# Neural Markov Logic Networks

arXiv: https://arxiv.org/abs/1905.13462 · HTML: https://mlsanity.com/paper/1905.13462/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2019.

## Built on by (most cited first, 27 of 27)

- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [A Survey on Neural-symbolic Learning Systems](https://mlsanity.com/paper/2111.08164/) (2021)
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- [Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computing](https://mlsanity.com/paper/2210.15889/) (2022)
- [Interpretability is in the Mind of the Beholder: A Causal Framework for Human-interpretable Representation Learning](https://mlsanity.com/paper/2309.07742/) (2023)
- [Neurosymbolic AI for Reasoning over Knowledge Graphs: A Survey](https://mlsanity.com/paper/2302.07200/) (2023)
- [A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcuts](https://mlsanity.com/paper/2406.10368/) (2024)
- [Neuro-Symbolic AI: Explainability, Challenges, and Future Trends](https://mlsanity.com/paper/2411.04383/) (2024)
- [ULLER: A Unified Language for Learning and Reasoning](https://mlsanity.com/paper/2405.00532/) (2024)
- [Logical Entity Representation in Knowledge-Graphs for Differentiable Rule Learning](https://mlsanity.com/paper/2305.12738/) (2023)
- [Defining neurosymbolic AI](https://mlsanity.com/paper/2507.11127/) (2025)
- [Systematic Relational Reasoning With Epistemic Graph Neural Networks](https://mlsanity.com/paper/2407.17396/) (2024)
- [Online inductive learning from answer sets for efficient reinforcement learning exploration](https://mlsanity.com/paper/2501.07445/) (2025)
- [Right for the Right Reasons: Avoiding Reasoning Shortcuts via Prototypical Neurosymbolic AI](https://mlsanity.com/paper/2510.25497/) (2025)
- [A Neuro-Symbolic Approach for Probabilistic Reasoning on Graph Data](https://mlsanity.com/paper/2507.21873/) (2025)
- [Logical GANs: Adversarial Learning through Ehrenfeucht Fraisse Games](https://mlsanity.com/paper/2510.22824/) (2025)
- [Current and Future Challenges in Knowledge Representation and Reasoning](https://mlsanity.com/paper/2308.04161/) (2023)
- [A Novel Neural-symbolic System under Statistical Relational Learning](https://mlsanity.com/paper/2309.08931/) (2023)
- [Spatial Knowledge-Infused Hierarchical Learning: An Application in Flood Mapping on Earth Imagery](https://mlsanity.com/paper/2312.07767/) (2023)
- [Relational Neural Markov Random Fields](https://mlsanity.com/paper/2110.09647/) (2021)
- [Neurosymbolic Decision Trees](https://mlsanity.com/paper/2503.08762/) (2025)
- [Symbolic Neural Generation with Applications to Lead Discovery in Drug Design](https://mlsanity.com/paper/2510.23379/) (2025)
- [Beyond Prompt Engineering: Neuro-Symbolic-Causal Architecture for Robust Multi-Objective AI Agents](https://mlsanity.com/paper/2510.23682/) (2025)
- [DeepProofLog: Efficient Proving in Deep Stochastic Logic Programs](https://mlsanity.com/paper/2511.08581/) (2025)
- [Lifted Relational Probabilistic Inference via Implicit Learning](https://mlsanity.com/paper/2602.14890/) (2026)
- [EM-NeSy: Expectation Maximization for Neurosymbolic Learning](https://mlsanity.com/paper/2606.14463/) (2026)
- [Parallel Noising in Neural Markov Logic Networks](https://mlsanity.com/paper/2607.19126/) (2026)

## Abstract (arXiv)

We introduce neural Markov logic networks (NMLNs), a statistical relational learning system that borrows ideas from Markov logic. Like Markov logic networks (MLNs), NMLNs are an exponential-family model for modelling distributions over possible worlds, but unlike MLNs, they do not rely on explicitly specified first-order logic rules. Instead, NMLNs learn an implicit representation of such rules as a neural network that acts as a potential function on fragments of the relational structure. Similarly to many neural symbolic methods, NMLNs can exploit embeddings of constants but, unlike them, NMLNs work well also in their absence. This is extremely important for predicting in settings other than the transductive one. We showcase the potential of NMLNs on knowledge-base completion, triple classification and on generation of molecular (graph) data.