Kolmogorov-Arnold networks (KANs) have gained attention for replacing fixed scalar weights with learnable univariate functions. However, most spectral implementations of KANs lean on Chebyshev polynomials, which are naturally defined only on a bounded interval. That forces practitioners to apply a saturating squashing function to the inputs before the polynomial expansion, which can distort the learning problem.
The new arXiv paper, FHKAN, proposes using fractional Hermite polynomials instead. Because Hermite polynomials live on the real line, they do not require the same bounded-domain workaround. The authors position this as a way to make KANs more natural for both data-driven regression and physics-informed tasks, where inputs may not be easily confined to a fixed range.
The abstract is truncated in the source, so details on the exact architecture, training procedure, and benchmark results are not yet available. But the core motivation is clear: moving beyond Chebyshev bases could remove a preprocessing step that many spectral KANs currently depend on.