# NeurASP: Embracing Neural Networks into Answer Set Programming

arXiv: https://arxiv.org/abs/2307.07700 · HTML: https://mlsanity.com/paper/2307.07700/

## Key facts

- Cited by 92 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 15 Jul 2023.

## Builds on (most cited first, 12 of 12)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [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)
- [KagNet: Knowledge-Aware Graph Networks for Commonsense Reasoning](https://mlsanity.com/paper/1909.02151/) (2019)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [Learning to Compose Neural Networks for Question Answering](https://mlsanity.com/paper/1601.01705/) (2016)
- [ASP-Core-2 Input Language Format](https://mlsanity.com/paper/1911.04326/) (2019)
- [Recurrent Relational Networks](https://mlsanity.com/paper/1711.08028/) (2017)
- [Lifted Relational Neural Networks](https://mlsanity.com/paper/1508.05128/) (2015)
- [RelNN: A Deep Neural Model for Relational Learning](https://mlsanity.com/paper/1712.02831/) (2017)

## Built on by (most cited first, 30 of 92)

- [BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcuts](https://mlsanity.com/paper/2402.12240/) (2024)
- [Learning Iterative Reasoning through Energy Diffusion](https://mlsanity.com/paper/2406.11179/) (2024)
- [Interpretability is in the Mind of the Beholder: A Causal Framework for Human-interpretable Representation Learning](https://mlsanity.com/paper/2309.07742/) (2023)
- [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)
- [Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomy](https://mlsanity.com/paper/2406.16087/) (2024)
- [Shortcuts and Identifiability in Concept-based Models from a Neuro-Symbolic Lens](https://mlsanity.com/paper/2502.11245/) (2025)
- [The Role of Foundation Models in Neuro-Symbolic Learning and Reasoning](https://mlsanity.com/paper/2402.01889/) (2024)
- [Learning with Logical Constraints but without Shortcut Satisfaction](https://mlsanity.com/paper/2403.00329/) (2024)
- [A Compositional Atlas for Algebraic Circuits](https://mlsanity.com/paper/2412.05481/) (2024)
- [NeSyA: Neurosymbolic Automata](https://mlsanity.com/paper/2412.07331/) (2024)
- [Building Intelligent Agents with Neuro-Symbolic Concepts](https://mlsanity.com/paper/2505.06191/) (2025)
- [ULLER: A Unified Language for Learning and Reasoning](https://mlsanity.com/paper/2405.00532/) (2024)
- [LogiCity: Advancing Neuro-Symbolic AI with Abstract Urban Simulation](https://mlsanity.com/paper/2411.00773/) (2024)
- [Defining neurosymbolic AI](https://mlsanity.com/paper/2507.11127/) (2025)
- [Data-Efficient Learning with Neural Programs](https://mlsanity.com/paper/2406.06246/) (2024)
- [Towards Efficient Neuro-Symbolic AI: From Workload Characterization to Hardware Architecture](https://mlsanity.com/paper/2409.13153/) (2024)
- [Deciphering Raw Data in Neuro-Symbolic Learning with Provable Guarantees](https://mlsanity.com/paper/2308.10487/) (2023)
- [Semirings for Probabilistic and Neuro-Symbolic Logic Programming](https://mlsanity.com/paper/2402.13782/) (2024)
- [EXPLAIN, AGREE, LEARN: Scaling Learning for Neural Probabilistic Logic](https://mlsanity.com/paper/2408.08133/) (2024)
- [Dspy-based Neural-Symbolic Pipeline to Enhance Spatial Reasoning in LLMs](https://mlsanity.com/paper/2411.18564/) (2024)
- [Answer Set Networks: Casting Answer Set Programming into Deep Learning](https://mlsanity.com/paper/2412.14814/) (2024)
- [Dolphin: A Programmable Framework for Scalable Neurosymbolic Learning](https://mlsanity.com/paper/2410.03348/) (2024)
- [Compositional Generalization Across Distributional Shifts with Sparse Tree Operations](https://mlsanity.com/paper/2412.14076/) (2024)
- [A Study on Neuro-Symbolic Artificial Intelligence: Healthcare Perspectives](https://mlsanity.com/paper/2503.18213/) (2025)
- [The DeepLog Neurosymbolic Machine](https://mlsanity.com/paper/2508.13697/) (2025)
- [Using Logic Programming and Kernel-Grouping for Improving Interpretability of Convolutional Neural Networks](https://mlsanity.com/paper/2310.13073/) (2023)
- [Variable Assignment Invariant Neural Networks for Learning Logic Programs](https://mlsanity.com/paper/2408.10709/) (2024)

## Abstract (arXiv)

We present NeurASP, a simple extension of answer set programs by embracing neural networks. By treating the neural network output as the probability distribution over atomic facts in answer set programs, NeurASP provides a simple and effective way to integrate sub-symbolic and symbolic computation. We demonstrate how NeurASP can make use of a pre-trained neural network in symbolic computation and how it can improve the neural network's perception result by applying symbolic reasoning in answer set programming. Also, NeurASP can be used to train a neural network better by training with ASP rules so that a neural network not only learns from implicit correlations from the data but also from the explicit complex semantic constraints expressed by the rules.