# Embedding Symbolic Knowledge into Deep Networks

arXiv: https://arxiv.org/abs/1909.01161 · HTML: https://mlsanity.com/paper/1909.01161/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2019.

## Built on by (most cited first, 30 of 49)

- [Hallucination is Inevitable: An Innate Limitation of Large Language Models](https://mlsanity.com/paper/2401.11817/) (2024)
- [InternVLA-M1: A Spatially Guided Vision-Language-Action Framework for Generalist Robot Policy](https://mlsanity.com/paper/2510.13778/) (2025)
- [Incorporating Domain Knowledge into Deep Neural Networks](https://mlsanity.com/paper/2103.00180/) (2021)
- [Neuro-Symbolic Artificial Intelligence: Current Trends](https://mlsanity.com/paper/2105.05330/) (2021)
- [Deep Learning with Logical Constraints](https://mlsanity.com/paper/2205.00523/) (2022)
- [A Survey on Neural-symbolic Learning Systems](https://mlsanity.com/paper/2111.08164/) (2021)
- [Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computing](https://mlsanity.com/paper/2210.15889/) (2022)
- [Neural-Logic Human-Object Interaction Detection](https://mlsanity.com/paper/2311.09817/) (2023)
- [Relation-aware Compositional Zero-shot Learning for Attribute-Object Pair Recognition](https://mlsanity.com/paper/2108.04603/) (2021)
- [A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcuts](https://mlsanity.com/paper/2406.10368/) (2024)
- [LOGICSEG: Parsing Visual Semantics with Neural Logic Learning and Reasoning](https://mlsanity.com/paper/2309.13556/) (2023)
- [Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomy](https://mlsanity.com/paper/2406.16087/) (2024)
- [Embedding Symbolic Temporal Knowledge into Deep Sequential Models](https://mlsanity.com/paper/2101.11981/) (2021)
- [CARE: Certifiably Robust Learning with Reasoning via Variational Inference](https://mlsanity.com/paper/2209.05055/) (2022)
- [Knowledge-augmented Deep Learning and Its Applications: A Survey](https://mlsanity.com/paper/2212.00017/) (2022)
- [Weakly Supervised Anomaly Detection via Knowledge-Data Alignment](https://mlsanity.com/paper/2402.03785/) (2024)
- [Learning with Logical Constraints but without Shortcut Satisfaction](https://mlsanity.com/paper/2403.00329/) (2024)
- [Tractable Boolean and Arithmetic Circuits](https://mlsanity.com/paper/2202.02942/) (2022)
- [ST4VLA: Spatially Guided Training for Vision-Language-Action Models](https://mlsanity.com/paper/2602.10109/) (2026)
- [AI Descartes: Combining Data and Theory for Derivable Scientific Discovery](https://mlsanity.com/paper/2109.01634/) (2021)
- [Sample-Efficient Learning of Novel Visual Concepts](https://mlsanity.com/paper/2306.09482/) (2023)
- [Naturally Supervised 3D Visual Grounding with Language-Regularized Concept Learners](https://mlsanity.com/paper/2404.19696/) (2024)
- [LogiCity: Advancing Neuro-Symbolic AI with Abstract Urban Simulation](https://mlsanity.com/paper/2411.00773/) (2024)
- [A Critical Review of Inductive Logic Programming Techniques for Explainable AI](https://mlsanity.com/paper/2112.15319/) (2021)
- [Neuro-Symbolic Learning: Principles and Applications in Ophthalmology](https://mlsanity.com/paper/2208.00374/) (2022)
- [Symbolic Knowledge Extraction and Injection with Sub-symbolic Predictors: A Systematic Literature Review](https://mlsanity.com/paper/2501.14836/) (2025)
- [The Need for Verification in AI-Driven Scientific Discovery](https://mlsanity.com/paper/2509.01398/) (2025)
- [Inclusion of Domain-Knowledge into GNNs using Mode-Directed Inverse Entailment](https://mlsanity.com/paper/2105.10709/) (2021)
- [Logical Reasoning for Task Oriented Dialogue Systems](https://mlsanity.com/paper/2202.04161/) (2022)
- [Neuro-Symbolic VQA: A review from the perspective of AGI desiderata](https://mlsanity.com/paper/2104.06365/) (2021)

## Abstract (arXiv)

In this work, we aim to leverage prior symbolic knowledge to improve the performance of deep models. We propose a graph embedding network that projects propositional formulae (and assignments) onto a manifold via an augmented Graph Convolutional Network (GCN). To generate semantically-faithful embeddings, we develop techniques to recognize node heterogeneity, and semantic regularization that incorporate structural constraints into the embedding. Experiments show that our approach improves the performance of models trained to perform entailment checking and visual relation prediction. Interestingly, we observe a connection between the tractability of the propositional theory representation and the ease of embedding. Future exploration of this connection may elucidate the relationship between knowledge compilation and vector representation learning.