Thesis Description & Objectives
Objective: Design, extend, and evaluate prototypical Logic Tensor Networks (LTNs) across diverse tasks and embedding geometries, with a particular focus on hyperbolic and other non-Euclidean representation spaces.
Context: Logic Tensor Networks offer a principled neuro-symbolic framework for integrating first-order logic constraints with learned representations. Recent work has introduced prototypical variants of LTNs, where concepts are grounded through prototype-based representations — drawing inspiration from prototypical networks in few-shot learning. However, existing investigations remain limited in scope: they typically target a narrow set of tasks and rely exclusively on Euclidean embedding spaces. This leaves open several important questions: How do prototypical LTNs behave across tasks with different structural properties (e.g., hierarchical classification, relational reasoning, few-shot learning)? Can hyperbolic embeddings — known to better capture hierarchical and tree-like structure — improve concept grounding and logical consistency in LTNs? How do different embedding geometries interact with the satisfaction of logical axioms and the interpretability of learned prototypes?
Thesis Activities: The goal of this thesis is to systematically extend and evaluate prototypical LTNs along two main axes. Depending on the candidate background and predisposition, the problem can be tackled either from a theoretical or experimental standpoint. Starting from an analysis of the current literature, techniques to be investigated include:
– adapting and testing the framework on a range of tasks beyond those considered in prior work, including hierarchical multi-label classification, relational learning, and low-data regimes; the extension of prototypical learning to other neuro-symbolic frameworks, such as probabilistic circuits or NeuPSL, will also be considered.
– replacing standard Euclidean embedding space will be replaced with alternative geometries — most notably hyperbolic space — and the effects on prototype quality, logical satisfiability, and downstream performance will be studied both empirically and analytically.
The candidate will benchmark these variants against standard LTN baselines and relevant deep learning models, with careful attention to reproducibility, robustness, hyperparameter sensitivity, and the theoretical and/or experimental properties induced by each geometric choice.
