https://github.com/alibayeh/trukan
TruKAN: Kolmogorov-Arnold Networks Using Truncated Power Functions
https://github.com/alibayeh/trukan
compiler kan-compiler kolmogorov-arnold-network kolmogorov-arnold-networks kolmogorov-arnold-representation physics-informed-neural-networks plotting-library sympy-expressions trukan truncated-power truncated-power-functions
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TruKAN: Kolmogorov-Arnold Networks Using Truncated Power Functions
- Host: GitHub
- URL: https://github.com/alibayeh/trukan
- Owner: alibayeh
- License: mit
- Created: 2025-12-22T16:33:13.000Z (6 months ago)
- Default Branch: main
- Last Pushed: 2026-06-20T03:41:50.000Z (9 days ago)
- Last Synced: 2026-06-20T05:23:09.977Z (9 days ago)
- Topics: compiler, kan-compiler, kolmogorov-arnold-network, kolmogorov-arnold-networks, kolmogorov-arnold-representation, physics-informed-neural-networks, plotting-library, sympy-expressions, trukan, truncated-power, truncated-power-functions
- Language: Python
- Homepage:
- Size: 66.4 KB
- Stars: 1
- Watchers: 0
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
- awesome-kan - TruKAN
README
# trukan
[](https://arxiv.org/abs/2602.03879)
**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](https://arxiv.org/abs/2602.03879)
**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
- [x] Compiler
- [x] Plotter
- [x] TruKAN
- [x] CustomKAN (ChebyKAN, EfficientKAN, SineKAN)
- [ ] Pruner
- [x] TruKAN
- [ ] CustomKAN
## 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:
```bibtex
@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](https://spdx.org/licenses/MIT.html) license.
## Acknowledgements
The design and implementation ideas for the compiler, pruner, and plotter components were influenced by the approaches used in PyKAN.