# Enhancing Symbolic Machine Learning by Subsymbolic Representations

arXiv: https://arxiv.org/abs/2506.14569 · HTML: https://mlsanity.com/paper/2506.14569/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 25 references that are in the map.
- First posted on arXiv 17 Jun 2025.

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

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [Distilling a Neural Network Into a Soft Decision Tree](https://mlsanity.com/paper/1711.09784/) (2017)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [Measuring a hate speech spectrum with faceted Rasch item response theory and perspective-aware, explainable-by-design deep learning](https://mlsanity.com/paper/2009.10277/) (2020)
- [The Tree Ensemble Layer: Differentiability meets Conditional Computation](https://mlsanity.com/paper/2002.07772/) (2020)
- [A Survey on Neural-symbolic Learning Systems](https://mlsanity.com/paper/2111.08164/) (2021)
- [Neurosymbolic AI and its Taxonomy: a survey](https://mlsanity.com/paper/2305.08876/) (2023)

## Built on by (most cited first, 2 of 2)

- [Weakly Supervised Concept Learning for Object-centric Visual Reasoning](https://mlsanity.com/paper/2605.08201/) (2026)
- [Weakly supervised concept Bottleneck Learning for Robust Two stage Object centric visual reasoning](https://mlsanity.com/paper/2608.22584/) (2026)

## Abstract (arXiv)

The goal of neuro-symbolic AI is to integrate symbolic and subsymbolic AI approaches, to overcome the limitations of either. Prominent systems include Logic Tensor Networks (LTN) or DeepProbLog, which offer neural predicates and end-to-end learning. The versatility of systems like LTNs and DeepProbLog, however, makes them less efficient in simpler settings, for instance, for discriminative machine learning, in particular in domains with many constants. Therefore, we follow a different approach: We propose to enhance symbolic machine learning schemes by giving them access to neural embeddings. In the present paper, we show this for TILDE and embeddings of constants used by TILDE in similarity predicates. The approach can be fine-tuned by further refining the embeddings depending on the symbolic theory. In experiments in three real-world domain, we show that this simple, yet effective, approach outperforms all other baseline methods in terms of the F1 score. The approach could be useful beyond this setting: Enhancing symbolic learners in this way could be extended to similarities between instances (effectively working like kernels within a logical language), for analogical reasoning, or for propositionalization.