Related papers: MILP-SAT-GNN: Yet Another Neural SAT Solver

We present the Neural Satisfiability Network (NSNet), a general neural framework that models satisfiability problems as probabilistic inference and meanwhile exhibits proper explainability. Inspired by the Belief Propagation (BP), NSNet…

Effectively predicting molecular interactions has the potential to accelerate molecular dynamics by multiple orders of magnitude and thus revolutionize chemical simulations. Graph neural networks (GNNs) have recently shown great successes…

While Annealing Machines (AM) have shown increasing capabilities in solving complex combinatorial problems, positioning themselves as a more immediate alternative to the expected advances of future fully quantum solutions, there are still…

Foundational optimization embeddings have recently emerged as powerful pre-trained representations for mixed-integer programming (MIP) problems. These embeddings were shown to enable cross-domain transfer and reduce reliance on…

This paper introduces the XOR-OR-AND normal form (XNF) for logical formulas. It is a generalization of the well-known Conjunctive Normal Form (CNF) where literals are replaced by XORs of literals. As a first theoretic result, we show that…

The recent advancements in graph neural networks (GNNs) have led to state-of-the-art performances in various applications, including chemo-informatics, question-answering systems, and recommender systems. However, scaling up these methods…

Graph similarity search is among the most important graph-based applications, e.g. finding the chemical compounds that are most similar to a query compound. Graph similarity computation, such as Graph Edit Distance (GED) and Maximum Common…

The CNF formula satisfiability problem (CNF-SAT) has been reduced to many fundamental problems in P to prove tight lower bounds under the Strong Exponential Time Hypothesis (SETH). Recently, the works of Abboud, Hansen, Vassilevska W. and…

By the MAXSAT problem, we are given a set $V$ of $m$ variables and a collection $C$ of $n$ clauses over $V$, i.e., a conjunctive normal form ($\textit{CNF}$) formula. We will seek a truth assignment to maximize the number of satisfied…

The Boolean Satisfiability problem (SAT), as the prototypical $\mathsf{NP}$-complete problem, is crucial in both theoretical computer science and practical applications. To address this problem, stochastic local search (SLS) algorithms,…

We obtain the smallest unsatisfiable formulas in subclasses of $k$-CNF (exactly $k$ distinct literals per clause) with bounded variable or literal occurrences. Smaller unsatisfiable formulas of this type translate into stronger…

Graph Neural Networks (GNNs) are powerful deep learning models to generate node embeddings on graphs. When applying deep GNNs on large graphs, it is still challenging to perform training in an efficient and scalable way. We propose a novel…

Mixed-integer linear programming (MILP), a widely used modeling framework for combinatorial optimization, are central to many scientific and engineering applications, yet remains computationally challenging at scale. Recent advances in deep…

In this paper we introduce Clause Cuts: linear inequalities obtained from clauses that are logically implied by a CNF formula, resembling strengthened no-good cuts. With these cuts, we tighten mixed-integer linear programming (MILP)…

Graph neural networks (GNNs) have exhibited impressive performance in modeling graph data as exemplified in various applications. Recently, the GNN calibration problem has attracted increasing attention, especially in cost-sensitive…

Equivariant Graph Neural Networks (GNNs) have demonstrated significant success across various applications. To achieve completeness -- that is, the universal approximation property over the space of equivariant functions -- the network must…

Graphs with complete node attributes have been widely explored recently. While in practice, there is a graph where attributes of only partial nodes could be available and those of the others might be entirely missing. This attribute-missing…

Uncertainty in surgery durations continues to be difficult to account for in operating room scheduling. In particular, it remains complex to accurately incorporate uncertainty in surgical overtime constraints within mixed-integer linear…

We propose an algorithm to explore the global optimization method, using SAT solvers, for training a neural net. Deep Neural Networks have achieved great feats in tasks like-image recognition, speech recognition, etc. Much of their success…

Changing the transmission system topology is an efficient and costless lever to reduce congestion or increase exchange capacities. The problem of finding the optimal switch states within substations is called Optimal Substation…