# InKAN: B-Spline KANs via Truncated Power Form

arXiv: https://arxiv.org/abs/2609.01956 · HTML: https://mlsanity.com/paper/2609.01956/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 16 references that are in the map.
- First posted on arXiv 2 Sep 2026.

## Builds on (most cited first, 8 of 8)

- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [ExSpliNet: An interpretable and expressive spline-based neural network](https://mlsanity.com/paper/2205.01510/) (2022)
- [PowerMLP: An Efficient Version of KAN](https://mlsanity.com/paper/2412.13571/) (2024)
- [MatrixKAN: Parallelized Kolmogorov-Arnold Network](https://mlsanity.com/paper/2502.07176/) (2025)
- [Lookup multivariate Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2509.07103/) (2025)
- [TruKAN: Towards More Efficient Kolmogorov-Arnold Networks Using Truncated Power Functions](https://mlsanity.com/paper/2602.03879/) (2026)
- [Multilevel Training for Kolmogorov Arnold Networks](https://mlsanity.com/paper/2603.04827/) (2026)

## Built on by (most cited first, 2 of 2)

- [Recovering Governing Dynamics from Distributed Observations via Exact Spline Merging](https://mlsanity.com/paper/2609.16579/) (2026)
- [Attention Manifolds: Steering or Blocking Language Models by Editing Learned B-Spline Surfaces](https://mlsanity.com/paper/2610.00257/) (2026)

## Abstract (arXiv)

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, eliminating recursion, span lookup, and scatter-gather operations; (2) a bounded-coordinate evaluation that clamps the normalized input to [0, k+1], preventing the growth of cancellation error at large off-support coordinates; and (3) an open-source package (pip install inkan). In the tested configurations, InKAN has 2.8--3.5× lower forward-pass latency than the Cox-de Boor recursion. Partition-of-unity errors remain below 10-5 for grid sizes up to 200.