# Neural-Symbolic Integration: A Compositional Perspective

arXiv: https://arxiv.org/abs/2010.11926 · HTML: https://mlsanity.com/paper/2010.11926/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2020.

## Built on by (most cited first, 30 of 45)

- [Improving Coherence and Consistency in Neural Sequence Models with Dual-System, Neuro-Symbolic Reasoning](https://mlsanity.com/paper/2107.02794/) (2021)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [DeepStochLog: Neural Stochastic Logic Programming](https://mlsanity.com/paper/2106.12574/) (2021)
- [Is Neuro-Symbolic AI Meeting its Promise in Natural Language Processing? A Structured Review](https://mlsanity.com/paper/2202.12205/) (2022)
- [Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computing](https://mlsanity.com/paper/2210.15889/) (2022)
- [Logic-induced Diagnostic Reasoning for Semi-supervised Semantic Segmentation](https://mlsanity.com/paper/2308.12595/) (2023)
- [Shifts 2.0: Extending The Dataset of Real Distributional Shifts](https://mlsanity.com/paper/2206.15407/) (2022)
- [Generative learning for nonlinear dynamics](https://mlsanity.com/paper/2311.04128/) (2023)
- [Deep Symbolic Learning: Discovering Symbols and Rules from Perceptions](https://mlsanity.com/paper/2208.11561/) (2022)
- [Neurosymbolic AI for Reasoning over Knowledge Graphs: A Survey](https://mlsanity.com/paper/2302.07200/) (2023)
- [Learning to Solve Constraint Satisfaction Problems with Recurrent Transformer](https://mlsanity.com/paper/2307.04895/) (2023)
- [FF-NSL: Feed-Forward Neural-Symbolic Learner](https://mlsanity.com/paper/2106.13103/) (2021)
- [On Learning Latent Models with Multi-Instance Weak Supervision](https://mlsanity.com/paper/2306.13796/) (2023)
- [Injecting Logical Constraints into Neural Networks via Straight-Through Estimators](https://mlsanity.com/paper/2307.04347/) (2023)
- [Neuro-Symbolic AI: Explainability, Challenges, and Future Trends](https://mlsanity.com/paper/2411.04383/) (2024)
- [Defining neurosymbolic AI](https://mlsanity.com/paper/2507.11127/) (2025)
- [Data-Efficient Learning with Neural Programs](https://mlsanity.com/paper/2406.06246/) (2024)
- [Neural Reward Machines](https://mlsanity.com/paper/2408.08677/) (2024)
- [Stop Reducing Responsibility in LLM-Powered Multi-Agent Systems to Local Alignment](https://mlsanity.com/paper/2510.14008/) (2025)
- [Deciphering Raw Data in Neuro-Symbolic Learning with Provable Guarantees](https://mlsanity.com/paper/2308.10487/) (2023)
- [End-to-End Neuro-Symbolic Architecture for Image-to-Image Reasoning Tasks](https://mlsanity.com/paper/2106.03121/) (2021)
- [Neurosymbolic AI for Reasoning on Biomedical Knowledge Graphs](https://mlsanity.com/paper/2307.08411/) (2023)
- [Differentiable Logic Programming for Distant Supervision](https://mlsanity.com/paper/2408.12591/) (2024)
- [Learning Reliable Logical Rules with SATNet](https://mlsanity.com/paper/2310.02133/) (2023)
- [Deep Algorithmic Question Answering: Towards a Compositionally Hybrid AI for Algorithmic Reasoning](https://mlsanity.com/paper/2109.08006/) (2021)
- [Parallel Neurosymbolic Integration with Concordia](https://mlsanity.com/paper/2306.00480/) (2023)
- [Efficient Learning of Discrete-Continuous Computation Graphs](https://mlsanity.com/paper/2307.14193/) (2023)
- [Neuro-Symbolic Recommendation Model based on Logic Query](https://mlsanity.com/paper/2309.07594/) (2023)
- [NeuralFastLAS: Fast Logic-Based Learning from Raw Data](https://mlsanity.com/paper/2310.05145/) (2023)
- [Imbalances in Neurosymbolic Learning: Characterization and Mitigating Strategies](https://mlsanity.com/paper/2407.10000/) (2024)

## Abstract (arXiv)

Despite significant progress in the development of neural-symbolic frameworks, the question of how to integrate a neural and a symbolic system in a compositional manner remains open. Our work seeks to fill this gap by treating these two systems as black boxes to be integrated as modules into a single architecture, without making assumptions on their internal structure and semantics. Instead, we expect only that each module exposes certain methods for accessing the functions that the module implements: the symbolic module exposes a deduction method for computing the function's output on a given input, and an abduction method for computing the function's inputs for a given output; the neural module exposes a deduction method for computing the function's output on a given input, and an induction method for updating the function given input-output training instances. We are, then, able to show that a symbolic module -- with any choice for syntax and semantics, as long as the deduction and abduction methods are exposed -- can be cleanly integrated with a neural module, and facilitate the latter's efficient training, achieving empirical performance that exceeds that of previous work.