Related papers: Local Reasoning for Global Graph Properties
Separation logic is a Hoare-style logic for reasoning about programs with heap-allocated mutable data structures. As a step toward extending separation logic to high-level languages with ML-style general (higher-order) storage, we…
The long-standing identification problem for causal effects in graphical models has many partial results but lacks a systematic study. We show how computer algebra can be used to either prove that a causal effect can be identified,…
Large language models are increasingly deployed as automated judges to evaluate the strength of arguments. As this role expands, their legitimacy depends on consistency, transparency, and the ability to separate argumentative structure from…
Belief systems are rarely globally consistent, yet effective reasoning often persists locally. We propose a novel graph-theoretic framework that cleanly separates credibility--external, a priori trust in sources--from confidence--an…
Partial duality generalizes the fundamental concept of the geometric dual of an embedded graph. A partial dual is obtained by forming the geometric dual with respect to only a subset of edges. While geometric duality preserves the genus of…
Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…
(Hyper)Graph decomposition is a family of problems that aim to break down large (hyper)graphs into smaller sub(hyper)graphs for easier analysis. The importance of this lies in its ability to enable efficient computation on large and complex…
Small language models fine-tuned for graph property estimation have demonstrated strong in-distribution performance, yet their generalization capabilities beyond training conditions remain poorly understood. In this work, we systematically…
We develop a global Hopf bifurcation theory for differential equations with a state-dependent delay governed by an algebraic equation, using the $S^1$-equivariant degree. We apply the global Hopf bifurcation theory to a model of genetic…
In this work, we consider an extension of graphical models to random graphs, trees, and other objects. To do this, many fundamental concepts for multivariate random variables (e.g., marginal variables, Gibbs distribution, Markov properties)…
Complex networks are relational data sets commonly represented as graphs. The analysis of their intricate structure is relevant to many areas of science and commerce, and data sets may reach sizes that require distributed storage and…
Separation logic is a substructural logic which has proved to have numerous and fruitful applications to the verification of programs working on dynamic data structures. Recently, Barthe, Hsu and Liao have proposed a new way of giving…
Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…
Inferring missing links or detecting spurious ones based on observed graphs, known as link prediction, is a long-standing challenge in graph data analysis. With the recent advances in deep learning, graph neural networks have been used for…
Large language models (LLMs) are being increasingly explored for graph tasks. Despite their remarkable success in text-based tasks, LLMs' capabilities in understanding explicit graph structures remain limited, particularly with large…
A graph $G$ covers a graph $H$ if there exists a locally bijective homomorphism from $G$ to $H$. We deal with regular covers in which this locally bijective homomorphism is prescribed by an action of a subgroup of ${\rm Aut}(G)$. Regular…
Detecting dense landmarks for diverse clothes, as a fundamental technique for clothes analysis, has attracted increasing research attention due to its huge application potential. However, due to the lack of modeling underlying semantic…
The notion of homomorphism indistinguishability offers a combinatorial framework for characterizing equivalence relations of graphs, in particular equivalences in counting logics within finite model theory. That is, for certain graph…
We define a new decidable logic for expressing and checking invariants of programs that manipulate dynamically-allocated objects via pointers and destructive pointer updates. The main feature of this logic is the ability to limit the…
Many important graph theoretic notions can be encoded as counting graph homomorphism problems, such as partition functions in statistical physics, in particular, independent sets and colourings. In this article we study the complexity of…