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Recent rehearsal-free continual learning (CL) methods guided by prompts achieve strong performance on vision tasks with non-stationary data but remain resource-intensive, hindering real-world edge deployment. We introduce resource-efficient…

Wave equations help us to understand phenomena ranging from earthquakes to tsunamis. These phenomena materialise over very large scales. It would be computationally infeasible to track them over a regular mesh. Yet, since the phenomena are…

In this paper we explore acceleration techniques for large scale nonconvex optimization problems with special focuses on deep neural networks. The extrapolation scheme is a classical approach for accelerating stochastic gradient descent for…

Large Reasoning Models (LRMs) have shown remarkable capabilities in solving complex problems through reinforcement learning (RL), particularly by generating long reasoning traces. However, these extended outputs often exhibit substantial…

While large language models (LLMs) have demonstrated impressive performance in question-answering tasks, their performance is limited when the questions require knowledge that is not included in the model's training data and can only be…

In this paper, we extend the implicit-explicit (IMEX) methods of Peer type recently developed in [Lang, Hundsdorfer, J. Comp. Phys., 337:203--215, 2017] to a broader class of two-step methods that allow the construction of super-convergent…

Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…

Multimodal Retrieval-Augmented Generation (MRAG) has shown promise in mitigating hallucinations in Multimodal Large Language Models (MLLMs) by incorporating external knowledge. However, existing methods typically adhere to rigid retrieval…

Multi-step retrieval-augmented generation (RAG) has become a widely adopted strategy for enhancing large language models (LLMs) on tasks that demand global comprehension and intensive reasoning. Although many RAG systems incorporate a…

Regular expression (RE) matching is a very common functionality that scans a text to find occurrences of patterns specified by an RE; it includes the simpler function of RE recognition. Here we address RE parsing, which subsumes matching by…

This paper describes a regularized variant of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex programs. It is shown that the pointwise iteration-complexity of the new method is better than the…

In this paper we present a second-order and continuous interpolation algorithm for cell-centered adaptive-mesh-refinement (AMR) grids. Continuity requirement poses a non-trivial problem at resolution changes. We develop a classification of…

The recursive Neville algorithm allows one to calculate interpolating functions recursively. Upon a judicious choice of the abscissas used for the interpolation (and extrapolation), this algorithm leads to a method for convergence…

When solving the time-dependent radiative transport equation (RTE), implicit time discretization is often employed for its robustness and stability. This results in a sequence of steady-state RTEs with identical cross-sections but varying…

Recently a new class of Monte Carlo methods, called Time Relaxed Monte Carlo (TRMC), designed for the simulation of the Boltzmann equation close to fluid regimes have been introduced. A generalized Wild sum expansion of the solution is at…

We contribute to advancing the understanding of Riemannian accelerated gradient methods. In particular, we revisit Accelerated Hybrid Proximal Extragradient(A-HPE), a powerful framework for obtaining Euclidean accelerated methods…

The Augmented Lagragian Method (ALM) and Alternating Direction Method of Multiplier (ADMM) have been powerful optimization methods for general convex programming subject to linear constraint. We consider the convex problem whose objective…

In this work, we propose a generalized alternating Anderson acceleration method, a periodic scheme composed of $t$ fixed-point iteration steps, interleaved with $s$ steps of Anderson acceleration with window size $m$, to solve linear and…

Computational multi-scale methods capitalize on a large time-scale separation to efficiently simulate slow dynamics over long time intervals. For stochastic systems, one often aims at resolving the statistics of the slowest dynamics. This…

Large Language Models (LLMs) increasingly rely on reinforcement learning with verifiable rewards (RLVR) to elicit reliable chain-of-thought reasoning. However, the training process remains bottlenecked by the computationally expensive…