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Graphs are essential for modeling complex interactions across domains such as social networks, biology, and recommendation systems. Traditional Graph Neural Networks, particularly Message Passing Neural Networks (MPNNs), rely heavily on…

We introduce the logic FOCN(P) which extends first-order logic by counting and by numerical predicates from a set P, and which can be viewed as a natural generalisation of various counting logics that have been studied in the literature. We…

Feedforward neural networks (FNNs) are typically viewed as pure prediction algorithms, and their strong predictive performance has led to their use in many machine-learning applications. However, their flexibility comes with an…

We present a general framework for good CNF-representations of boolean constraints, to be used for translating decision problems into SAT problems (i.e., deciding satisfiability for conjunctive normal forms). We apply it to the…

Boolean Satisfiability Problem (SAT) is one of the core problems in computer science. As one of the fundamental NP-complete problems, it can be used - by known reductions - to represent instances of variety of hard decision problems.…

Polynomial threshold gates are basic processing units of an artificial neural network. When the input vectors are binary vectors, these gates correspond to Boolean functions and can be analyzed via their polynomial representations. In…

In this paper, our aim is to briefly survey and articulate the logical and philosophical foundations of using (first-order) logic to represent (probabilistic) knowledge in a non-technical fashion. Our motivation is three fold. First, for…

The quest for efficient and robust deep learning models for molecular systems representation is increasingly critical in scientific exploration. The advent of message passing neural networks has marked a transformative era in graph-based…

Interpretable graph learning is in need as many scientific applications depend on learning models to collect insights from graph-structured data. Previous works mostly focused on using post-hoc approaches to interpret pre-trained models…

Graph neural networks (GNNs) have proven their efficacy in a variety of real-world applications, but their underlying mechanisms remain a mystery. To address this challenge and enable reliable decision-making, many GNN explainers have been…

In some contexts, well-formed natural language cannot be expected as input to information or communication systems. In these contexts, the use of grammar-independent input (sequences of uninflected semantic units like e.g.…

Entity interaction prediction is essential in many important applications such as chemistry, biology, material science, and medical science. The problem becomes quite challenging when each entity is represented by a complex structure,…

As integrated circuit scale grows and design complexity rises, effective circuit representation helps support logic synthesis, formal verification, and other automated processes in electronic design automation. And-Inverter Graphs (AIGs),…

Active learning optimizes the exploration of large parameter spaces by strategically selecting which experiments or simulations to conduct, thus reducing resource consumption and potentially accelerating scientific discovery. A key…

Scalability of Graph Neural Networks (GNNs) remains a significant challenge. To tackle this, methods like coarsening, condensation, and computation trees are used to train on a smaller graph, resulting in faster computation. Nonetheless,…

Today we have a good theoretical understanding of the representational power of Graph Neural Networks (GNNs). For example, their limitations have been characterized in relation to a hierarchy of Weisfeiler-Lehman (WL) isomorphism tests.…

Intrinsic interpretability of graph neural networks (GNNs) is to find a small subset of the input graph's features -- rationale -- which guides the model prediction. Unfortunately, the leading rationalization models often rely on data…

Flow Oriented Perturbation Theory (FOPT) is a novel approach to Feynman diagrams based on the coordinate (position) space description of Quantum Field Theories (QFT). FOPT offers interesting features regarding the computation of higher-loop…

Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to…

Transformer-based pre-trained models have gained much advance in recent years, becoming one of the most important backbones in natural language processing. Recent work shows that the attention mechanism inside Transformer may not be…