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arXiv · 2512.10817

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·Greg Olmschenk·Jorge Martinez-Palomera
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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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Brian P. Powell, Jordan A. Caraballo-Vega, Mark L. Carroll, Thomas Maxwell, Andrew Ptak, Greg Olmschenk, Jorge Martinez-Palomera. 2025-12-11. Extrapolation of Periodic Functions Using Binary Encoding of Continuous Numerical Values. https://arxiv.org/abs/2512.10817

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