7 papers
What are the Right Symmetries for Formal Theorem Proving?
Krzysztof Olejniczak, Radoslav Dimitrov, Xingyue Huang +3
Formal theorem provers based on large language models (LLMs) are highly sensitive to superficial variations in problem representation: semantically equivalent statements can exhibi…
Sufficient Conditions for Stability of Minimum-Norm Interpolating Deep ReLU Networks
Ouns El Harzli, Yoonsoo Nam, Ilja Kuzborskij +2
Algorithmic stability is a classical framework for analyzing the generalization error of learning algorithms. It predicts that an algorithm has small generalization error if it is…
From Neural Networks to Logical Theories: The Correspondence between Fibring Modal Logics and Fibring Neural Networks
Ouns El Harzli, Bernardo Cuenca Grau, Artur d'Avila Garcez +2
Fibring of modal logics is a well-established formalism for combining countable families of modal logics into a single fibred language with common semantics, characterized by fibre…
Logical Expressivity and Explanations for Monotonic GNNs with Scoring Functions
Matthew Morris, David J. Tena Cucala, Bernardo Cuenca Grau
Graph neural networks (GNNs) are often used for the task of link prediction: predicting missing binary facts in knowledge graphs (KGs). To address the lack of explainability of GNN…
The Correspondence Between Bounded Graph Neural Networks and Fragments of First-Order Logic
Bernardo Cuenca Grau, Eva Feng, Przemysław Andrzej Wałęga
Graph Neural Networks (GNNs) address two key challenges in applying deep learning to graph-structured data: they handle varying size input graphs and ensure invariance under graph…
Relational Graph Convolutional Networks Do Not Learn Sound Rules
Matthew Morris, David J. Tena Cucala, Bernardo Cuenca Grau +1
Graph neural networks (GNNs) are frequently used to predict missing facts in knowledge graphs (KGs). Motivated by the lack of explainability for the outputs of these models, recent…
Double-descent curves in neural networks: a new perspective using Gaussian processes
Ouns El Harzli, Bernardo Cuenca Grau, Guillermo Valle-Pérez +1
Double-descent curves in neural networks describe the phenomenon that the generalisation error initially descends with increasing parameters, then grows after reaching an optimal n…