相关论文: Optimal Design of Multiple Description Lattice Vec…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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,…

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…

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}…

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…

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…

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…

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…

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…

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…