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The impact of random seeds in fine-tuning large language models (LLMs) has been largely overlooked despite its potential influence on model performance.In this study, we systematically evaluate the effects of random seeds on LLMs using the…

Alignment algorithms usually rely on simplified models of gaps for computational efficiency. Based on an isomorphism between alignments and physical helix-coil models, we show in statistical mechanics that alignments with realistic laws for…

Recently, it has been claimed that a linear relationship between a measure of information content and word length is expected from word length optimization and it has been shown that this linearity is supported by a strong correlation…

As large language models (LLMs) have grown in prevalence, particular benchmarks have become essential for the evaluation of these models and for understanding model capabilities. Most commonly, we use test accuracy averaged across multiple…

In empirical risk optimization, it has been observed that stochastic gradient implementations that rely on random reshuffling of the data achieve better performance than implementations that rely on sampling the data uniformly. Recent works…

We propose a homology theory for locally compact spaces with ends in which the ends play a special role. The approach is motivated by results for graphs with ends, where it has been highly successful. But it was unclear how the original…

Large language models (LLMs) excel across diverse natural language processing tasks but face resource demands and limited context windows. Although techniques like pruning, quantization, and token dropping can mitigate these issues, their…

Existing algorithms for aligning cross-lingual word vector spaces assume that vector spaces are approximately isomorphic. As a result, they perform poorly or fail completely on non-isomorphic spaces. Such non-isomorphism has been…

Without any explicit cross-lingual training data, multilingual language models can achieve cross-lingual transfer. One common way to improve this transfer is to perform realignment steps before fine-tuning, i.e., to train the model to build…

The extent to which a sequence of finite length differs from a shifted version of itself is measured by its aperiodic autocorrelations. Of particular interest are sequences whose entries are 1 or -1, called binary sequences, and sequences…

Existing large language models (LLMs) evaluation methods typically focus on testing the performance on some closed-environment and domain-specific benchmarks with human annotations. In this paper, we explore a novel unsupervised evaluation…

The nearest-neighbor level spacing distribution is numerically investigated by directly diagonalizing disordered Anderson Hamiltonians for systems of sizes up to 100 x 100 x 100 lattice sites. The scaling behavior of the level statistics is…

String matching is the problem of finding all the occurrences of a pattern in a text. We propose improved versions of the fast family of string matching algorithms based on hashing $q$-grams. The improvement consists of considering minimal…

All poetic forms come from somewhere. Prosodic templates can be copied for generations, altered by individuals, imported from foreign traditions, or fundamentally changed under the pressures of language evolution. Yet these relationships…

Synchronization is critical for system level behaviour in physical, chemical, biological and social systems. Empirical evidence has shown that the network topology strongly impacts the synchronizablity of the system, and the analysis of…

Single-arm studies in the early development phases of new treatments are not uncommon in the context of rare diseases or in paediatrics. If an assessment of efficacy is to be made at the end of such a study, the observed endpoints can be…

Selective labels are a common feature of consequential decision-making applications, referring to the lack of observed outcomes under one of the possible decisions. This paper reports work in progress on learning decision policies in the…

Many schools in large urban districts have more applicants than seats. Centralized school assignment algorithms ration seats at over-subscribed schools using randomly assigned lottery numbers, non-lottery tie-breakers like test scores, or…

Classifier predictions often rely on the assumption that new observations come from the same distribution as training data. When the underlying distribution changes, so does the optimal classification rule, and performance may degrade. We…

Handwritten text recognition aims to convert visual input into machine-readable text, and it remains challenging due to the evolving and context-dependent nature of handwriting. Character sets change over time, and character frequency…