相关论文: Interaction Graphs: Additives

Graph Neural Networks (GNNs) have been successfully used in many problems involving graph-structured data, achieving state-of-the-art performance. GNNs typically employ a message-passing scheme, in which every node aggregates information…

A hypergraph is a generalization of an ordinary graph, and it naturally represents group interactions as hyperedges (i.e., arbitrary-sized subsets of nodes). Such group interactions are ubiquitous in many domains: the sender and receivers…

We introduce a taxonomy of interaction types and show that graphs are focal hypergraphs: every graph is canonically a focal hypergraph via its closed neighbourhood structure, and every graph dynamical model is a special case of the general…

Multimodal machine learning has been widely studied for the development of general intelligence. Recently, the Perceiver and Perceiver IO, show competitive results for diverse dataset domains and tasks. However, recent works, Perceiver and…

Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an…

We introduce Generalized Integrated Gradients (GIG), a formal extension of the Integrated Gradients (IG) (Sundararajan et al., 2017) method for attributing credit to the input variables of a predictive model. GIG improves IG by explaining a…

The ISO standard Property Graph model has become increasingly popular for representing complex, interconnected data. However, it lacks native support for querying metadata and reification, which limits its abilities to deal with the demands…

In the quest of accurate vertex classification, we introduce GRAVITY (Graph-based Representation leArning via Vertices Interaction TopologY), a framework inspired by physical systems where objects self-organize under attractive forces.…

This paper introduces a logical system, called BV, which extends multiplicative linear logic by a non-commutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved…

While machine learning methods have significantly improved model performance over traditional methods, their black-box structure makes it difficult for researchers to interpret results. For highly regulated financial industries, model…

Standard combinatorial construction, due to Kontsevich, associates to any $\ai$-algebra with an invariant inner product, an inhomogeneous class in the cohomology of the moduli spaces of Riemann surfaces with marked points. We propose an…

Analysis of indoor spaces requires topological information. In this paper, we propose to extract topological information from room attributes using what we call Iterative and adaptive graph Topology Learning (ITL). ITL progressively…

We apply some basic notions from combinatorial topology to establish various algebraic properties of edge ideals of graphs and more general Stanley-Reisner rings. In this way we provide new short proofs of some theorems from the literature…

The concepts of geometric-arithmetic and harmonic indices were introduced in the area of chemical graph theory recently. They have proven to correlate well with physical and chemical properties of some molecules. The aim of this paper is to…

Generating graphs with hierarchical structures remains a fundamental challenge due to the limitations of Euclidean geometry in capturing exponential complexity. Here we introduce \textbf{GGBall}, a novel hyperbolic framework for graph…

Let $\mathbb{N}_0$ denote the set of all non-negative integers and $X$ be any subset of $X$. Also denote the power set of $X$ by $\mathcal{P}(X)$. An integer additive set-labeling (IASL) of a graph $G$ is an injective function $f:V(G)\to…

This paper develops and evaluates a new tensor field representation to express the geometric affordance of one object over another. We expand the well known bisector surface representation to one that is weight-driven and that retains the…

This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…

In this paper we investigate two logics from an algebraic point of view. The two logics are: MALL (multiplicative-additive Linear Logic) and LL (classical Linear Logic). Both logics turn out to be strongly algebraizable in the sense of Blok…

The property graph is an increasingly popular data model. Pattern construction and pattern matching are important tasks when dealing with property graphs. Given a property graph schema S, a property graph G, and a query pattern P, all…