# Deep Symbolic Learning: Discovering Symbols and Rules from Perceptions

arXiv: https://arxiv.org/abs/2208.11561 · HTML: https://mlsanity.com/paper/2208.11561/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 14 of its 32 references that are in the map.
- First posted on arXiv 24 Aug 2022.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

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

- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [Failures of Gradient-Based Deep Learning](https://mlsanity.com/paper/1703.07950/) (2017)
- [DeepStochLog: Neural Stochastic Logic Programming](https://mlsanity.com/paper/2106.12574/) (2021)
- [Neural-Symbolic Integration: A Compositional Perspective](https://mlsanity.com/paper/2010.11926/) (2020)
- [Abductive Knowledge Induction From Raw Data](https://mlsanity.com/paper/2010.03514/) (2020)
- [Adaptivity without Compromise: A Momentumized, Adaptive, Dual Averaged Gradient Method for Stochastic Optimization](https://mlsanity.com/paper/2101.11075/) (2021)
- [Techniques for Symbol Grounding with SATNet](https://mlsanity.com/paper/2106.11072/) (2021)

## Built on by (most cited first, 21 of 21)

- [Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcuts](https://mlsanity.com/paper/2305.19951/) (2023)
- [Generative learning for nonlinear dynamics](https://mlsanity.com/paper/2311.04128/) (2023)
- [A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcuts](https://mlsanity.com/paper/2406.10368/) (2024)
- [Interpretable Concept-Based Memory Reasoning](https://mlsanity.com/paper/2407.15527/) (2024)
- [Shortcuts and Identifiability in Concept-based Models from a Neuro-Symbolic Lens](https://mlsanity.com/paper/2502.11245/) (2025)
- [The Role of Foundation Models in Neuro-Symbolic Learning and Reasoning](https://mlsanity.com/paper/2402.01889/) (2024)
- [Neuro-Symbolic AI: Explainability, Challenges, and Future Trends](https://mlsanity.com/paper/2411.04383/) (2024)
- [ProtoArgNet: Interpretable Image Classification with Super-Prototypes and Argumentation [Technical Report]](https://mlsanity.com/paper/2311.15438/) (2023)
- [On the use of neurosymbolic AI for defending against cyber attacks](https://mlsanity.com/paper/2408.04996/) (2024)
- [Interpretable Hierarchical Concept Reasoning through Attention-Guided Graph Learning](https://mlsanity.com/paper/2506.21102/) (2025)
- [Simple and Effective Transfer Learning for Neuro-Symbolic Integration](https://mlsanity.com/paper/2402.14047/) (2024)
- [CiteFusion: An Ensemble Framework for Citation Intent Classification Harnessing Dual-Model Binary Couples and SHAP Analyses](https://mlsanity.com/paper/2407.13329/) (2024)
- [Gradient-Based Optimization on G"odel Logic as Discrete Local Search](https://mlsanity.com/paper/2503.01817/) (2025)
- [Logic of Hypotheses: from Zero to Full Knowledge in Neurosymbolic Integration](https://mlsanity.com/paper/2509.21663/) (2025)
- [Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Models](https://mlsanity.com/paper/2605.18202/) (2026)
- [Concept Modulation Models: A Unified Framework for Identifiability and Extrapolation](https://mlsanity.com/paper/2606.18509/) (2026)
- [Aligning Knowledge Graphs Provided by Humans and Generated from Neural Networks in Specific Tasks](https://mlsanity.com/paper/2404.16884/) (2024)
- [Bridging the Gap: Representation Spaces in Neuro-Symbolic AI](https://mlsanity.com/paper/2411.04393/) (2024)
- [Neural-Symbolic Integration with Evolvable Policies](https://mlsanity.com/paper/2601.04799/) (2026)
- [Deep Arguing](https://mlsanity.com/paper/2605.10569/) (2026)
- [Neurosymbolic Learning of Interpretable World Models](https://mlsanity.com/paper/2610.19955/) (2026)

## Abstract (arXiv)

Neuro-Symbolic (NeSy) integration combines symbolic reasoning with Neural Networks (NNs) for tasks requiring perception and reasoning. Most NeSy systems rely on continuous relaxation of logical knowledge, and no discrete decisions are made within the model pipeline. Furthermore, these methods assume that the symbolic rules are given. In this paper, we propose Deep Symbolic Learning (DSL), a NeSy system that learns NeSy-functions, i.e., the composition of a (set of) perception functions which map continuous data to discrete symbols, and a symbolic function over the set of symbols. DSL learns simultaneously the perception and symbolic functions while being trained only on their composition (NeSy-function). The key novelty of DSL is that it can create internal (interpretable) symbolic representations and map them to perception inputs within a differentiable NN learning pipeline. The created symbols are automatically selected to generate symbolic functions that best explain the data. We provide experimental analysis to substantiate the efficacy of DSL in simultaneously learning perception and symbolic functions.