# Neural-Symbolic Integration with Evolvable Policies

arXiv: https://arxiv.org/abs/2601.04799 · HTML: https://mlsanity.com/paper/2601.04799/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 49 references that are in the map.
- First posted on arXiv 8 Jan 2026.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Using Centroidal Voronoi Tessellations to Scale Up the Multi-dimensional Archive of Phenotypic Elites Algorithm](https://mlsanity.com/paper/1610.05729/) (2016)
- [From Statistical Relational to Neuro-Symbolic Artificial Intelligence](https://mlsanity.com/paper/2003.08316/) (2020)
- [Quality-Diversity Optimization: a novel branch of stochastic optimization](https://mlsanity.com/paper/2012.04322/) (2020)
- [Neural-Symbolic Integration: A Compositional Perspective](https://mlsanity.com/paper/2010.11926/) (2020)
- [Abductive Knowledge Induction From Raw Data](https://mlsanity.com/paper/2010.03514/) (2020)
- [Differentiable Programs with Neural Libraries](https://mlsanity.com/paper/1611.02109/) (2016)
- [EXplainable Neural-Symbolic Learning (X-NeSyL) methodology to fuse deep learning representations with expert knowledge graphs: the MonuMAI cultural heritage use case](https://mlsanity.com/paper/2104.11914/) (2021)
- [ChatABL: Abductive Learning via Natural Language Interaction with ChatGPT](https://mlsanity.com/paper/2304.11107/) (2023)
- [On the price of explainability for some clustering problems](https://mlsanity.com/paper/2101.01576/) (2021)
- [Deep Symbolic Learning: Discovering Symbols and Rules from Perceptions](https://mlsanity.com/paper/2208.11561/) (2022)
- [Neuro-Symbolic Learning of Answer Set Programs from Raw Data](https://mlsanity.com/paper/2205.12735/) (2022)
- [The Price of Interpretability](https://mlsanity.com/paper/1907.03419/) (2019)

## Abstract (arXiv)

Neural-Symbolic (NeSy) Artificial Intelligence has emerged as a promising approach for combining the learning capabilities of neural networks with the interpretable reasoning of symbolic systems. However, existing NeSy frameworks typically require either predefined symbolic policies or policies that are differentiable, limiting their applicability when domain expertise is unavailable or when policies are inherently non-differentiable. We propose a framework that addresses this limitation by enabling the concurrent learning of both non-differentiable symbolic policies and neural network weights through an evolutionary process. Our approach casts NeSy systems as organisms in a population that evolve through mutations (both symbolic rule additions and neural weight changes), with fitness-based selection guiding convergence toward hidden target policies. The framework extends the NEUROLOG architecture to make symbolic policies trainable, adapts Valiant's Evolvability framework to the NeSy context, and employs Machine Coaching semantics for mutable symbolic representations. Neural networks are trained through abductive reasoning from the symbolic component, eliminating differentiability requirements. Through extensive experimentation, we demonstrate that NeSy systems starting with empty policies and random neural weights can successfully approximate hidden non-differentiable target policies, achieving median correct performance approaching 100%. This work represents a step toward enabling NeSy research in domains where the acquisition of symbolic knowledge from experts is challenging or infeasible.