Related papers: Kernels, Truth and Satisfaction
Graph neural tangent kernels give a principled infinite-width theory for graph neural networks, but inherit a basic limitation of graph models: they see only pairwise structure. Many relational systems contain higher-order interactions that…
Besides their use for efficient computation, quantum computers are a base for studying quantum systems that create valid physical theories using mathematics and physics. An essential part of the validation process for quantum mechanics is…
A number of network structural characteristics have recently been the subject of particularly intense research, including degree distributions, community structure, and various measures of vertex centrality, to mention only a few. Vertices…
In the present paper, we study algorithmic questions for the arc-intersection graph of directed paths on a tree. Such graphs are known to be perfect (proved by Monma and Wei in 1986). We present faster algorithms than all previously known…
A topological group $X$ is called connected if the only subsets which are both open and closed are the whole space $X$ and the null set $\emptyset$. A subset of a topological group is connected if the subspace is connected. We say that a…
A new method for hierarchical clustering is presented. It combines treelets, a particular multiscale decomposition of data, with a projection on a reproducing kernel Hilbert space. The proposed approach, called kernel treelets (KT),…
We propose a new graph-theoretic benchmark in this paper. The benchmark is developed to address shortcomings of an existing widely-used graph benchmark. We thoroughly studied a large number of traditional and contemporary graph algorithms…
Given the degree sequence $d$ of a graph, the realization graph of $d$ is the graph having as its vertices the labeled realizations of $d$, with two vertices adjacent if one realization may be obtained from the other via an edge-switching…
Kernel Estimation provides an unbinned and non-parametric estimate of the probability density function from which a set of data is drawn. In the first section, after a brief discussion on parametric and non-parametric methods, the theory of…
Assume that there is a free group action of automorphisms on a bipartite graph. If there is a perfect matching on the factor graph, then obviously there is a perfect matching on the graph. Surprisingly, the reversed is also true for…
Given a directed graph G=(V,E) an independent set A of the vertices V is called quasi-kernel (quasi-sink) iff for each point v there is a path of length at most 2 from some point of A to v (from v to some point of A). Every finite directed…
In signal analysis and synthesis, linear approximation theory considers a linear decomposition of any given signal in a set of atoms, collected into a so-called dictionary. Relevant sparse representations are obtained by relaxing the…
While state-of-the-art kernels for graphs with discrete labels scale well to graphs with thousands of nodes, the few existing kernels for graphs with continuous attributes, unfortunately, do not scale well. To overcome this limitation, we…
We explore the equivalence between neural networks and kernel methods by deriving the first exact representation of any finite-size parametric classification model trained with gradient descent as a kernel machine. We compare our exact…
Building on a specific formalization of analogical relationships of the form "A relates to B as C relates to D", we establish a connection between two important subfields of artificial intelligence, namely analogical reasoning and…
Multi-kernel learning (MKL) has been widely used in function approximation tasks. The key problem of MKL is to combine kernels in a prescribed dictionary. Inclusion of irrelevant kernels in the dictionary can deteriorate accuracy of MKL,…
We define a perfect coloring of a graph $G$ as a proper coloring of $G$ such that every connected induced subgraph $H$ of $G$ uses exactly $\omega(H)$ many colors where $\omega(H)$ is the clique number of $H$. A graph is perfectly colorable…
We initiate the study of the Diverse Pair of (Maximum/ Perfect) Matchings problems which given a graph $G$ and an integer $k$, ask whether $G$ has two (maximum/perfect) matchings whose symmetric difference is at least $k$. Diverse Pair of…
Information extraction methods proved to be effective at triple extraction from structured or unstructured data. The organization of such triples in the form of (head entity, relation, tail entity) is called the construction of Knowledge…
We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…