arXiv:2512.10817 · v2

Extrapolation of Periodic Functions Using Binary Encoding of Continuous Numerical Values

首次提交 2025-12-12 01:08

版本更新 2026-11-12 02:42

雷达观测 2026-11-13 14:16

摘要

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.