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While scaling laws for large language models (LLMs) during pre-training have been extensively studied, their behavior under reinforcement learning (RL) post-training remains largely unexplored. This paper presents a systematic empirical…

We investigate the theoretical foundations of the simulated tempering method and use our findings to design efficient algorithms. Employing a large deviation argument first used for replica exchange molecular dynamics [Plattner et al., J.…

Interacting quantum spin models are remarkably useful for describing different types of physical, chemical, and biological systems. Significant understanding of their equilibrium properties has been achieved to date, especially for the case…

We apply a meron cluster algorithm to the XY spin chain, which describes a quantum rotor. This is a multi-cluster simulation supplemented by an improved estimator, which deals with objects of half-integer topological charge. This method is…

Facilitated spin models on random graphs provide an ideal microscopic realization of the mode-coupling theory of supercooled liquids: they undergo a purely dynamic glass transition with no thermodynamic singularity. In this paper we study…

Large language models (LLMs), despite strong performance on complex mathematical problems, exhibit systematic limitations in counting tasks. This issue arises from the architectural limits of transformers, where counting is performed across…

By a high-order numerical homogenization method, a heterogeneous multiscale scheme was developed in Jin & Li (2022) for evolving differential equations containing two time scales. In this paper, we further explore the technique to propose…

The rapid growth of Large Language Models (LLMs) has been a driving force in transforming various domains, reshaping the artificial general intelligence landscape. However, the increasing computational and memory demands of these models…

Large Language Models (LLMs) are traditionally viewed as black-box algorithms, therefore reducing trustworthiness and obscuring potential approaches to increasing performance on downstream tasks. In this work, we apply an effective LLM…

LLM alignment ensures that large language models behave safely and effectively by aligning their outputs with human values, goals, and intentions. Aligning LLMs employ huge amounts of data, computation, and time. Moreover, curating data…

We study the intermittent dynamics and the fluctuations of the dynamic correlation function of a simple aging system. Given its size $L$ and its coherence length $\xi$, the system can be divided into $N$ independent subsystems, where…

Real world evolves in continuous time but computations are done from finite samples. Therefore, we study algorithms using finite observations in continuous-time linear dynamical systems. We first study the system identification problem, and…

Effective LLM training depends on predictable scaling of key quantities -- such as final loss and optimal hyperparameters -- with model and dataset size. Qiu et al. (2025) recently showed that this predictability can extend beyond scalars:…

We apply the recently developed critical minimum energy subspace scheme for the investigation of the random-field Ising model. We point out that this method is well suited for the study of this model. The density of states is obtained via…

We consider the problem of simultaneous variable selection and constant coefficient identification in high-dimensional varying coefficient models based on B-spline basis expansion. Both objectives can be considered as some type of model…

It is essential that all algorithms are exhaustively, somewhat, and intelligently evaluated. Nonetheless, evaluating the effectiveness of optimization algorithms equitably and fairly is not an easy process for various reasons. Choosing and…

Although Large Language Models (LLMs) excel in NLP tasks, they still need external tools to extend their ability. Current research on tool learning with LLMs often assumes mandatory tool use, which does not always align with real-world…

We propose a new method to analyze fluctuations in the strength function phenomena in highly excited nuclei. Extending the method of multifractal analysis to the cases where the strength fluctuations do not obey power scaling laws, we…

Despite their success in many natural language tasks, solving math problems remains a significant challenge for large language models (LLMs). A large gap exists between LLMs' pass-at-one and pass-at-N performance in solving math problems,…

A trend across most areas where simulation-driven development is used is the ever increasing size and complexity of the systems under consideration, pushing established methods of modeling and simulation towards their limits. This paper…