Related papers: Weakly reflecting graph properties
In this work, we focus on the task of weakly supervised affordance grounding, where a model is trained to identify affordance regions on objects using human-object interaction images and egocentric object images without dense labels.…
Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world…
Given a countable graph, we say a set $A$ of its vertices is \emph{universal} if it contains every countable graph as an induced subgraph, and $A$ is \emph{weakly universal} if it contains every finite graph as an induced subgraph. We show…
A graph is $\ell$-reconstructible if it is determined by its multiset of induced subgraphs obtained by deleting $\ell$ vertices. We prove that strongly regular graphs with at least six vertices are $2$-reconstructible.
We address the problem of defining graph transformations by the simultaneous application of direct transformations even when these cannot be applied independently of each other. An algebraic approach is adopted, with production rules of the…
(English) This monograph aims at presenting the core weak convergence theory for sequences of random vectors with values in $\mathbb{R}^k$. In some places, a more general formulation in metric spaces is provided. It lays out the necessary…
The notion of stationary reflection is one of the most important notions of combinatorial set theory. We investigate weak reflection, which is, as the name suggests, a weak version of stationary reflection. This sort of reflection was…
Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general…
Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or…
Due to the superior performance of Graph Neural Networks (GNNs) in various domains, there is an increasing interest in the GNN explanation problem "\emph{which fraction of the input graph is the most crucial to decide the model's…
We study properties of semi-elementary imsets and elementary imsets introduced by Studeny (2005). The rules of the semi-graphoid axiom (decomposition, weak union and contraction) for conditional independence statements can be translated…
Graphs are growing rapidly, along with the number of distinct label categories associated with them. Applications like e-commerce, healthcare, recommendation systems, and various social media platforms are rapidly moving towards graph…
Weakly-supervised learning is a paradigm for alleviating the scarcity of labeled data by leveraging lower-quality but larger-scale supervision signals. While existing work mainly focuses on utilizing a certain type of weak supervision, we…
We study a notion of potential isomorphism, where two structures are said to be potentially isomorphic if they are isomorphic in some generic extension that preserves stationary sets and does not add new sets of cardinality less than the…
This work examines the problem of graph learning over a diffusion network when data can be collected from a limited portion of the network (partial observability). The main question is to establish technical guarantees of consistent…
We study the problem #IndSub(P) of counting all induced subgraphs of size k in a graph G that satisfy the property P. This problem was introduced by Jerrum and Meeks and shown to be #W[1]-hard when parameterized by k for some families of…
We focus our attention on well-covered graphs that are vertex decomposable. We show that for many known families of these vertex decomposable graphs, the set of shedding vertices forms a dominating set. We then construct three new infinite…
Random graphs have proven to be one of the most important and fruitful concepts in modern Combinatorics and Theoretical Computer Science. Besides being a fascinating study subject for their own sake, they serve as essential instruments in…
Generative models can be trained to emulate complex empirical data, but are they useful to make predictions in the context of previously unobserved environments? An intuitive idea to promote such extrapolation capabilities is to have the…
We show that any countable model of a model complete theory has an elementary extension with a "pseudofinite-like" quasidimension that detects dividing.