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.

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

• Compiler
• Plotter
  • TruKAN
  • CustomKAN (ChebyKAN, EfficientKAN, SineKAN)
• Pruner
  • TruKAN
  • CustomKAN

• Compile a SymPy symbolic expression into a TruKan model.

• 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 isoutput_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.

• 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.

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"
}

trukan is distributed under the terms of the MIT license.

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