Related papers: On Representing Mixed-Integer Linear Programs by G…

We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be used for a number of important tasks, such as verifying…

Graph Neural Networks (GNNs) have become the standard approach for learning and reasoning over relational data, leveraging the message-passing mechanism that iteratively propagates node embeddings through graph structures. While GNNs have…

Graph mining is an important area in data mining and machine learning that involves extracting valuable information from graph-structured data. In recent years, significant progress has been made in this field through the development of…

A standard approach to solving optimistic bilevel linear programs (BLPs) is to replace the lower-level problem with its Karush-Kuhn-Tucker (KKT) optimality conditions and reformulate the resulting complementarity constraints using auxiliary…

Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting…

Binary (0-1) integer programming (BIP) is pivotal in scientific domains requiring discrete decision-making. As the advance of AI computing, recent works explore neural network-based solvers for integer linear programming (ILP) problems.…

Recent work has shown potential in using Mixed Integer Programming (MIP) solvers to optimize certain aspects of neural networks (NNs). However the intriguing approach of training NNs with MIP solvers is under-explored.…

Graph Neural Networks (GNNs), a generalization of deep neural networks on graph data have been widely used in various domains, ranging from drug discovery to recommender systems. However, GNNs on such applications are limited when there are…

In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph…

Link prediction is a fundamental problem in many graph based applications, such as protein-protein interaction prediction. Graph neural network (GNN) has recently been widely used for link prediction. However, existing GNN based link…

Graph neural networks (GNNs) are a type of deep learning models that are trained on graphs and have been successfully applied in various domains. Despite the effectiveness of GNNs, it is still challenging for GNNs to efficiently scale to…

Recently, implicit graph neural networks (GNNs) have been proposed to capture long-range dependencies in underlying graphs. In this paper, we introduce and justify two weaknesses of implicit GNNs: the constrained expressiveness due to their…

Graphs play an important role in representing complex relationships in various domains like social networks, knowledge graphs, and molecular discovery. With the advent of deep learning, Graph Neural Networks (GNNs) have emerged as a…

Autonomous systems must solve motion planning problems subject to increasingly complex, time-sensitive, and uncertain missions. These problems often involve high-level task specifications, such as temporal logic or chance constraints, which…

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

Graphs are a powerful data structure to represent relational data and are widely used to describe complex real-world data structures. Probabilistic Graphical Models (PGMs) have been well-developed in the past years to mathematically model…

The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…

Graph Neural Networks (GNNs) are a predominant method for graph representation learning. However, beyond subgraph frequency estimation, their application to network motif significance-profile (SP) prediction remains under-explored, with no…

Our interest is in scientific problems with the following characteristics: (1) Data are naturally represented as graphs; (2) The amount of data available is typically small; and (3) There is significant domain-knowledge, usually expressed…

We consider the feasibility problem of integer linear programming (ILP). We show that solutions of any ILP instance can be naturally represented by an FO-definable class of graphs. For each solution there may be many graphs representing it.…