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Entity alignment (EA) for knowledge graphs (KGs) plays a critical role in knowledge engineering. Existing EA methods mostly focus on utilizing the graph structures and entity attributes (including literals), but ignore images that are…
The recently introduced series of description logics under the common moniker DL-Lite has attracted attention of the description logic and semantic web communities due to the low computational complexity of inference, on the one hand, and…
Logical anomaly detection in industrial inspection remains challenging due to variations in visual appearance (e.g., background clutter, illumination shift, and blur), which often distract vision-centric detectors from identifying…
Learning continuous representations of discrete objects such as text, users, movies, and URLs lies at the heart of many applications including language and user modeling. When using discrete objects as input to neural networks, we often…
Over the past decade, physicists have developed deep but non-rigorous techniques for studying phase transitions in discrete structures. Recently, their ideas have been harnessed to obtain improved rigorous results on the phase transitions…
We study a certain relaxation of the classic vertex coloring problem, namely, a coloring of vertices of undirected, simple graphs, such that there are no monochromatic triangles. We give the first classification of the problem in terms of…
Deploying guardrails for custom policies remains challenging, as generic safety models fail to capture task-specific requirements, while prompting LLMs suffers from inconsistent boundary-case performance and high inference costs. Training…
LR(1) parsing was a focus of extensive research in the past 50 years. Though most fundamental mysteries have been resolved, a few remain hidden in the dark corners. The one we bumped into is the minimization of the LR(1) state machines,…
Following a general program of studying limits of discrete structures, and motivated by the theory of limit objects of converge sequences of dense simple graphs, we study the limit of graph sequences such that every edge is labeled by an…
For an $r$-regular graph $G$, we define an edge-coloring $c$ with colors from $\{1,2,\cdots,$ $k\}$, in such a way that any vertex of $G$ is incident to at least one edge of each color. The multiset-color $c_m(v)$ of a vertex $v$ is defined…
Zero forcing is an iterative graph coloring process whereby a colored vertex with a single uncolored neighbor forces that neighbor to be colored. It is NP-hard to find a minimum zero forcing set - a smallest set of initially colored…
Theoretical constructs of logical gates implemented with plant roots are morphological computing asynchronous devices. Values of Boolean variables are represented by plant roots. A presence of a plant root at a given site symbolises the…
The Bandwidth Coloring Problem (BCP) generalizes graph coloring by enforcing minimum separation constraints between adjacent vertices and arises in frequency assignment applications. While SAT-based approaches have shown promise for exact…
Recent studies have shown that Large Language Models (LLMs) can achieve strong reasoning performance by incorporating functional symbolic representations that abstractly describe graph traversal algorithms and step-by-step reasoning in…
Humans often use visual aids, for example diagrams or sketches, when solving complex problems. Training multimodal models to do the same, known as Visual Chain of Thought (Visual CoT), is challenging due to: (1) poor off-the-shelf visual…
Neuro-symbolic systems combine the abilities of neural perception and logical reasoning. However, end-to-end learning of neuro-symbolic systems is still an unsolved challenge. This paper proposes a natural framework that fuses neural…
The color code is a topological quantum error-correcting code supporting a variety of valuable fault-tolerant logical gates. Its two-dimensional version, the triangular color code, may soon be realized with currently available…
Locating-dominating sets and identifying codes are two closely related notions in the area of separating systems. Roughly speaking, they consist in a dominating set of a graph such that every vertex is uniquely identified by its…
We present a new algorithm for finding large independent sets in $3$-colorable graphs with small $1$-sided threshold rank. Specifically, given an $n$-vertex $3$-colorable graph whose uniform random walk matrix has at most $r$ eigenvalues…
We study quantum analogs of graph colorings and chromatic number. Initially defined via an interactive protocol, quantum colorings can also be viewed as a natural operator relaxation of graph coloring. Since there is no known algorithm for…