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Standard methods for aligning large language models with human preferences learn from pairwise comparisons among sampled candidate responses and regularize toward a reference policy. Despite their effectiveness, the effects of sampling and…
Consider two independent random strings having same length and taking values uniformly in a common finite alphabet. We study the order of the variance of the length of the longest common subsequences (LCS) of these strings when long blocks,…
The word order of a sentence is shaped by multiple principles. The principle of syntactic dependency distance minimization is in conflict with the principle of surprisal minimization (or predictability maximization) in single head syntactic…
We relate a balancing property of letters for bi-infinite sequences to the invariance of the resulting 1-dimensional tiling dynamics under changes in the lengths of the tiles. If the language of the sequence space is finitely balanced, then…
Modern neural networks have greatly improved performance across speech recognition benchmarks. However, gains are often driven by frequent words with limited semantic weight, which can obscure meaningful differences in word error rate, the…
Alignment with human preferences is commonly framed using a universal reward function, even though human preferences are inherently heterogeneous. We formalize this heterogeneity by introducing user types and examine the limits of the…
We investigate the problem of designing optimal classifiers in the strategic classification setting, where the classification is part of a game in which players can modify their features to attain a favorable classification outcome (while…
We present three large-scale experiments on binary text matching classification task both in Chinese and English to evaluate the effectiveness and generalizability of random text perturbations as a data augmentation approach for NLP. It is…
In this paper we provide a novel mathematical optimization based methodology to perturb the features of a given observation to be re-classified, by a tree ensemble classification rule, to a certain desired class. The method is based on…
Neural sequence-to-sequence systems deliver state-of-the-art performance for automatic speech recognition. When using appropriate modeling units, e.g., byte-pair encoding, these systems are in principle open vocabulary systems. In practice,…
Large Language Models (LLMs) have demonstrated the capability to refine their generated answers through self-correction, enabling continuous performance improvement over multiple rounds. However, the mechanisms underlying how and why…
Rankings play a crucial role in decision-making. However, if minor changes to items significantly alter their rankings, the quality of the decisions being made can be compromised. The stability of ranking is a measure used to assess how…
The ability to reliably distinguish human-written text from that generated by large language models is of profound societal importance. The dominant approach to this problem exploits the likelihood hypothesis: that machine-generated text…
Unbalanced translocations are among the most frequent chromosomal alterations, accounted for 30\% of all losses of heterozygosity, a major genetic event causing inactivation of tumor suppressor genes. Despite of their central role in…
We consider the problem of sequencing a set of positive numbers. We try to find the optimal sequence to maximize the variance of its partial sums. The optimal sequence is shown to have a beautiful structure. It is interesting to note that…
A pattern $\alpha$ is a string of variables and terminal letters. We say that $\alpha$ matches a word $w$, consisting only of terminal letters, if $w$ can be obtained by replacing the variables of $\alpha$ by terminal words. The matching…
We present a general approach to the problem of determining tight asymptotic lower bounds for generalized central moments of the optimal alignment score of two independent sequences of i.i.d. random variables. At first, these are obtained…
One of the most common methods for statistical inference is the maximum likelihood estimator (MLE). The MLE needs to compute the normalization constant in statistical models, and it is often intractable. Using unnormalized statistical…
We develop a unified theory to analyze the microcanonical ensembles with several constraints given by unbounded observables. Several interesting phenomena that do not occur in the single constraint case can happen under the multiple…
In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In…