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Neuro-Symbolic Learning of Answer Set Programs from Raw Data

Daniel Cunnington, Mark Law, Jorge Lobo, Alessandra Russo

TL;DR

This work tackles the challenge of learning from raw data with interpretable symbolic reasoning by proposing NSIL, a framework that jointly learns a neural perception module and an expressive ASP-based knowledge base mapping latent concepts to labels. It introduces corrective examples with weighted biases to balance exploration and exploitation in the symbolic search, and integrates NeurASP-based semantic loss to train the neural component. Across three domains, NSIL achieves state-of-the-art accuracy and data efficiency, learning expressive rules that solve NP-complete problems and enabling generation of all valid answer sets. The approach advances interpretability and practical applicability of neuro-symbolic learning for complex decision tasks, with potential extensions to multi-concept reasoning and unsupervised learning.

Abstract

One of the ultimate goals of Artificial Intelligence is to assist humans in complex decision making. A promising direction for achieving this goal is Neuro-Symbolic AI, which aims to combine the interpretability of symbolic techniques with the ability of deep learning to learn from raw data. However, most current approaches require manually engineered symbolic knowledge, and where end-to-end training is considered, such approaches are either restricted to learning definite programs, or are restricted to training binary neural networks. In this paper, we introduce Neuro-Symbolic Inductive Learner (NSIL), an approach that trains a general neural network to extract latent concepts from raw data, whilst learning symbolic knowledge that maps latent concepts to target labels. The novelty of our approach is a method for biasing the learning of symbolic knowledge, based on the in-training performance of both neural and symbolic components. We evaluate NSIL on three problem domains of different complexity, including an NP-complete problem. Our results demonstrate that NSIL learns expressive knowledge, solves computationally complex problems, and achieves state-of-the-art performance in terms of accuracy and data efficiency. Code and technical appendix: https://github.com/DanCunnington/NSIL

Neuro-Symbolic Learning of Answer Set Programs from Raw Data

TL;DR

This work tackles the challenge of learning from raw data with interpretable symbolic reasoning by proposing NSIL, a framework that jointly learns a neural perception module and an expressive ASP-based knowledge base mapping latent concepts to labels. It introduces corrective examples with weighted biases to balance exploration and exploitation in the symbolic search, and integrates NeurASP-based semantic loss to train the neural component. Across three domains, NSIL achieves state-of-the-art accuracy and data efficiency, learning expressive rules that solve NP-complete problems and enabling generation of all valid answer sets. The approach advances interpretability and practical applicability of neuro-symbolic learning for complex decision tasks, with potential extensions to multi-concept reasoning and unsupervised learning.

Abstract

One of the ultimate goals of Artificial Intelligence is to assist humans in complex decision making. A promising direction for achieving this goal is Neuro-Symbolic AI, which aims to combine the interpretability of symbolic techniques with the ability of deep learning to learn from raw data. However, most current approaches require manually engineered symbolic knowledge, and where end-to-end training is considered, such approaches are either restricted to learning definite programs, or are restricted to training binary neural networks. In this paper, we introduce Neuro-Symbolic Inductive Learner (NSIL), an approach that trains a general neural network to extract latent concepts from raw data, whilst learning symbolic knowledge that maps latent concepts to target labels. The novelty of our approach is a method for biasing the learning of symbolic knowledge, based on the in-training performance of both neural and symbolic components. We evaluate NSIL on three problem domains of different complexity, including an NP-complete problem. Our results demonstrate that NSIL learns expressive knowledge, solves computationally complex problems, and achieves state-of-the-art performance in terms of accuracy and data efficiency. Code and technical appendix: https://github.com/DanCunnington/NSIL
Paper Structure (20 sections, 9 equations, 9 figures, 5 tables)

This paper contains 20 sections, 9 equations, 9 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Neuro-Symbolic Inductive Learner
  4. Problem Setting
  5. Neural and Symbolic Components
  6. Corrective Examples
  7. Experiments
  8. Cumulative Arithmetic
  9. Two-Digit Arithmetic
  10. Hitting Set Problem
  11. Ablations
  12. Conclusion
  13. Appendix
  14. Experiment Setup
  15. Relying on neural network confidence for corrective example weights
  16. ...and 5 more sections

Figures (9)

  • Figure 1: (a) nsl learning with a single data point $\langle X,y \rangle \in D$. (b) nsl inference over a single input $X$.
  • Figure 2: Cumulative Arithmetic network accuracy.
  • Figure 3: Two-Digit Arithmetic results with reduced training sets.
  • Figure 4: Hitting Set accuracy.
  • Figure 5: nsl learned knowledge.
  • ...and 4 more figures

Theorems & Definitions (5)

  • Example 1
  • Example 2
  • Example 3
  • Example 4
  • Example 5