# A Survey on Neural-symbolic Learning Systems

arXiv: https://arxiv.org/abs/2111.08164 · HTML: https://mlsanity.com/paper/2111.08164/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 70 of its 152 references that are in the map.
- First posted on arXiv 10 Nov 2021.

## Builds on (most cited first, 30 of 70)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Generalizing from a Few Examples: A Survey on Few-Shot Learning](https://mlsanity.com/paper/1904.05046/) (2019)
- [COMET: Commonsense Transformers for Automatic Knowledge Graph Construction](https://mlsanity.com/paper/1906.05317/) (2019)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Neural Module Networks](https://mlsanity.com/paper/1511.02799/) (2015)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [Multi-Task Identification of Entities, Relations, and Coreference for Scientific Knowledge Graph Construction](https://mlsanity.com/paper/1808.09602/) (2018)
- [Neural-Symbolic VQA: Disentangling Reasoning from Vision and Language Understanding](https://mlsanity.com/paper/1810.02338/) (2018)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning](https://mlsanity.com/paper/1707.06690/) (2017)
- [Neurosymbolic AI: The 3rd Wave](https://mlsanity.com/paper/2012.05876/) (2020)
- [Inductive Relation Prediction by Subgraph Reasoning](https://mlsanity.com/paper/1911.06962/) (2019)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systems](https://mlsanity.com/paper/1903.12394/) (2019)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [The Next Decade in AI: Four Steps Towards Robust Artificial Intelligence](https://mlsanity.com/paper/2002.06177/) (2020)
- [Compositional Attention Networks for Machine Reasoning](https://mlsanity.com/paper/1803.03067/) (2018)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Zero-shot Recognition via Semantic Embeddings and Knowledge Graphs](https://mlsanity.com/paper/1803.08035/) (2018)
- [Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning](https://mlsanity.com/paper/1905.06088/) (2019)
- [Harnessing Deep Neural Networks with Logic Rules](https://mlsanity.com/paper/1603.06318/) (2016)
- [Learning by Abstraction: The Neural State Machine](https://mlsanity.com/paper/1907.03950/) (2019)

## Built on by (most cited first, 30 of 39)

- [Distilling System 2 into System 1](https://mlsanity.com/paper/2407.06023/) (2024)
- [T2VPhysBench: A First-Principles Benchmark for Physical Consistency in Text-to-Video Generation](https://mlsanity.com/paper/2505.00337/) (2025)
- [Neuro-Symbolic AI in 2024: A Systematic Review](https://mlsanity.com/paper/2501.05435/) (2025)
- [Explain Before You Answer: A Survey on Compositional Visual Reasoning](https://mlsanity.com/paper/2508.17298/) (2025)
- [SymbolicAI: A framework for logic-based approaches combining generative models and solvers](https://mlsanity.com/paper/2402.00854/) (2024)
- [A Survey on Verification and Validation, Testing and Evaluations of Neurosymbolic Artificial Intelligence](https://mlsanity.com/paper/2401.03188/) (2024)
- [Weakly Supervised Anomaly Detection via Knowledge-Data Alignment](https://mlsanity.com/paper/2402.03785/) (2024)
- [From Frege to chatGPT: Compositionality in language, cognition, and deep neural networks](https://mlsanity.com/paper/2405.15164/) (2024)
- [Neural-Symbolic VideoQA: Learning Compositional Spatio-Temporal Reasoning for Real-world Video Question Answering](https://mlsanity.com/paper/2404.04007/) (2024)
- [Neurosymbolic Graph Enrichment for Grounded World Models](https://mlsanity.com/paper/2411.12671/) (2024)
- [Position: Foundation Models for Tabular Data within Systemic Contexts Need Grounding](https://mlsanity.com/paper/2505.19825/) (2025)
- [Augmenting deep neural networks with symbolic knowledge: Towards trustworthy and interpretable AI for education](https://mlsanity.com/paper/2311.00393/) (2023)
- [Take A Step Back: Rethinking the Two Stages in Visual Reasoning](https://mlsanity.com/paper/2407.19666/) (2024)
- [A Smooth Transition Between Induction and Deduction: Fast Abductive Learning Based on Probabilistic Symbol Perception](https://mlsanity.com/paper/2502.12919/) (2025)
- [Nature's Insight: A Novel Framework and Comprehensive Analysis of Agentic Reasoning Through the Lens of Neuroscience](https://mlsanity.com/paper/2505.05515/) (2025)
- [SatelliteFormula: Multi-Modal Symbolic Regression from Remote Sensing Imagery for Physics Discovery](https://mlsanity.com/paper/2506.06176/) (2025)
- [Egocentric Co-Pilot: Web-Native Smart-Glasses Agents for Assistive Egocentric AI](https://mlsanity.com/paper/2603.01104/) (2026)
- [Multi-Excitation Projective Simulation with a Many-Body Physics Inspired Inductive Bias](https://mlsanity.com/paper/2402.10192/) (2024)
- [A Synergistic Approach In Network Intrusion Detection By Neurosymbolic AI](https://mlsanity.com/paper/2406.00938/) (2024)
- [CiteFusion: An Ensemble Framework for Citation Intent Classification Harnessing Dual-Model Binary Couples and SHAP Analyses](https://mlsanity.com/paper/2407.13329/) (2024)
- [From Understanding the World to Intervening in It: A Unified Multi-Scale Framework for Embodied Cognition](https://mlsanity.com/paper/2503.00727/) (2025)
- [Enhancing Symbolic Machine Learning by Subsymbolic Representations](https://mlsanity.com/paper/2506.14569/) (2025)
- [A Neuro-Symbolic Approach for Probabilistic Reasoning on Graph Data](https://mlsanity.com/paper/2507.21873/) (2025)
- [Quantitative Estimation of Target Task Performance from Unsupervised Pretext Task in Semi/Self-Supervised Learning](https://mlsanity.com/paper/2508.07299/) (2025)
- [Neural Logic Networks for Interpretable Classification](https://mlsanity.com/paper/2508.08172/) (2025)
- [Towards Commonsense Knowledge based Fuzzy Systems for Supporting Size-Related Fine-Grained Object Detection](https://mlsanity.com/paper/2303.09026/) (2023)
- [Synergizing Machine Learning & Symbolic Methods: A Survey on Hybrid Approaches to Natural Language Processing](https://mlsanity.com/paper/2401.11972/) (2024)
- [A Survey on the Integration of Generative AI for Critical Thinking in Mobile Networks](https://mlsanity.com/paper/2404.06946/) (2024)
- [Context-aware knowledge graph framework for traffic speed forecasting using graph neural network](https://mlsanity.com/paper/2407.17703/) (2024)
- [Verification Learning: Make Unsupervised Neuro-Symbolic System Feasible](https://mlsanity.com/paper/2503.12917/) (2025)

## Abstract (arXiv)

In recent years, neural systems have demonstrated highly effective learning ability and superior perception intelligence. However, they have been found to lack effective reasoning and cognitive ability. On the other hand, symbolic systems exhibit exceptional cognitive intelligence but suffer from poor learning capabilities when compared to neural systems. Recognizing the advantages and disadvantages of both methodologies, an ideal solution emerges: combining neural systems and symbolic systems to create neural-symbolic learning systems that possess powerful perception and cognition. The purpose of this paper is to survey the advancements in neural-symbolic learning systems from four distinct perspectives: challenges, methods, applications, and future directions. By doing so, this research aims to propel this emerging field forward, offering researchers a comprehensive and holistic overview. This overview will not only highlight the current state-of-the-art but also identify promising avenues for future research.