Related papers: Beyond formulas-as-cographs: an extension of Boole…

In this work, we propose a methodology for investigating the use of semantic attention to enhance the explainability of Graph Neural Network (GNN)-based models. Graph Deep Learning (GDL) has emerged as a promising field for tasks like scene…

Graph Neural Networks (GNNs) are a popular approach for predicting graph structured data. As GNNs tightly entangle the input graph into the neural network structure, common explainable AI approaches are not applicable. To a large extent,…

We analyse the power of graph neural networks (GNNs) in terms of Boolean circuit complexity and descriptive complexity. We prove that the graph queries that can be computed by a polynomial-size bounded-depth family of GNNs are exactly those…

Hybridizing machine learning techniques with metaheuristics has attracted significant attention in recent years. Many attempts employ supervised or reinforcement learning to support the decision-making of heuristic methods. However, in some…

Game comonads provide categorical semantics for comparison games in Finite Model Theory, thus providing an abstract characterisation of logical equivalence for a wide range of logics, each one captured through a specific choice of comonad.…

Interpretable Graph Neural Networks (GNNs) aim to reveal the underlying reasoning behind model predictions, attributing their decisions to specific subgraphs that are informative. However, existing subgraph-based interpretable methods…

The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…

We describe a class calculus that is expressive enough to describe and improve its own learning process. It can design and debug programs that satisfy given input/output constraints, based on its ontology of previously learned programs. It…

We develop an algebraic and operational framework for quantum isomorphisms of hypergraphs, using tools from compact quantum group theory. We introduce a new synchronous version of the hypergraph isomorphism game whose game algebra uniformly…

Graph problems are fundamentally challenging for large language models (LLMs). While LLMs excel at processing unstructured text, graph tasks require reasoning over explicit structure, permutation invariance, and computationally complex…

Graph Neural Networks (GNNs) have become a powerful tool for modeling and analyzing data with graph structures. The wide adoption in numerous applications underscores the value of these models. However, the complexity of these methods often…

Pattern recognition with concise and flat AND-rules makes the Tsetlin Machine (TM) both interpretable and efficient, while the power of Tsetlin automata enables accuracy comparable to deep learning on an increasing number of datasets. We…

Graph learning is a prevalent domain that endeavors to learn the intricate relationships among nodes and the topological structure of graphs. Over the years, graph learning has transcended from graph theory to graph data mining. With the…

Question answering (QA) is a core challenge in AI, particularly for complex queries requiring multi-hop reasoning across documents, or symbolic operations like aggregation or exhaustive listing. Retrieval-augmented generation has become the…

Boolean networks can be viewed as functions on the set of binary strings of a given length, described via logical rules. They were introduced as dynamic models into biology, in particular as logical models of intracellular regulatory…

Graphs play an important role in many applications. Recently, Graph Neural Networks (GNNs) have achieved promising results in graph analysis tasks. Some state-of-the-art GNN models have been proposed, e.g., Graph Convolutional Networks…

Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…

A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…

Graph classes of bounded tree rank were introduced recently in the context of the model checking problem for first-order logic of graphs. These graph classes are a common generalization of graph classes of bounded degree and bounded…

We develop a direct method to recover an orthoalgebra from its poset of Boolean subalgebras. For this a new notion of direction is introduced. Directions are also used to characterize in purely order-theoretic terms those posets that are…