Extrapolation of Periodic Functions Using Binary Encoding of Continuous Numerical Values

Brian P. Powell, Jordan A. Caraballo-Vega, Mark L. Carroll, Thomas Maxwell, Andrew Ptak +2 more
12/11/2025
cs.LGcs.AIcs.CV

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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.

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Cite this paper

@article{powell2025extrapolation,
  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},
  year   = {2025},
  eprint = {2512.10817},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2512.10817v1}
}

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