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Chain-of-Thought (CoT) prompting symbolized a huge improvement of reasoning capabilities of Large Language Models (LLMs). However, scaling up test-time computation yields extensive CoT sequences, introducing severe inference latency and…

As computers reach exascale and beyond, the incidence of faults will increase. Solutions to this problem are an active research topic. We focus on strategies to make the preconditioned conjugate gradient (PCG) solver resilient against node…

This work gives the asymptotic error distribution of the stochastic Runge--Kutta (SRK) method of strong order $1$ applied to Stratonovich-type stochastic differential equations. For dealing with the implicitness introduced in the diffusion…

We study unconstrained smooth convex optimization under stochastic first- and zeroth-order oracles subject only to finite-moment bounds, naturally admitting persistent bias and heavy-tailed noise. In this hostile environment, integrating…

This article extends the theory of dual-consistent summation-by-parts (SBP) and generalized SBP (GSBP) time-marching methods by showing that they are implicit Runge-Kutta schemes. Through this connection, the accuracy theory for the…

We consider the efficient numerical solution of coupled dynamical systems, consisting of a small nonlinear part and a large linear time invariant part, possibly stemming from spatial discretization of an underlying partial differential…

Low-storage explicit Runge-Kutta schemes are particularly popular for the numerical integration of time-dependent partial differential equations based on the method-of-lines due to their efficiency and their reduced memory requirements. We…

This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. The proposed methods are based on a specific subset of explicit one-step…

From logistics to the natural sciences, combinatorial optimisation on graphs underpins numerous real-world applications. Reinforcement learning (RL) has shown particular promise in this setting as it can adapt to specific problem structures…

Retrieval-Augmented Generation (RAG) has emerged as a powerful paradigm for Large Language Models (LLMs) to address knowledge-intensive queries requiring domain-specific or up-to-date information. To handle complex multi-hop questions that…

Fully implicit Runge-Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly used in practice with numerical PDEs due to the difficulty…

Despite the superior performance of Large language models on many NLP tasks, they still face significant limitations in memorizing extensive world knowledge. Recent studies have demonstrated that leveraging the Retrieval-Augmented…

Retrieval-Augmented Generation (RAG) encounters efficiency challenges when scaling to massive knowledge bases while preserving contextual relevance. We propose Hash-RAG, a framework that integrates deep hashing techniques with systematic…

Large Language Models (LLMs) have demonstrated impressive ability in generation and reasoning tasks but struggle with handling up-to-date knowledge, leading to inaccuracies or hallucinations. Retrieval-Augmented Generation (RAG) mitigates…

Robots are increasingly deployed in dynamic and crowded environments, such as urban areas and shopping malls, where efficient and robust navigation is crucial. Traditional risk-based motion planning algorithms face challenges in such…

The increasing adoption of Electric Vehicles (EVs) for service and goods distribution operations has led to the emergence of Electric Vehicle Routing Problems (EVRPs), a class of vehicle routing problems addressing the unique challenges…

Deep reinforcement learning (DRL) has been used to learn effective heuristics for solving complex combinatorial optimisation problem via policy networks and have demonstrated promising performance. Existing works have focused on solving…

Retrieval-augmented generation (RAG), which combines large language models (LLMs) with retrievals from external knowledge databases, is emerging as a popular approach for reliable LLM serving. However, efficient RAG serving remains an open…

The Container Relocation Problem (CRP) is concerned with finding a sequence of moves of containers that minimizes the number of relocations needed to retrieve all containers, while respecting a given order of retrieval. However, the…

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a…