# Scalable Neural-Probabilistic Answer Set Programming

arXiv: https://arxiv.org/abs/2306.08397 · HTML: https://mlsanity.com/paper/2306.08397/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 54 references that are in the map.
- First posted on arXiv 14 Jun 2023.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [Multi-Object Representation Learning with Iterative Variational Inference](https://mlsanity.com/paper/1903.00450/) (2019)
- [Neural-Symbolic VQA: Disentangling Reasoning from Vision and Language Understanding](https://mlsanity.com/paper/1810.02338/) (2018)
- [Neurosymbolic AI: The 3rd Wave](https://mlsanity.com/paper/2012.05876/) (2020)
- [SPACE: Unsupervised Object-Oriented Scene Representation via Spatial Attention and Decomposition](https://mlsanity.com/paper/2001.02407/) (2020)
- [Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning](https://mlsanity.com/paper/1905.06088/) (2019)
- [Neural Logic Machines](https://mlsanity.com/paper/1904.11694/) (2019)
- [Learning by Abstraction: The Neural State Machine](https://mlsanity.com/paper/1907.03950/) (2019)
- [Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuits](https://mlsanity.com/paper/2004.06231/) (2020)
- [Right for the Right Concept: Revising Neuro-Symbolic Concepts by Interacting with their Explanations](https://mlsanity.com/paper/2011.12854/) (2020)
- [ASP-Core-2 Input Language Format](https://mlsanity.com/paper/1911.04326/) (2019)
- [DeepStochLog: Neural Stochastic Logic Programming](https://mlsanity.com/paper/2106.12574/) (2021)
- [Generative Neurosymbolic Machines](https://mlsanity.com/paper/2010.12152/) (2020)
- [Inductive logic programming at 30](https://mlsanity.com/paper/2102.10556/) (2021)
- [ShapeWorld - A new test methodology for multimodal language understanding](https://mlsanity.com/paper/1704.04517/) (2017)
- [Deep Probabilistic Programming](https://mlsanity.com/paper/1701.03757/) (2017)
- [A Neuro-Symbolic ASP Pipeline for Visual Question Answering](https://mlsanity.com/paper/2205.07548/) (2022)
- [Leveraging Probabilistic Circuits for Nonparametric Multi-Output Regression](https://mlsanity.com/paper/2106.08687/) (2021)
- [Recent, rapid advancement in visual question answering architecture: a review](https://mlsanity.com/paper/2203.01322/) (2022)

## Built on by (most cited first, 14 of 14)

- [Neural Concept Binder](https://mlsanity.com/paper/2406.09949/) (2024)
- [The Role of Foundation Models in Neuro-Symbolic Learning and Reasoning](https://mlsanity.com/paper/2402.01889/) (2024)
- [Building Intelligent Agents with Neuro-Symbolic Concepts](https://mlsanity.com/paper/2505.06191/) (2025)
- [Synthesizing Visual Concepts as Vision-Language Programs](https://mlsanity.com/paper/2511.18964/) (2025)
- [Dolphin: A Programmable Framework for Scalable Neurosymbolic Learning](https://mlsanity.com/paper/2410.03348/) (2024)
- [Right for the Right Reasons: Avoiding Reasoning Shortcuts via Prototypical Neurosymbolic AI](https://mlsanity.com/paper/2510.25497/) (2025)
- [On the Hardness of Approximating Distributions with Tractable Probabilistic Models](https://mlsanity.com/paper/2506.01281/) (2025)
- [A Neuro-Symbolic Approach for Probabilistic Reasoning on Graph Data](https://mlsanity.com/paper/2507.21873/) (2025)
- [The Constitutional Controller: Doubt-Calibrated Steering of Compliant Agents](https://mlsanity.com/paper/2507.15478/) (2025)
- [Neural Decision-Propagation for Answer Set Programming](https://mlsanity.com/paper/2605.01797/) (2026)
- [CALM: Contextual Analog Logic with Multimodality](https://mlsanity.com/paper/2506.14936/) (2025)
- [Right in Time: Reactive Reasoning in Regulated Traffic Spaces](https://mlsanity.com/paper/2603.03977/) (2026)
- [Accelerating NeurASP with vectorization and caching](https://mlsanity.com/paper/2606.10787/) (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)

The goal of combining the robustness of neural networks and the expressiveness of symbolic methods has rekindled the interest in Neuro-Symbolic AI. Deep Probabilistic Programming Languages (DPPLs) have been developed for probabilistic logic programming to be carried out via the probability estimations of deep neural networks. However, recent SOTA DPPL approaches allow only for limited conditional probabilistic queries and do not offer the power of true joint probability estimation. In our work, we propose an easy integration of tractable probabilistic inference within a DPPL. To this end, we introduce SLASH, a novel DPPL that consists of Neural-Probabilistic Predicates (NPPs) and a logic program, united via answer set programming (ASP). NPPs are a novel design principle allowing for combining all deep model types and combinations thereof to be represented as a single probabilistic predicate. In this context, we introduce a novel +/- notation for answering various types of probabilistic queries by adjusting the atom notations of a predicate. To scale well, we show how to prune the stochastically insignificant parts of the (ground) program, speeding up reasoning without sacrificing the predictive performance. We evaluate SLASH on a variety of different tasks, including the benchmark task of MNIST addition and Visual Question Answering (VQA).