trukan

May 28, 2026 · View on GitHub

TruKAN is a Python package implementing a novel, efficient variation of Kolmogorov-Arnold Networks (KANs). It replaces the B-spline basis with truncated power functions derived from k-order spline theory, better interpretability, and strong performance on real-world tasks.

About TruKAN

TruKAN preserves the canonical KAN topology and learnable univariate activations but replaces the computationally heavy B-spline basis with a family of truncated power functions (x - t_j)_+^k combined with a low-order polynomial term. This design maintains full expressiveness while improved the performance.

Key advantages demonstrated in the paper:

Efficiency: Lower GPU memory compared to standard KAN (pykan) and some other variants.
Interpretability: Explicit decomposition into polynomial + truncated-power terms makes learned functions easy to analyze and visualize.
Flexibility: Supports both shared knots (more efficient) and individual knots (more expressive).
Performance: Outperforms MLP, standard KAN, and SineKAN on CIFAR-10/100, STL-10, and Oxford-IIIT Pets when integrated into an EfficientNet-V2 backbone.

Paper: TruKAN: Towards More Efficient Kolmogorov-Arnold Networks Using Truncated Power Functions
Authors: Ali Bayeh, Samira Sadaoui, Malek Mouhoub
arXiv: 2602.03879 (February 2026)

TruKAN Layer Structure

_{(a) Fixed-knot version (equal intervals)}

_{(b) Learnable-knot version (trainable knot positions with ordering constraints)}

Learned Activations

_{(a) Trained TruKAN}

_{(b) Pruned TruKAN}

Features

Compiler

Compile a SymPy symbolic expression into a TruKan model.

Design differences vs. pykan's compiler

Pykan pins each edge to a symbolic function using fix_symbolic, which writes to a parallel Symbolic_KANLayer. TruKan has no symbolic layer. Instead, we fit the truncated-power-basis coefficients to the target 1-D function via ordinary least squares over knots_range. The fit quality depends on how well a degree-degree truncated-power spline can represent the function; cubic (degree=3) is accurate for smooth elementary functions with a reasonably dense knot grid.
Pykan stores per-node and per-subnode affine parameters (node_scale, node_bias, subnode_scale, subnode_bias) as learnable tensors. TruKan only has bias_out per layer, and the constant basis function (the '1' in [1, u, u², u³, …]) already absorbs constant offsets. We fold every affine transformation extracted during tree-parsing directly into the least-squares target function so the compiled model is self-contained and needs no extra parameters.
Standard TruKan is a sum-only KAN: the output of each layer is output_j = Σ_i basis(x_i) @ coeffs[i, j, :] Expressions with products of distinct symbolic variables (e.g. x*y, sin(x)*cos(y)) cannot be represented and are rejected.

Generic Plotter & Pruner

Why it is generic?
- trukan tools work with any KAN-style model that follows a minimal interface:
  - Consistent naming convention.
  - Implementation of a single method that returns the numerical activation functions.
How it works?
- Any compatible KAN variation can be plotted automatically. No forking or rewriting of visualization code is required.

Citation

If you use this code in your research, please cite the following paper:

@ARTICLE{Bayeh2026TruKAN,
  title         = "{TruKAN}: Towards more efficient {Kolmogorov-Arnold}
                   networks using truncated power functions",
  author        = "Bayeh, Ali and Sadaoui, Samira and Mouhoub, Malek",  
  month         =  feb,
  year          =  2026,
  copyright     = "http://creativecommons.org/licenses/by/4.0/",
  archivePrefix = "arXiv",
  primaryClass  = "cs.CV",
  eprint        = "2602.03879"
}

License

trukan is distributed under the terms of the MIT license.

Acknowledgements

The design and implementation ideas for the compiler, pruner, and plotter components were influenced by the approaches used in PyKAN.