# Answer Set Networks: Casting Answer Set Programming into Deep Learning

arXiv: https://arxiv.org/abs/2412.14814 · HTML: https://mlsanity.com/paper/2412.14814/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 39 references that are in the map.
- First posted on arXiv 19 Dec 2024.

## Builds on (most cited first, 16 of 16)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [VQA: Visual Question Answering](https://mlsanity.com/paper/1505.00468/) (2015)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [OK-VQA: A Visual Question Answering Benchmark Requiring External Knowledge](https://mlsanity.com/paper/1906.00067/) (2019)
- [A-OKVQA: A Benchmark for Visual Question Answering using World Knowledge](https://mlsanity.com/paper/2206.01718/) (2022)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [NeurASP: Embracing Neural Networks into Answer Set Programming](https://mlsanity.com/paper/2307.07700/) (2023)
- [ASP-Core-2 Input Language Format](https://mlsanity.com/paper/1911.04326/) (2019)
- [Solving and Verifying the boolean Pythagorean Triples problem via Cube-and-Conquer](https://mlsanity.com/paper/1605.00723/) (2016)
- [KLay: Accelerating Arithmetic Circuits for Neurosymbolic AI](https://mlsanity.com/paper/2410.11415/) (2024)
- [Dolphin: A Programmable Framework for Scalable Neurosymbolic Learning](https://mlsanity.com/paper/2410.03348/) (2024)
- [Mission Design for Unmanned Aerial Vehicles using Hybrid Probabilistic Logic Programs](https://mlsanity.com/paper/2406.03454/) (2024)
- [Error Decomposition for Hybrid Localization Systems](https://mlsanity.com/paper/2410.14264/) (2024)
- [Graph Based Answer Set Programming Solver Systems](https://mlsanity.com/paper/2109.08681/) (2021)

## Built on by (most cited first, 6 of 6)

- [Constraint-Based Analysis of Reasoning Shortcuts in Neurosymbolic Learning](https://mlsanity.com/paper/2604.23377/) (2026)
- [NASP-T: A Fuzzy Neuro-Symbolic Transformer for Logic-Constrained Aviation Safety Report Classification](https://mlsanity.com/paper/2510.05451/) (2025)
- [ASP-Bench: From Natural Language to Logic Programs](https://mlsanity.com/paper/2602.01171/) (2026)
- [Right in Time: Reactive Reasoning in Regulated Traffic Spaces](https://mlsanity.com/paper/2603.03977/) (2026)
- [Streamliners for Answer Set Programming](https://mlsanity.com/paper/2604.19251/) (2026)
- [Driving, Fast or Slow? Neuro-Symbolic Guidance for Motion Prediction in Multi-Modal Ground Mobility](https://mlsanity.com/paper/2606.15251/) (2026)

## Abstract (arXiv)

Although Answer Set Programming (ASP) allows constraining neural-symbolic (NeSy) systems, its employment is hindered by the prohibitive costs of computing stable models and the CPU-bound nature of state-of-the-art solvers. To this end, we propose Answer Set Networks (ASN), a NeSy solver. Based on Graph Neural Networks (GNN), ASNs are a scalable approach to ASP-based Deep Probabilistic Logic Programming (DPPL). Specifically, we show how to translate ASPs into ASNs and demonstrate how ASNs can efficiently solve the encoded problem by leveraging GPU's batching and parallelization capabilities. Our experimental evaluations demonstrate that ASNs outperform state-of-the-art CPU-bound NeSy systems on multiple tasks. Simultaneously, we make the following two contributions based on the strengths of ASNs. Namely, we are the first to show the finetuning of Large Language Models (LLM) with DPPLs, employing ASNs to guide the training with logic. Further, we show the "constitutional navigation" of drones, i.e., encoding public aviation laws in an ASN for routing Unmanned Aerial Vehicles in uncertain environments.