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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

R2 v1 2026-07-01T08:20:52.537Z