Data-Driven Variational Basis Learning Beyond Neural Networks: A Non-Neural Framework for Adaptive Basis Discovery

ArXi:2605.05221v1 Announce Type: new Classical representation systems such as Fourier series, wavelets, and fixed dictionaries provide analytically tractable basis expansions, but they are not intrinsically adapted to the empirical structure of modern high-dimensional data. Neural networks overcome this limitation by learning features from data, yet they do so through layered nonlinear parameterizations that often sacrifice interpretability, explicit control over basis structure, and mathematical transparency.