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First-order stochastic methods for solving large-scale non-convex optimization problems are widely used in many big-data applications, e.g. training deep neural networks as well as other complex and potentially non-convex machine learning…
Let $H$ be an arbitrary family of hyper-planes in $d$-dimensions. We show that the point-location problem for $H$ can be solved by a linear decision tree that only uses a special type of queries called \emph{generalized comparison queries}.…
Contracting tensor networks is often computationally demanding. Well-designed contraction sequences can dramatically reduce the contraction cost. We explore the performance of simulated annealing and genetic algorithms, two common discrete…
Join order selection plays a significant role in query performance. However, modern query optimizers typically employ static join enumeration algorithms that do not receive any feedback about the quality of the resulting plan. Hence,…
Graph neural networks have been shown to be very effective in utilizing pairwise relationships across samples. Recently, there have been several successful proposals to generalize graph neural networks to hypergraph neural networks to…
Join query evaluation with ordering is a fundamental data processing task in relational database management systems. SQL and custom graph query languages such as Cypher offer this functionality by allowing users to specify the order via the…
As RDF becomes more widely established and the amount of linked data is rapidly increasing, the efficient querying of large amount of data becomes a significant challenge. In this paper, we propose a family of algorithms for querying large…
It is known that the current graph neural networks (GNNs) are difficult to make themselves deep due to the problem known as over-smoothing. Multi-scale GNNs are a promising approach for mitigating the over-smoothing problem. However, there…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
The paper outlines the principles of construction of a broad class of hierarchical aggregation algorithms of cluster analysis, essentially based on minimum distance mergers, which are derived from the general bi-partial objective function.…
Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data. Despite several appealing properties, incorporating PDs in learning pipelines can be challenging because their natural geometry is not…
The paper "Stack-based Algorithms for Pattern Matching on DAGs" generalizes the classical holistic twig join algorithms and proposes PathStackD, TwigStackD and DagStackD to respectively evaluate path, twig and DAG pattern queries on…
Higher-order graph neural networks (HOGNNs) and the related architectures from Topological Deep Learning are an important class of GNN models that harness polyadic relations between vertices beyond plain edges. They have been used to…
We consider the problem of sampling and approximately counting an arbitrary given motif $H$ in a graph $G$, where access to $G$ is given via queries: degree, neighbor, and pair, as well as uniform edge sample queries. Previous algorithms…
The Classic Howard's algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A special beneficial characteristic of the method is the…
Hypergraphs are a generalized data structure of graphs to model higher-order correlations among entities, which have been successfully adopted into various research domains. Meanwhile, HyperGraph Neural Network (HGNN) is currently the…
By recursively summing node features over entire neighborhoods, spatial graph convolution operators have been heralded as key to the success of Graph Neural Networks (GNNs). Yet, despite the multiplication of GNN methods across tasks and…
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…
Trustworthy Artificial Intelligence solutions are essential in today's data-driven applications, prioritizing principles such as robustness, safety, transparency, explainability, and privacy among others. This has led to the emergence of…
Numerous subgraph-enhanced graph neural networks (GNNs) have emerged recently, provably boosting the expressive power of standard (message-passing) GNNs. However, there is a limited understanding of how these approaches relate to each other…