Extrapolation of Periodic Functions Using Binary Encoding of Continuous Numerical Values
Machine Learning
2025-12-12 v1 Artificial Intelligence
Computer Vision and Pattern Recognition
Machine Learning
Abstract
We report the discovery that binary encoding allows neural networks to extrapolate periodic functions beyond their training bounds. 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 diverse periodic signals without prior knowledge of their functional form. Internal activation analysis reveals that NB2E induces bit-phase representations, enabling MLPs to learn and extrapolate signal structure independently of position.
Cite
@article{arxiv.2512.10817,
title = {Extrapolation of Periodic Functions Using Binary Encoding of Continuous Numerical Values},
author = {Brian P. Powell and Jordan A. Caraballo-Vega and Mark L. Carroll and Thomas Maxwell and Andrew Ptak and Greg Olmschenk and Jorge Martinez-Palomera},
journal= {arXiv preprint arXiv:2512.10817},
year = {2025}
}
Comments
Submitted to JMLR, under review