arXiv cs.AI· Brian P. Powell, Jordan A. Caraballo-Vega, Mark L. Carroll, Thomas Maxwell, Andrew Ptak, Greg Olmschenk, Jorge Martinez-Palomera·· 1 天前AI 评分24
用二进制编码连续数值：MLP 实现周期函数外推的新方法 NB2E
Extrapolation of Periodic Functions Using Binary Encoding of Continuous Numerical Values
AI 导读
研究者提出 Normalized Base-2 Encoding（NB2E）连续数值编码方法，让普通多层感知机（MLP）在不知函数形式的情况下成功外推四种周期波形。
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