Related papers: Letters, Colors, and Words: Constructing the Ideal…
We consider an urn model, whose replacement matrix has all entries nonnegative and is balanced, that is, has constant row sums. We obtain the rates of the counts of balls corresponding to each color for the strong laws to hold. The analysis…
Large Language Models (LLMs) have recently achieved impressive performance in math and reasoning benchmarks. However, they often struggle with logic problems and puzzles that are relatively easy for humans. To further investigate this, we…
Given an edge-colored graph, the Maximum Rainbow Matching problem asks for a maximum-cardinality matching of the graph that contains at most one edge from each color. We provide the following complexity dichotomy for this problem based on…
Narrow sieves, representative sets and divide-and-color are three breakthrough color coding-related techniques, which led to the design of extremely fast parameterized algorithms. We present a novel family of strategies for applying…
In the current landscape of automatic language generation, there is a need to understand, evaluate, and mitigate demographic biases as existing models are becoming increasingly multilingual. To address this, we present the initial eight…
In Euclidean Ramsey Theory usually we are looking for monochromatic configurations in the Euclidean space, whose points are colored with a fixed number of colors. In the canonical version, the number of colors is arbitrary, and we are…
Given an undirected graph $G$, the Minimum Sum Coloring problem (MSCP) is to find a legal assignment of colors (represented by natural numbers) to each vertex of $G$ such that the total sum of the colors assigned to the vertices is…
Color coding is an algorithmic technique used in parameterized complexity theory to detect "small" structures inside graphs. The idea is to derandomize algorithms that first randomly color a graph and then search for an easily-detectable,…
Words in some natural languages can have a composite structure. Elements of this structure include the root (that could also be composite), prefixes and suffixes with which various nuances and relations to other words can be expressed.…
In neural network-based models for natural language processing (NLP), the largest part of the parameters often consists of word embeddings. Conventional models prepare a large embedding matrix whose size depends on the vocabulary size.…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…
We study the complexity of the problem of searching for a set of patterns that separate two given sets of strings. This problem has applications in a wide variety of areas, most notably in data mining, computational biology, and in…
We propose a new kind of sliding-block puzzle, called Gourds, where the objective is to rearrange 1 x 2 pieces on a hexagonal grid board of 2n + 1 cells with n pieces, using sliding, turning and pivoting moves. This puzzle has a single…
As large language models (LLMs) are increasingly deployed across diverse domains, ensuring their safety has become a critical concern. In response, studies on jailbreak attacks have been actively growing. Existing approaches typically rely…
Pixel-based language models aim to solve the vocabulary bottleneck problem in language modeling, but the challenge of uncertainty quantification remains open. The novelty of this work consists of analysing uncertainty and confidence in…
Block-based programming languages like Scratch have become increasingly popular as introductory languages for novices. These languages are intended to be used with a "tinkering" approach which allows learners and teachers to quickly…
Colors play a crucial role in the design of vector graphic documents by enhancing visual appeal, facilitating communication, improving usability, and ensuring accessibility. In this context, color recommendation involves suggesting…
Motivated by applications in polymer-based data storage, we study the problem of reconstructing a string from part of its composition multiset. We give a full description of the structure of the strings that cannot be uniquely reconstructed…
For any fixed surface Sigma of genus g, we give an algorithm to decide whether a graph G of girth at least five embedded in Sigma is colorable from an assignment of lists of size three in time O(|V(G)|). Furthermore, we can allow a subgraph…