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Prior research has demonstrated noticeable performance gains through the use of probabilistic tokenizations, an approach that involves employing multiple tokenizations of the same input string during the training phase of a language model.…
Large language models (LLMs) have exhibited impressive performance and surprising emergent properties. However, their effectiveness remains limited by the fixed context window of the transformer architecture, posing challenges for…
We prove that a random automaton with $n$ states and any fixed non-singleton alphabet is synchronizing with high probability (modulo an unpublished result about unique highest trees of random graphs). Moreover, we also prove that the…
Large audio-language models (LALMs) are often used in tasks that involve reasoning over ordered options. An open question is whether their predictions are influenced by the order of answer choices, which would indicate a form of position…
String matching algorithm plays the vital role in the Computational Biology. The functional and structural relationship of the biological sequence is determined by similarities on that sequence. For that, the researcher is supposed to aware…
Variation in language is ubiquitous and often systematically linked to regional, social, and contextual factors. Tokenizers split texts into smaller units and might behave differently for less common linguistic forms. This might affect…
Optimal prefix codes are studied for pairs of independent, integer-valued symbols emitted by a source with a geometric probability distribution of parameter $q$, $0{<}q{<}1$. By encoding pairs of symbols, it is possible to reduce the…
The assignment of papers to reviewers is a crucial part of the peer review processes of large publication venues, where organizers (e.g., conference program chairs) rely on algorithms to perform automated paper assignment. As such, a major…
We generalize the optimal coupling theorem to multiple random variables: Given a collection of random variables, it is possible to couple all of them so that any two differ with probability comparable to the total-variation distance between…
Fine-tuning LLMs on tabular classification tasks can lead to the phenomenon of fine-tuning multiplicity where equally well-performing models make conflicting predictions on the same input. Fine-tuning multiplicity can arise due to…
This paper demonstrates many immediate connections between adaptive control and optimization methods commonly employed in machine learning. Starting from common output error formulations, similarities in update law modifications are…
Despite growing interest in using Large Language Models (LLMs) for educational assessment, it remains unclear how closely they align with human scoring. We present a systematic evaluation of instruction-tuned LLMs across three open…
Various approaches to alignment-free sequence comparison are based on the length of exact or inexact word matches between two input sequences. Haubold {\em et al.} (2009) showed how the average number of substitutions between two DNA…
We give a characterization of the effect of sequences of pivot operations on a graph by relating it to determinants of adjacency matrices. This allows us to deduce that two sequences of pivot operations are equivalent iff they contain the…
Surprisal theory has provided a unifying framework for understanding many phenomena in sentence processing (Hale, 2001; Levy, 2008a), positing that a word's conditional probability given all prior context fully determines processing…
The Pr\"ufer code is a bijection between trees on the vertex set $[n]$ and strings on the set $[n]$ of length $n-2$ (Pr\"ufer strings of order $n$). In this paper we examine the `locality' properties of the Pr\"ufer code, i.e. the effect of…
The correlation measure is a testimony of the pseudorandomness of a sequence $\infw{s}$ and provides information about the independence of some parts of $\infw{s}$ and their shifts. Combined with the well-distribution measure, a sequence…
We seek to understand the interplay between amino acid sequence and local structure in proteins. Are some amino acids unique in their ability to fit harmoniously into certain local structures? What is the role of sequence in sculpting the…
This work focuses on the convergence analysis of adaptive distributed beamforming schemes that can be reformulated as local random search algorithms via a random search framework. Once reformulated as local random search algorithms, it is…
The idea that many important classes of signals can be well-represented by linear combinations of a small set of atoms selected from a given dictionary has had dramatic impact on the theory and practice of signal processing. For practical…