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We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are…

Numerical Analysis · Mathematics 2019-09-06 Lutz Kämmerer

This paper studies the multivariate approximation of functions in weighted Korobov spaces using multiple rank-1 lattice rules. It has been shown by K\"{a}mmerer and Volkmer (2019) that algorithms based on multiple rank-1 lattices achieve…

Numerical Analysis · Mathematics 2026-04-03 Mou Cai , Takashi Goda

This paper provides the theoretical foundation for the construction of lattice algorithms for multivariate $L_2$ approximation in the worst case setting, for functions in a periodic space with general weight parameters. Our construction…

Numerical Analysis · Mathematics 2026-03-04 Ronald Cools , Frances Y. Kuo , Dirk Nuyens , Ian H. Sloan

In conventional prediction tasks, a machine learning algorithm outputs a single best model that globally optimizes its objective function, which typically is accuracy. Therefore, users cannot access the other models explicitly. In contrast…

Machine Learning · Computer Science 2019-06-06 Kentaro Kanamori , Satoshi Hara , Masakazu Ishihata , Hiroki Arimura

The key-value (KV) cache is a foundational optimization in Transformer-based large language models (LLMs), eliminating redundant recomputation of past token representations during autoregressive generation. However, its memory footprint…

Machine Learning · Computer Science 2026-03-24 Yichun Xu , Navjot K. Khaira , Tejinder Singh

In this paper we present the first known deterministic algorithm for the construction of multiple rank-1 lattices for the approximation of periodic functions of many variables. The algorithm works by converting a potentially large…

Numerical Analysis · Mathematics 2020-03-24 Craig Gross , Mark A. Iwen , Lutz Kämmerer , Toni Volkmer

This work concerns the analysis and design of distributed first-order optimization algorithms over time-varying graphs. The goal of such algorithms is to optimize a global function that is the average of local functions using only local…

Optimization and Control · Mathematics 2020-02-17 Akhil Sundararajan , Bryan Van Scoy , Laurent Lessard

We address the connection between the multiple-description (MD) problem and Delta-Sigma quantization. The inherent redundancy due to oversampling in Delta-Sigma quantization, and the simple linear-additive noise model resulting from…

Information Theory · Computer Science 2009-07-15 Jan Ostergaard , Ram Zamir

How to efficiently serve LLMs in practice has become exceptionally challenging due to their prohibitive memory and computation requirements. In this study, we investigate optimizing the KV cache, whose memory footprint poses a critical…

Computation and Language · Computer Science 2025-06-10 Akshat Sharma , Hangliang Ding , Jianping Li , Neel Dani , Minjia Zhang

We study a randomized quadrature algorithm to approximate the integral of periodic functions defined over the high-dimensional unit cube. Recent work by Kritzer, Kuo, Nuyens and Ullrich (2019) shows that rank-1 lattice rules with a randomly…

Numerical Analysis · Mathematics 2023-04-28 Josef Dick , Takashi Goda , Kosuke Suzuki

Efficiently serving large language models (LLMs) requires batching of many requests to reduce the cost per request. Yet, with larger batch sizes and longer context lengths, the key-value (KV) cache, which stores attention keys and values to…

Computation and Language · Computer Science 2024-07-26 Zirui Liu , Jiayi Yuan , Hongye Jin , Shaochen Zhong , Zhaozhuo Xu , Vladimir Braverman , Beidi Chen , Xia Hu

A new parameter estimation algorithm, known as Sub-band Dual Frequency Conjugate LVT (SDFC-LVT), is proposed for the ground moving targets. This algorithm first constructs two sub-band signals with different central frequencies. After that,…

Information Theory · Computer Science 2015-02-03 Jing Tian , Wei Cui , Si-liang Wu

We study how to construct compressed datasets that suffice to recover optimal decisions in linear programs with an unknown cost vector $c$ lying in a prior set $\mathcal{C}$. Recent work by Bennouna et al. provides an exact geometric…

Optimization and Control · Mathematics 2026-05-25 Yuhan Ye , Saurabh Amin , Asuman Ozdaglar

Lattice rules are among the most prominently studied quasi-Monte Carlo methods to approximate multivariate integrals. A rank-1 lattice rule to approximate an $s$-dimensional integral is fully specified by its generating vector $\mathbf{z}…

Numerical Analysis · Mathematics 2020-01-10 Adrian Ebert , Peter Kritzer , Dirk Nuyens , Onyekachi Osisiogu

Large Language Model (LLM) inference is increasingly constrained by memory bandwidth, with frequent access to the key-value (KV) cache dominating data movement. While attention sparsity reduces some memory traffic, the relevance of past…

Hardware Architecture · Computer Science 2025-09-16 Yunhua Fang , Rui Xie , Asad Ul Haq , Linsen Ma , Kaoutar El Maghraoui , Naigang Wang , Meng Wang , Liu Liu , Tong Zhang

We present an algorithm for the exact computer-aided construction of the Voronoi cells of lattices with known symmetry group. Our algorithm scales better than linearly with the total number of faces and is applicable to dimensions beyond…

Information Theory · Computer Science 2025-10-28 Daniel Pook-Kolb , Bruce Allen , Erik Agrell

As the length of input text increases, the key-value (KV) cache in LLMs imposes prohibitive GPU memory costs and limits long-context inference on resource constrained devices. Existing approaches, such as KV quantization and pruning, reduce…

Machine Learning · Computer Science 2025-12-24 Tenghui Li , Guoxu Zhou , Xuyang Zhao , Yuning Qiu , Qibin Zhao

This paper investigates the problem of finding an optimal nonbinary index assignment from (M) quantization levels of a maximum entropy scalar quantizer to (M)-PSK symbols transmitted over a symmetric memoryless channel with additive noise…

Information Theory · Computer Science 2021-07-01 Yunxiang Yao , Wai Ho Mow

Large Language Models (LLMs) have demonstrated remarkable capabilities but typically require extensive computational resources and memory for inference. Post-training quantization (PTQ) can effectively reduce these demands by storing…

Machine Learning · Computer Science 2026-01-27 Xi Zhang , Xiaolin Wu , Jiamang Wang , Weisi Lin

Large Language Models (LLMs) have achieved remarkable progress across reasoning, generation, and decision-making tasks, yet deploying them on mobile, embedded, and edge devices remains particularly challenging. On-device LLM inference is…

Computer Vision and Pattern Recognition · Computer Science 2026-04-07 Sayed Pedram Haeri Boroujeni , Niloufar Mehrabi , Patrick Woods , Gabriel Hillesheim , Abolfazl Razi