Related papers: A Tutorial on Multi-time Scale Optimization Models…

Efficient motion planning algorithms are of central importance for deploying robots in the real world. Unfortunately, these algorithms often drastically reduce the dimensionality of the problem for the sake of feasibility, thereby foregoing…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

The number of parameters in large-scale language models based on transformers is gradually increasing, and the scale of computing clusters is also growing. The technology of quickly mobilizing large amounts of computing resources for…

This paper introduces a multiscale analysis based on optimal piecewise linear approximations of time series. An optimality criterion is formulated and on its base a computationally effective algorithm is constructed for decomposition of a…

Pipeline parallelism (PP) has become a standard technique for scaling large language model (LLM) training across multiple devices. However, despite recent progress in reducing memory consumption through activation offloading, existing…

Optimization problems in engineering and applied mathematics are typically solved in an iterative fashion, by systematically adjusting the variables of interest until an adequate solution is found. The iterative algorithms that govern these…

Modular design maximizes utility by using standardized components in large-scale systems. From a manufacturing perspective, it supports green technology by reducing material waste and improving reusability. Industrially, it offers economic…

AI accelerator processing capabilities and memory constraints largely dictate the scale in which machine learning workloads (e.g., training and inference) can be executed within a desirable time frame. Training a state of the art,…

The family of Multiscale Hybrid-Mixed (MHM) finite element methods has received considerable attention from the mathematics and engineering community in the last few years. The MHM methods allow solving highly heterogeneous problems on…

Multimodal recommendation systems are increasingly popular for their potential to improve performance by integrating diverse data types. However, the actual benefits of this integration remain unclear, raising questions about when and how…

To mitigate dissipative effects from environmental interactions and efficiently stabilize quantum states, time-optimal control has emerged as an effective strategy for open quantum systems. This paper extends the framework by incorporating…

Mass scaling is widely used in finite element models of structural dynamics for increasing the critical time step of explicit time integration methods. While the field has been flourishing over the years, it still lacks a strong theoretical…

Scheduling query execution plans is a particularly complex problem in shared-nothing parallel systems, where each site consists of a collection of local time-shared (e.g., CPU(s) or disk(s)) and space-shared (e.g., memory) resources and…

Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization…

Enabling LLMs to improve their outputs by using more test-time computation is a critical step towards building generally self-improving agents that can operate on open-ended natural language. In this paper, we study the scaling of…

Mathematical models simulate various events under different conditions, enabling an early overview of the system to be implemented in practice, reducing the waste of resources and in less time. In project optimization, these models play a…

Test-time scaling (TTS) -- the dynamic allocation of compute during inference -- is a promising direction for improving reasoning in large language models (LLMs). However, a systematic comparison of well-known TTS strategies under identical…

To integrate strategic, tactical and operational decisions, the two-stage optimization has been widely used to guide dynamic decision making. In this paper, we study the two-stage stochastic programming for complex systems with unknown…

Modern computational advertising platforms typically rely on recommendation systems to predict user responses, such as click-through rates, conversion rates, and other optimization events. To support a wide variety of product surfaces and…

The heterogeneous multi-scale method (HMM) is a general strategy for dealing with problems involving multi-scales, with multi-physics, using multi-grids. It not only unifies several existing multi-scale methods, but also provide a…