Related papers: Tinker, tailor, solver, proof
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…
Graphs and networks provide a canonical representation of relational data, with massive network data sets becoming increasingly prevalent across a variety of scientific fields. Although tools from mathematics and computer science have been…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
The explainability of deep networks is becoming a central issue in the deep learning community. It is the same for learning on graphs, a data structure present in many real world problems. In this paper, we propose a method that is more…
Recent advancements in graph representation learning have led to the emergence of condensed encodings that capture the main properties of a graph. However, even though these abstract representations are powerful for downstream tasks, they…
Graph neural networks (GNNs) have various practical applications, such as drug discovery, recommendation engines, and chip design. However, GNNs lack transparency as they cannot provide understandable explanations for their predictions. To…
Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…
Real data collected from different applications that have additional topological structures and connection information are amenable to be represented as a weighted graph. Considering the node labeling problem, Graph Neural Networks (GNNs)…
System development is not a linear, one-shot process. It proceeds through refinements and revisions. To support assurance that the system satisfies its requirements, it is desirable that continuous verification can be performed after each…
Isabelle is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a meta-logic (or `logical framework') in…
We address the problem of reasoning on graph transformations featuring actions such as \emph{addition} and \emph{deletion} of nodes and edges, node \emph{merging} and \emph{cloning}, node or edge \emph{labelling} and edge…
In the modern era, abundant information is easily accessible from various sources, however only a few of these sources are reliable as they mostly contain unverified contents. We develop a system to validate the truthfulness of a given…
The widespread use of black box prediction methods has sparked an increasing interest in algorithm/model-agnostic approaches for quantifying goodness-of-fit, with direct ties to specification testing, model selection and variable importance…
In the problem of edge sign prediction, we are given a directed graph (representing a social network), and our task is to predict the binary labels of the edges (i.e., the positive or negative nature of the social relationships). Many…
Given a set of snapshots from a temporal network we develop, analyze, and experimentally validate a so-called network interpolation scheme. Our method allows us to build a plausible, albeit random, sequence of graphs that transition between…
This study addresses the challenge of forming effective groups in collaborative problem-solving environments. Recognizing the complexity of human interactions and the necessity for efficient collaboration, we propose a novel approach…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
We introduce a technique called graph fission which takes in a graph which potentially contains only one observation per node (whose distribution lies in a known class) and produces two (or more) independent graphs with the same node/edge…
Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for…
Current AI-assisted innovation systems typically apply a single ideation methodology (such as TRIZ or Design Thinking) using sequential prompt-based workflows that do not preserve intermediate reasoning structure. As a result, insights…