# SLASH: Embracing Probabilistic Circuits into Neural Answer Set Programming

arXiv: https://arxiv.org/abs/2110.03395 · HTML: https://mlsanity.com/paper/2110.03395/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 47 references that are in the map.
- First posted on arXiv 7 Oct 2021.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [MONet: Unsupervised Scene Decomposition and Representation](https://mlsanity.com/paper/1901.11390/) (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)
- [On the Binding Problem in Artificial Neural Networks](https://mlsanity.com/paper/2012.05208/) (2020)
- [GENESIS: Generative Scene Inference and Sampling with Object-Centric Latent Representations](https://mlsanity.com/paper/1907.13052/) (2019)
- [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)
- [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)
- [Deep Set Prediction Networks](https://mlsanity.com/paper/1906.06565/) (2019)
- [Generative Neurosymbolic Machines](https://mlsanity.com/paper/2010.12152/) (2020)
- [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)

## Built on by (most cited first, 8 of 8)

- [ULLER: A Unified Language for Learning and Reasoning](https://mlsanity.com/paper/2405.00532/) (2024)
- [Efficient Knowledge Compilation Beyond Weighted Model Counting](https://mlsanity.com/paper/2205.07496/) (2022)
- [ActivationReasoning: Logical Reasoning in Latent Activation Spaces](https://mlsanity.com/paper/2510.18184/) (2025)
- [Probabilistic Mission Design for Neuro-Symbolic Unmanned Aircraft Systems](https://mlsanity.com/paper/2501.01439/) (2024)
- [Toward Foundation Models for Online Complex Event Detection in CPS-IoT: A Case Study](https://mlsanity.com/paper/2503.12282/) (2025)
- [Language-Based Causal Representation Learning](https://mlsanity.com/paper/2207.05259/) (2022)
- [Probabilistic Circuits for Knowledge Graph Completion with Reduced Rule Sets](https://mlsanity.com/paper/2508.06706/) (2025)
- [AS2 -- Attention-Based Soft Answer Sets: An End-to-End Differentiable Neuro-Soft-Symbolic Reasoning Architecture](https://mlsanity.com/paper/2603.18436/) (2026)

## Abstract (arXiv)

The goal of combining the robustness of neural networks and the expressivity of symbolic methods has rekindled the interest in neuro-symbolic AI. Recent advancements in neuro-symbolic AI often consider specifically-tailored architectures consisting of disjoint neural and symbolic components, and thus do not exhibit desired gains that can be achieved by integrating them into a unifying framework. We introduce SLASH -- a novel deep probabilistic programming language (DPPL). At its core, SLASH consists of Neural-Probabilistic Predicates (NPPs) and logical programs which are united via answer set programming. The probability estimates resulting from NPPs act as the binding element between the logical program and raw input data, thereby allowing SLASH to answer task-dependent logical queries. This allows SLASH to elegantly integrate the symbolic and neural components in a unified framework. We evaluate SLASH on the benchmark data of MNIST addition as well as novel tasks for DPPLs such as missing data prediction and set prediction with state-of-the-art performance, thereby showing the effectiveness and generality of our method.