Related papers: When GNNs meet symmetry in ILPs: an orbit-based fe…
In this paper, we fully answer the above question through a key algebraic condition on graph functions, called \textit{permutation compatibility}, that relates permutations of weights and features of the graph to functional constraints. We…
Graph neural networks (GNNs) have become a core paradigm for learning on relational data. In materials science, equivariant GNNs (EGNNs) have emerged as a compelling backbone for crystalline-structure prediction, owing to their ability to…
Deep neural networks have achieved great success in the last decade. When designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, it is critical that the model can maintain invariance towards…
Correspondence is a ubiquitous problem in computer vision and graph matching has been a natural way to formalize correspondence as an optimization problem. Recently, graph matching solvers have included higher-order terms representing…
Graph Neural Networks (GNNs) are recently proposed neural network structures for the processing of graph-structured data. Due to their employed neighbor aggregation strategy, existing GNNs focus on capturing node-level information and…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…
While the interaction of ultra-intense ultra-short laser pulses with near- and overcritical plasmas cannot be directly observed, experimentally accessible quantities (observables) often only indirectly give information about the underlying…
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…
Linear regression without correspondences is the problem of performing a linear regression fit to a dataset for which the correspondences between the independent samples and the observations are unknown. Such a problem naturally arises in…
The expressive power of Graph Neural Networks (GNNs) has been studied extensively through the Weisfeiler-Leman (WL) graph isomorphism test. However, standard GNNs and the WL framework are inapplicable for geometric graphs embedded in…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
Machine learning (ML) methods have become popular for parameter inference in cosmology, although their reliance on specific training data can cause difficulties when applied across different data sets. By reproducing and testing networks…
Automated program analysis is a pivotal research domain in many areas of Computer Science -- Formal Methods and Artificial Intelligence, in particular. Due to the undecidability of the problem of program equivalence, comparing two programs…
Hypernetworks, neural networks that predict the parameters of another neural network, are powerful models that have been successfully used in diverse applications from image generation to multi-task learning. Unfortunately, existing…
Recognizing symmetries in data allows for significant boosts in neural network training, which is especially important where training data are limited. In many cases, however, the exact underlying symmetry is present only in an idealized…
In this paper we generalize the Interior Point-Proximal Method of Multipliers (IP-PMM) presented in [An Interior Point-Proximal Method of Multipliers for Convex Quadratic Programming, Computational Optimization and Applications, 78,…
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) have established themselves as a key component in addressing diverse graph-based tasks. Despite their notable successes, GNNs remain susceptible to input perturbations in the form of adversarial attacks. This…
We introduce an extension of decision problems called resiliency problems. In resiliency problems, the goal is to decide whether an instance remains positive after any (appropriately defined) perturbation has been applied to it. To tackle…