symbolic parameter learning and inference in NeuPSL. Through an extensive empirical evaluation, we demonstrate the benefits of using NeSy methods, achieving upwards of 30% improvement over independent neural network models. On a well-established NeSy task, MNIST-Addition, NeuPSL demonstrates its joint reasoning capabilities by outperforming existing NeSy approaches by up to 10% in low-data settings. Furthermore, NeuPSL achieves a 5% boost in performance over state-of-the-art NeSy methods in a canonical citation network task with up to a 40 times speed up.