{"ID":2830349,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.10817","arxiv_id":"2512.10817","title":"Extrapolation of Periodic Functions Using Binary Encoding of Continuous Numerical Values","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.","short_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) s...","url_abs":"https://arxiv.org/abs/2512.10817","url_pdf":"https://arxiv.org/pdf/2512.10817v1","authors":"[\"Brian P. Powell\",\"Jordan A. Caraballo-Vega\",\"Mark L. Carroll\",\"Thomas Maxwell\",\"Andrew Ptak\",\"Greg Olmschenk\",\"Jorge Martinez-Palomera\"]","published":"2025-12-11T17:08:28Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"cs.CV\",\"stat.ML\"]","methods":"[]","has_code":false}