InKAN: B-Spline KANs via Truncated Power Form

תקציר מקורי באנגליתarXiv:2609.01956v3 Announce Type: replace 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. InKAN 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. The resulting expression computes exact B-spline basis values: the same mathematical function as the Cox-de Boor recursion, evaluated without sequential passes. This paper documents three contributions: (1) an implementation structured for torch . compile fusion