Scalable neuro-symbolic reasoning and learning
File(s)
Author(s)
Aspis, Yaniv
Type
Thesis
Abstract
Neuro-Symbolic AI bridges the gap between highly performant connectionist learning methods and the formal reasoning capabilities of symbolic methods. While neural networks can learn tasks with minimal engineering, their black-box nature prevents their inference from being examined, disallowing application in mission-critical settings. Symbolic systems provide interpretable inference with guarantees, but cannot be applied directly to fuzzy data and require some manual engineering. The complementary nature of the approaches motivates developing hybrid systems.
Bridging the continuous nature of neural networks and the discrete nature of symbolic AI is challenging. Approaches generally come in two flavours: either logical operations are approximated using continuous operations, or a loss function is computed using a symbolic solver. The former is more scalable but comes at the expense of exact inference, and offers limited representation capabilities and transferability. The latter gives the full power of a symbolic solver, but lacks scalability. In this work, we address how to bring about inference with guarantees in neuro-symbolic AI while maintaining scalability. We consider both neuro-symbolic reasoning: performing logical deduction from facts observed by neural networks; and neuro-symbolic learning: inducing rules from such observed data.
We begin by introducing a method for embedding a given normal logic program in continuous space using real matrices, allowing differentiable logical deduction while maintaining exact inference. We then show how this matrix representation enables end-to-end training of perception networks for neuro-symbolic reasoning tasks, and study the advantages and limitations of this approach. Building on these observations, we develop a novel approach to neuro-symbolic reasoning and learning, by combining end-to-end pretraining of a neural network, clustering of latent space embeddings, and exact symbolic inference and learning. We achieve a perception training speedup of several orders of magnitude over existing methods, even in the presence of limited labelling of latent features.
Bridging the continuous nature of neural networks and the discrete nature of symbolic AI is challenging. Approaches generally come in two flavours: either logical operations are approximated using continuous operations, or a loss function is computed using a symbolic solver. The former is more scalable but comes at the expense of exact inference, and offers limited representation capabilities and transferability. The latter gives the full power of a symbolic solver, but lacks scalability. In this work, we address how to bring about inference with guarantees in neuro-symbolic AI while maintaining scalability. We consider both neuro-symbolic reasoning: performing logical deduction from facts observed by neural networks; and neuro-symbolic learning: inducing rules from such observed data.
We begin by introducing a method for embedding a given normal logic program in continuous space using real matrices, allowing differentiable logical deduction while maintaining exact inference. We then show how this matrix representation enables end-to-end training of perception networks for neuro-symbolic reasoning tasks, and study the advantages and limitations of this approach. Building on these observations, we develop a novel approach to neuro-symbolic reasoning and learning, by combining end-to-end pretraining of a neural network, clustering of latent space embeddings, and exact symbolic inference and learning. We achieve a perception training speedup of several orders of magnitude over existing methods, even in the presence of limited labelling of latent features.
Version
Open Access
Date Issued
2025-09-01
Date Awarded
2026-06-01
Copyright Statement
Attribution-NonCommercial-ShareAlike 4.0 International Licence (CC BY NC-SA)
Advisor
Russo, Alessandra
Broda, Krysia
Lobo, Jorge
Publisher Department
Department of Computing
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)