Extrapolation of Periodic Functions Using Binary Encoding of Continuous Numerical Values
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Abstract (arXiv)
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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References · 9
- 2016SGDR: Stochastic Gradient Descent with Warm Restartscited by 5,045
- 2018Neural Ordinary Differential Equationscited by 3,779
- 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,238
- 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,200
- 2018Self-Attention with Relative Position Representationscited by 1,120
- 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,070
- 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 548
- 2016Extrapolation and learning equationscited by 110
- 2025The TESS Ten Thousand Catalog: 10,001 uniformly-vetted and -validated Eclipsing Binary Stars detected in Full-Frame Image data by machine learning and analyzed by citizen scientistscited by 2
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