Symbolic discovery in continuous space with end-to-end differentiability
File(s)
Author(s)
Gu, Kexin
Type
Thesis or dissertation
Abstract
Neural networks achieve remarkable success across domains, yet their black-box nature poses challenges in safety-critical applications. Neuro-symbolic approaches address this by integrating symbolic inference with deep learning to enhance interpretability. Many works follow the principle of differentiable inductive logical programming, but typically require prior knowledge to define or restrict the search space, thus limiting expressivity and applicability. The neural Disjunctive Normal Form (DNF) model stands out as a fully end-to-end differentiable model that provides integration with neural components for predicate invention from raw data and logical interpretation via post-training rule extraction. Yet, its effectiveness is only demonstrated in synthetic binary classification tasks. This thesis proposes a family of neural DNF-based models that perform fully differentiable rule learning across classification and reinforcement learning (RL) tasks. These models retain the interpretability of the original and are shown to be amenable to behaviour modification via weight editing.
This thesis presents four main contributions. Firstly, it formalises the behaviour and interpretation of neural DNF-based models, establishing a bidirectional translation with truth-value equivalence guaranteed between neural and bivalent logic forms at post-training, supporting model interpretation and intervention.
Secondly and thirdly, the thesis explores the application of neural DNF-based models in classification and actor-critic RL settings, which impose different behavioural constraints: classification requires logically deterministic predictions and mutual exclusivity for multi-class problems, while RL actors should output probabilistic mutually exclusive action distributions. In both setups, the models perform on par with competing methods while providing compact, interpretable, and intervenable logical forms.
Finally, the thesis investigates performance degradation when translating trained neural DNF-based models into logical forms. It identifies a knowledge entanglement problem encoded in models' weights, and proposes a disentanglement solution that splits nodes encoding nested rules into smaller, independent ones. Experiments show that this method better preserves models' representation, achieving performance closer to pre-translation levels.
This thesis presents four main contributions. Firstly, it formalises the behaviour and interpretation of neural DNF-based models, establishing a bidirectional translation with truth-value equivalence guaranteed between neural and bivalent logic forms at post-training, supporting model interpretation and intervention.
Secondly and thirdly, the thesis explores the application of neural DNF-based models in classification and actor-critic RL settings, which impose different behavioural constraints: classification requires logically deterministic predictions and mutual exclusivity for multi-class problems, while RL actors should output probabilistic mutually exclusive action distributions. In both setups, the models perform on par with competing methods while providing compact, interpretable, and intervenable logical forms.
Finally, the thesis investigates performance degradation when translating trained neural DNF-based models into logical forms. It identifies a knowledge entanglement problem encoded in models' weights, and proposes a disentanglement solution that splits nodes encoding nested rules into smaller, independent ones. Experiments show that this method better preserves models' representation, achieving performance closer to pre-translation levels.
Version
Open Access
Date Issued
2026-01-05
Date Awarded
2026-09-01
Copyright Statement
Attribution-NonCommercial-ShareAlike 4.0 International Licence (CC BY NC-SA)
Advisor
Russo, Alessandra
Dickens, Luke
Publisher Department
Department of Computing
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)