arXiv cs.AI· Brian P. Powell, Jordan A. Caraballo-Vega, Mark L. Carroll, Thomas Maxwell, Andrew Ptak, Greg Olmschenk, Jorge Martinez-Palomera·· 3 小时前AI 评分35
用连续数值的二进制编码（NB2E）实现 MLP 对周期函数的外推
Extrapolation of Periodic Functions Using Binary Encoding of Continuous Numerical Values
AI 导读
arXiv 论文提出归一化二进制编码（NB2E）方法用于编码连续数值，实验显示普通 MLP 借助该编码无需知道函数形式即可外推四种周期波形。对比发现，固定 Fourier 编码仅在归一化域内信号周期数为偶整数时外推良好，NB2E 在其他数值处退化平缓且更精确。研究限于单一 MLP 架构和一维精确周期合成信号，作者仅给出经验观察，未提出机理解释。
正文 · 原文
Abstract:We introduce Normalized Base-2 Encoding (NB2E) as a method for encoding continuous numerical values and demonstrate that, using this input encoding, vanilla multi-layer perceptrons (MLP) successfully extrapolate four periodic waveforms without prior knowledge of their functional form. We contrast this finding with fixed Fourier encoding, which extrapolates well when the number of signal cycles over the normalized domain is an even integer and loses coherence at most other values, whereas NB2E degrades gradually away from those values and, except near odd cycle counts, remains substantially more accurate. These findings are limited to a single MLP architecture trained on one synthetic, exactly periodic, one-dimensional signal at a time, with extrapolation extending only to the end of the normalized domain. We do not propose a mechanism for this phenomenon. Rather, we present empirical observations which merit further study.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computer Vision and Pattern Recognition (cs.CV); Machine Learning (stat.ML) |
| Cite as: | arXiv:2512.10817 [cs.LG] |
| (or arXiv:2512.10817v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2512.10817 arXiv-issued DOI via DataCite |
Submission history
From: Brian Powell [view email]
[v1]
Thu, 11 Dec 2025 17:08:28 UTC (7,547 KB)
[v2]
Wed, 11 Nov 2026 18:42:44 UTC (2,608 KB)
来源：arXiv cs.AI · arxiv.org