# An energy-based model for neuro-symbolic reasoning on knowledge graphs

arXiv: https://arxiv.org/abs/2110.01639 · HTML: https://mlsanity.com/paper/2110.01639/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 30 references that are in the map.
- First posted on arXiv 4 Oct 2021.

## Builds on (most cited first, 11 of 11)

- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [A Review of Relational Machine Learning for Knowledge Graphs](https://mlsanity.com/paper/1503.00759/) (2015)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Graph Representations for Higher-Order Logic and Theorem Proving](https://mlsanity.com/paper/1905.10006/) (2019)
- [Hardware Implementation of Deep Network Accelerators Towards Healthcare and Biomedical Applications](https://mlsanity.com/paper/2007.05657/) (2020)
- [Large-Scale Neuromorphic Spiking Array Processors: A quest to mimic the brain](https://mlsanity.com/paper/1805.08932/) (2018)
- [Versatile emulation of spiking neural networks on an accelerated neuromorphic substrate](https://mlsanity.com/paper/1912.12980/) (2019)
- [Event-Driven Contrastive Divergence for Spiking Neuromorphic Systems](https://mlsanity.com/paper/1311.0966/) (2013)
- [SpikE: spike-based embeddings for multi-relational graph data](https://mlsanity.com/paper/2104.13398/) (2021)
- [Machine learning on knowledge graphs for context-aware security monitoring](https://mlsanity.com/paper/2105.08741/) (2021)

## Built on by (most cited first, 4 of 4)

- [R2-Guard: Robust Reasoning Enabled LLM Guardrail via Knowledge-Enhanced Logical Reasoning](https://mlsanity.com/paper/2407.05557/) (2024)
- [Neuro-Symbolic AI in 2024: A Systematic Review](https://mlsanity.com/paper/2501.05435/) (2025)
- [Relational representation learning with spike trains](https://mlsanity.com/paper/2205.09140/) (2022)
- [Detection, Explanation and Filtering of Cyber Attacks Combining Symbolic and Sub-Symbolic Methods](https://mlsanity.com/paper/2212.13991/) (2022)

## Abstract (arXiv)

Machine learning on graph-structured data has recently become a major topic in industry and research, finding many exciting applications such as recommender systems and automated theorem proving. We propose an energy-based graph embedding algorithm to characterize industrial automation systems, integrating knowledge from different domains like industrial automation, communications and cybersecurity. By combining knowledge from multiple domains, the learned model is capable of making context-aware predictions regarding novel system events and can be used to evaluate the severity of anomalies that might be indicative of, e.g., cybersecurity breaches. The presented model is mappable to a biologically-inspired neural architecture, serving as a first bridge between graph embedding methods and neuromorphic computing - uncovering a promising edge application for this upcoming technology.