FlashKAN: B-Spline KANs via Truncated Power Form

Abstract:Kolmogorov-Arnold Networks (KANs) place learnable B-spline activations on network edges rather than fixed activations on nodes. The standard Cox-de Boor recursion evaluates these activations through k sequential passes for degree-k splines, consuming over 90% of forward-pass time. FlashKAN replaces this recursion with the truncated power form, a classical result from approximation theory that expresses each uniform cubic B-spline as five (x)_+^3 terms at shifted knot positions. This paper makes three contributions: (1) a this http URL-fused implementation that collapses these operations into a single GPU kernel, eliminating all recursion, span lookup, and scatter-gather operations; (2) a bounded-coordinate stabilization that clamps the normalized input to [0, k+1], preventing the catastrophic cancellation that historically motivated the Cox-de Boor recursion; and (3) a production-ready, open-source package (pip install flashkan) that serves as a drop-in replacement for existing KAN layers.

Machine Learning (cs.LG); Numerical Analysis (math.NA)

arXiv:2609.01956 [cs.LG]

(or arXiv:2609.01956v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.01956 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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