发表机构
University of Minnesota, Twin Cities（明尼苏达大学双城分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对现有编码计算未利用数据内在结构的问题，提出流形感知通用编码策略，在神经网络推理和高维多项式评估实验中，该策略可显著降低抗掉队节点场景下的均方恢复误差。
AI 中文摘要
现有编码计算设计未明确利用输入数据的内在结构。在通信系统中，统计结构和冗余常通过信源编码（或压缩）去除后再应用信道编码，然而该原则无法直接迁移至编码计算。在诸多计算任务，尤其是机器学习中，数据结构正是计算用于推断输出或学习有意义模式的关键，因此编码计算方案应在编码设计中保留并利用该结构，而非通过信源编码忽略或消除它。这一观察为编码构造提供了不同视角：许多信道编码方案（如里德-所罗门码）通过在选定点评估低维代数表示生成编码符号，而许多高维数据集天然集中在低维流形附近。本文利用这种内在几何，设计遵循数据自然流形的编码样本，而非强加与数据分布无关的人工低维结构。受基于图的流形学习启发，本文提出面向通用编码计算（GCC）的流形感知编码策略。神经网络推理和高维多项式评估实验表明，与标准GCC相比，所提策略在存在掉队节点时，能持续显著降低均方恢复误差。
英文摘要
Existing coded-computing designs do not explicitly exploit the intrinsic structure of the input data. In communication systems, statistical structure and redundancy are often removed through source coding (or compression) before channel coding is applied. This principle, however, does not transfer directly to coded computation. In many computational tasks, particularly in machine learning, the structure of the data is precisely what the computation seeks to exploit to infer outputs or learn meaningful patterns. Consequently, coded-computing schemes should preserve and leverage this structure in their code design, rather than ignoring or eliminating it through source coding. This observation motivates a different perspective on code construction. In many channel-coding schemes, such as Reed-Solomon codes, coded symbols are generated by evaluating a low-dimensional algebraic representation at selected points. In contrast, many high-dimensional datasets naturally concentrate near low-dimensional manifolds. In this paper, we exploit this intrinsic geometry by designing coded samples that follow the natural manifold of the data, rather than imposing an artificial low-dimensional structure unrelated to the data distribution. Inspired by graph-based manifold learning, we propose a manifold-aware encoding strategy for general coded computing (GCC). Experiments on neural network inference and high-dimensional polynomial evaluation demonstrate that the proposed strategy consistently and significantly reduces the mean squared recovery error under straggling compared with standard GCC.
Comments5 pages, 4 figures
