Dimensions overall score 7.0

• Hybrid FI-KAN outperforms standard KAN at every Hölder regularity level from α=0.2 to α=2.0, with improvements ranging from 1.3x to 33x.result 95%
• FI-KAN achieves up to 6.3x reduction in mean squared error (MSE) over KAN on fractal targets, maintaining a 4.7x advantage at 5 dB signal-to-noise ratio.result 95%
• Hybrid FI-KAN achieves up to 79x improvement over KAN on rough-coefficient diffusion PDE solutions and 3.5x improvement on L-shaped domain corner singularities.result 95%
• Pure FI-KAN underperforms on smooth targets while dominating on rough targets, demonstrating that basis geometry must match target regularity.result 90%
• FI-KAN incorporates learnable fractal interpolation function (FIF) bases from iterated function system (IFS) theory into KAN, with two variants: Pure FI-KAN and Hybrid FI-KAN.method 95%
• The IFS contraction parameters give each edge a differentiable fractal dimension that adapts to target regularity during training.technical 90%
• A fractal dimension regularizer provides interpretable complexity control, and its learned values recover the true fractal dimension of each target.technical 85%
• FI-KAN is not a general-purpose replacement for KAN but a principled extension for function classes with non-trivial geometric regularity.limitation 90%

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