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Generalized Linear Models (GLM) form a wide class of regression and classification models, where prediction is a function of a linear combination of the input variables. For statistical inference in high dimension, sparsity inducing…
Implicit-explicit (IMEX) time stepping methods can efficiently solve differential equa- tions with both stiff and nonstiff components. IMEX Runge-Kutta methods and IMEX linear multistep methods have been studied in the literature. In this…
In this paper, we consider a class of possibly nonconvex, nonsmooth and non-Lipschitz optimization problems arising in many contemporary applications such as machine learning, variable selection and image processing. To solve this class of…
Advancements in large language models (LLMs) have led to a surge of prompt engineering (PE) techniques that can enhance various requirements engineering (RE) tasks. However, current LLMs are often characterized by significant uncertainty…
We show that standard extragradient methods (i.e. mirror prox and dual extrapolation) recover optimal accelerated rates for first-order minimization of smooth convex functions. To obtain this result we provide a fine-grained…
Despite the rapid progress that existing automated feedback methods have made in correcting the output of large language models (LLMs), these methods cannot be well applied to the relation extraction (RE) task due to their designated…
A growing body of literature has been leveraging techniques of machine learning (ML) to build novel approaches to approximating the solutions to partial differential equations. Noticeably absent from the literature is a systematic…
This article proposes a new class of general linear method with $p=q$ and $r=s=p+1$. The construction of the present method is carried out using order conditions and error minimization subject to $A$- stability constraints. The proposed…
Model-free deep reinforcement learning (RL) algorithms have been widely used for a range of complex control tasks. However, slow convergence and sample inefficiency remain challenging problems in RL, especially when handling continuous and…
The multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared to…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
Recent advances in large language models (LLMs) have demonstrated that reinforcement learning with verifiable rewards (RLVR) can significantly enhance reasoning abilities by directly optimizing correctness, rather than relying solely on…
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…
This paper introduces two decomposition-based methods for two-block mixed-integer linear programs (MILPs), which aim to take advantage of separable structures of the original problem by solving a sequence of lower-dimensional MILPs. The…
Large Language Models (LLMs) hold significant promise for mathematics education, yet they often struggle with complex mathematical reasoning. While Retrieval-Augmented Generation (RAG) mitigates these issues by grounding LLMs in external…
Despite the prevalence of retrieval-augmented language models (RALMs), the seamless integration of these models with retrieval mechanisms to enhance performance in document-based tasks remains challenging. While some post-retrieval…
We consider the construction of semi-implicit linear multistep methods which can be applied to time dependent PDEs where the separation of scales in additive form, typically used in implicit-explicit (IMEX) methods, is not possible. As…
Empirical scaling laws for language models have encouraged the development of ever-larger LLMs, despite their growing computational and memory costs. Sparse Mixture-of-Experts (MoEs) offer a promising alternative by activating only a subset…
Linear Mixed-Effects (LME) models are a fundamental tool for modeling clustered data, including cohort studies, longitudinal data analysis, and meta-analysis. The design and analysis of variable selection methods for LMEs is considerably…
Explicit stabilized methods are highly efficient time integrators for large and stiff systems of ordinary differential equations especially when applied to semi-discrete parabolic problems. However, when local spatial mesh refinement is…