Related papers: Microlocal Lefschetz classes of graph trace kernel…
Graph neural networks (GNNs) have achieved superior performance on node classification tasks in the last few years. Commonly, this is framed in a transductive semi-supervised learning setup wherein the entire graph, including the target…
Graph-structured data appears frequently in domains including chemistry, natural language semantics, social networks, and knowledge bases. In this work, we study feature learning techniques for graph-structured inputs. Our starting point is…
In this article, we discuss the Lefschetz trace formula for an adic space which is separated smooth of finite type but not necessarily proper over an algebraically closed non-archimedean field. Under a certain condition on the absence of…
Traces in symmetric monoidal categories are well-known and have many applications; for instance, their functoriality directly implies the Lefschetz fixed point theorem. However, for some applications, such as generalizations of the…
We propose a representation of graph as a functional object derived from the power iteration of the underlying adjacency matrix. The proposed functional representation is a graph invariant, i.e., the functional remains unchanged under any…
Many applications such as election forecasting, environmental monitoring, health policy, and graph based machine learning require taking expectation of functions defined on the vertices of a graph. We describe a construction of a sampling…
Graph kernels are often used in bioinformatics and network applications to measure the similarity between graphs; therefore, they may be used to construct efficient graph classifiers. Many graph kernels have been developed thus far, but to…
Subgraph isomorphism counting is known as #P-complete and requires exponential time to find the accurate solution. Utilizing representation learning has been shown as a promising direction to represent substructures and approximate the…
In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…
Meta-theorems for polynomial (linear) kernels have been the subject of intensive research in parameterized complexity. Heretofore, meta-theorems for linear kernels exist on graphs of bounded genus, $H$-minor-free graphs, and…
This paper proposes a categorical framework for knowledge graphs linking combinatorial graph structure with topos-theoretic semantics. Knowledge graphs are represented as labelled directed multigraphs and analysed through incidence matrices…
Graph kernels based on the $1$-dimensional Weisfeiler-Leman algorithm and corresponding neural architectures recently emerged as powerful tools for (supervised) learning with graphs. However, due to the purely local nature of the…
In this paper, we define and study the concept of traceable regressions. These are sequences of regressions in joint or single responses for which a corresponding regression graph captures not only an independence structure but represents,…
Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous…
The theory of Generalized Locally Toeplitz (GLT) sequences of matrices has been developed in order to study the asymptotic behaviour of particular spectral distributions when the dimension of the matrices tends to infinity. A key concepts…
Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design…
Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the…
A convenient technique for proving kernel theorems for (LF)-spaces (countable inductive limits of Frechet spaces)is developed. The proposed approach is based on introducing a suitable modification of the functor of the completed inductive…
It is well known that kernels in graphs are powerful and useful structures, for instance in the theory of games. However, a kernel does not always exist and Chv\'atal proved in 1973 that it is an NP-Complete problem to decide its existence.…
In this paper we present a novel graph kernel framework inspired the by the Weisfeiler-Lehman (WL) isomorphism tests. Any WL test comprises a relabelling phase of the nodes based on test-specific information extracted from the graph, for…