Related papers: Letters, Colors, and Words: Constructing the Ideal…
We introduce a new model to study algorithm design under unreliable information, and apply this model for the problem of finding the uncorrupted maximum element of a list containing $n$ elements, among which are $k$ corrupted elements.…
The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…
Knowing which strings in a massive text are significant -- that is, which strings are common and distinct from other strings -- is valuable for several applications, including text compression and tokenization. Frequency in itself is not…
Word embeddings are ubiquitous in NLP and information retrieval, but it is unclear what they represent when the word is polysemous. Here it is shown that multiple word senses reside in linear superposition within the word embedding and…
Designing short DNA words is a problem of constructing a set (i.e., code) of n DNA strings (i.e., words) with the minimum length such that the Hamming distance between each pair of words is at least k and the n words satisfy a set of…
Language learning is thought to be a highly complex process. One of the hurdles in learning a language is to learn the rules of syntax of the language. Rules of syntax are often ordered in that before one rule can applied one must apply…
Let $C \subseteq [r]^m$ be a code such that any two words of $C$ have Hamming distance at least $t$. It is not difficult to see that determining a code $C$ with the maximum number of words is equivalent to finding the largest $n$ such that…
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…
Although board games and video games have been studied for decades in artificial intelligence research, challenging word games remain relatively unexplored. Word games are not as constrained as games like chess or poker. Instead, word game…
This is a review of a set of recent papers with some new data added. After a brief biological introduction a visualization scheme of the string composition of long DNA sequences, in particular, of bacterial complete genomes, will be…
Source code clones pose risks ranging from intellectual property violations to unintended vulnerabilities. Effective and efficient scalable clone detection, especially for diverged clones, remains challenging. Large language models (LLMs)…
Given a large social or information network, how can we partition the vertices into sets (i.e., colors) such that no two vertices linked by an edge are in the same set while minimizing the number of sets used. Despite the obvious practical…
Whole word masking (WWM), which masks all subwords corresponding to a word at once, makes a better English BERT model. For the Chinese language, however, there is no subword because each token is an atomic character. The meaning of a word…
The input of the Maximum Colored Cut problem consists of a graph $G=(V,E)$ with an edge-coloring $c:E\to \{1,2,3,\ldots , p\}$ and a positive integer $k$, and the question is whether $G$ has a nontrivial edge cut using at least $k$ colors.…
Beam search is a go-to strategy for decoding neural sequence models. The algorithm can naturally be viewed as a subset optimization problem, albeit one where the corresponding set function does not reflect interactions between candidates.…
We settle the complexity of the $(\Delta+1)$-coloring and $(\Delta+1)$-list coloring problems in the CONGESTED CLIQUE model by presenting a simple deterministic algorithm for both problems running in a constant number of rounds. This…
Set membership of points in the plane can be visualized by connecting corresponding points via graphical features, like paths, trees, polygons, ellipses. In this paper we study the \emph{bus embeddability problem} (BEP): given a set of…
We investigate certain word-construction games with variable turn orders. In these games, Alice and Bob take turns on choosing consecutive letters of a word of fixed length, with Alice winning if the result lies in a predetermined target…
Best match graphs (BMGs) are a class of colored digraphs that naturally appear in mathematical phylogenetics and can be approximated with the help of similarity measures between gene sequences, albeit not without errors. The corresponding…
Making an informed choice of pre-trained language model (LM) is critical for performance, yet environmentally costly, and as such widely underexplored. The field of Computer Vision has begun to tackle encoder ranking, with promising forays…