Related papers: A Systematic Study of Single-Anchor Logical Gadget…
Consider a graph whose vertices are colored in one of two colors, say black or white. A white vertex is called integrated if it has at least as many black neighbors as white neighbors, and similarly for a black vertex. The coloring as a…
Solving grounded language tasks often requires reasoning about relationships between objects in the context of a given task. For example, to answer the question "What color is the mug on the plate?" we must check the color of the specific…
Given a digraph with two terminal vertices $s$ and $t$ as well as a conservative cost function and several not necessarily disjoint color classes on its arc set, our goal is to find a minimum-cost subset of the arcs such that its…
Point-based interactive colorization techniques allow users to effortlessly colorize grayscale images using user-provided color hints. However, point-based methods often face challenges when different colors are given to semantically…
Edge-coloured directed graphs provide an essential structure for modelling and analysis of complex systems arising in many scientific disciplines (e.g. feature-oriented systems, gene regulatory networks, etc.). One of the fundamental…
Cross-domain scientific synthesis requires connecting mechanistic explanations across fragmented literature, a capability that remains challenging for both retrieval-based systems and unconstrained language models. While recent work has…
Vision--language models (VLMs) often fail on abstract visual reasoning benchmarks such as Bongard problems, raising the question of whether the main bottleneck lies in reasoning or representation. We study this on Bongard-LOGO, a synthetic…
The colouring defect of a cubic graph, introduced by Steffen in 2015, is the minimum number of edges that are left uncovered by any set of three perfect matchings. Since a cubic graph has defect $0$ if and only if it is $3$-edge-colourable,…
Chain-of-Thought (CoT) has become a cornerstone of reasoning in large language models, yet its effectiveness is constrained by the limited expressiveness of discrete token sampling. Recent latent reasoning approaches attempt to alleviate…
Graph colorings have been of interest to mathematicians for a long time, but relatively recently, social scientists have also found them to be interesting tools for studying group behavior. In the last 20 years, scientists have begun to…
We study a graph coloring problem motivated by a fun Sudoku-style puzzle. Given a bipartition of the edges of a graph into {\em near} and {\em far} sets and an integer threshold $t$, a {\em threshold-coloring} of the graph is an assignment…
With the rapid progress of Large Language Models (LLMs), it becomes increasingly important to understand their abilities and limitations. In two experiments, we investigate the causal and compositional reasoning abilities of LLMs and humans…
We consider the problem of $q$-colouring a $k$-uniform random hypergraph, where $q,k \geq 3$, and determine the rigidity threshold. For edge densities above the rigidity threshold, we show that almost all solutions have a linear number of…
Academic question answering (QA) in heterogeneous scholarly networks presents unique challenges requiring both structural understanding and interpretable reasoning. While graph neural networks (GNNs) capture structured graph information and…
A lambda colouring (or $L(2,1)-$colouring) of a graph is an assignment of non-negative integers (with minimum assignment $0$) to its vertices such that the adjacent vertices must receive integers at least two apart and vertices at distance…
Large language models perform well on many logical reasoning benchmarks, but it remains unclear which core logical skills they truly master. To address this, we introduce LogicSkills, a benchmark that isolates three fundamental logical…
3D visual grounding is a challenging task that often requires direct and dense supervision, notably the semantic label for each object in the scene. In this paper, we instead study the naturally supervised setting that learns from only 3D…
We study weighted edge coloring of graphs, where we are given an undirected edge-weighted general multi-graph $G := (V, E)$ with weights $w : E \rightarrow [0, 1]$. The goal is to find a proper weighted coloring of the edges with as few…
We study the coloring problem: Given a graph G, decide whether $c(G) \leq q$ or $c(G) \ge Q$, where c(G) is the chromatic number of G. We derive conditional hardness for this problem for any constant $3 \le q < Q$. For $q\ge 4$, our result…
Given a rectilinear grid $G$, in which cells are either assigned a single color, out of $k$ possible colors, or remain white, can we color white grid cells of $G$ to minimize the total number of corners of the resulting colored rectilinear…