# DeepStochLog: Neural Stochastic Logic Programming

arXiv: https://arxiv.org/abs/2106.12574 · HTML: https://mlsanity.com/paper/2106.12574/

## Key facts

- Cited by 58 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 55 references that are in the map.
- First posted on arXiv 23 Jun 2021.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Recurrent Neural Network Grammars](https://mlsanity.com/paper/1602.07776/) (2016)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [From Statistical Relational to Neuro-Symbolic Artificial Intelligence](https://mlsanity.com/paper/2003.08316/) (2020)
- [Closed Loop Neural-Symbolic Learning via Integrating Neural Perception, Grammar Parsing, and Symbolic Reasoning](https://mlsanity.com/paper/2006.06649/) (2020)
- [Neural-Symbolic Integration: A Compositional Perspective](https://mlsanity.com/paper/2010.11926/) (2020)
- [Programming with a Differentiable Forth Interpreter](https://mlsanity.com/paper/1605.06640/) (2016)
- [Synthesizing Datalog Programs Using Numerical Relaxation](https://mlsanity.com/paper/1906.00163/) (2019)
- [Analyzing Differentiable Fuzzy Implications](https://mlsanity.com/paper/2006.03472/) (2020)

## Built on by (most cited first, 30 of 58)

- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcuts](https://mlsanity.com/paper/2305.19951/) (2023)
- [Interpretable Neural-Symbolic Concept Reasoning](https://mlsanity.com/paper/2304.14068/) (2023)
- [A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inference](https://mlsanity.com/paper/2212.12393/) (2022)
- [NeuPSL: Neural Probabilistic Soft Logic](https://mlsanity.com/paper/2205.14268/) (2022)
- [Neuro-Symbolic Continual Learning: Knowledge, Reasoning Shortcuts and Concept Rehearsal](https://mlsanity.com/paper/2302.01242/) (2023)
- [VAEL: Bridging Variational Autoencoders and Probabilistic Logic Programming](https://mlsanity.com/paper/2202.04178/) (2022)
- [Neural Probabilistic Logic Programming in Discrete-Continuous Domains](https://mlsanity.com/paper/2303.04660/) (2023)
- [Interpretability is in the Mind of the Beholder: A Causal Framework for Human-interpretable Representation Learning](https://mlsanity.com/paper/2309.07742/) (2023)
- [Deep Symbolic Learning: Discovering Symbols and Rules from Perceptions](https://mlsanity.com/paper/2208.11561/) (2022)
- [On the Independence Assumption in Neurosymbolic Learning](https://mlsanity.com/paper/2404.08458/) (2024)
- [Interpretable Concept-Based Memory Reasoning](https://mlsanity.com/paper/2407.15527/) (2024)
- [Softened Symbol Grounding for Neuro-symbolic Systems](https://mlsanity.com/paper/2403.00323/) (2024)
- [KLay: Accelerating Arithmetic Circuits for Neurosymbolic AI](https://mlsanity.com/paper/2410.11415/) (2024)
- [Relational Concept Bottleneck Models](https://mlsanity.com/paper/2308.11991/) (2023)
- [Scalable Neural-Probabilistic Answer Set Programming](https://mlsanity.com/paper/2306.08397/) (2023)
- [LASER: A Neuro-Symbolic Framework for Learning Spatial-Temporal Scene Graphs with Weak Supervision](https://mlsanity.com/paper/2304.07647/) (2023)
- [NeSyA: Neurosymbolic Automata](https://mlsanity.com/paper/2412.07331/) (2024)
- [GLUECons: A Generic Benchmark for Learning Under Constraints](https://mlsanity.com/paper/2302.10914/) (2023)
- [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)
- [EXPLAIN, AGREE, LEARN: Scaling Learning for Neural Probabilistic Logic](https://mlsanity.com/paper/2408.08133/) (2024)
- [logLTN: Differentiable Fuzzy Logic in the Logarithm Space](https://mlsanity.com/paper/2306.14546/) (2023)
- [Compositional Generalization Across Distributional Shifts with Sparse Tree Operations](https://mlsanity.com/paper/2412.14076/) (2024)
- [Variable Assignment Invariant Neural Networks for Learning Logic Programs](https://mlsanity.com/paper/2408.10709/) (2024)
- [Differentiable Logic Programming for Distant Supervision](https://mlsanity.com/paper/2408.12591/) (2024)
- [DeepPSL: End-to-end perception and reasoning](https://mlsanity.com/paper/2109.13662/) (2021)
- [Weakly Supervised Knowledge Transfer with Probabilistic Logical Reasoning for Object Detection](https://mlsanity.com/paper/2303.05148/) (2023)
- [On the use of neurosymbolic AI for defending against cyber attacks](https://mlsanity.com/paper/2408.04996/) (2024)

## Abstract (arXiv)

Recent advances in neural symbolic learning, such as DeepProbLog, extend probabilistic logic programs with neural predicates. Like graphical models, these probabilistic logic programs define a probability distribution over possible worlds, for which inference is computationally hard. We propose DeepStochLog, an alternative neural symbolic framework based on stochastic definite clause grammars, a type of stochastic logic program, which defines a probability distribution over possible derivations. More specifically, we introduce neural grammar rules into stochastic definite clause grammars to create a framework that can be trained end-to-end. We show that inference and learning in neural stochastic logic programming scale much better than for neural probabilistic logic programs. Furthermore, the experimental evaluation shows that DeepStochLog achieves state-of-the-art results on challenging neural symbolic learning tasks.