Structural Kolmogorov-Arnold Convolutions: Learnable Function on the Values or the Filter Shape as Parameter-Efficient Alternative to Per-Edge Convolutional KANs

2026-06-23 · Source: Takara TLDR - Daily AI Papers · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, medium

Summary

Structural Kolmogorov-Arnold Convolutions (KANs) are introduced as a parameter-efficient alternative to traditional per-edge Convolutional KANs, which are often parameter-heavy and prone to overfitting. This new approach places learnable univariate functions within the convolution's structure, either acting on pixel values or the filter shape. Three realizations are explored: SV-KAN, AG-KAN, and RF-KAN. Notably, RF-KAN and SV-KAN achieve 88.47±0.10% and 88.20±0.31% accuracy on CIFAR-10, and 64.40±0.19% and 64.57±0.30% on CIFAR-100, using approximately 0.4M parameters. These models outperform plain convolutions and existing per-edge KANs, including the official Gram variant, at roughly a fifth of the parameter count. RF-KAN's performance gain is attributed to its intrinsically localized oscillatory basis and content adaptivity.

Key takeaway

For Machine Learning Engineers designing efficient convolutional neural networks, consider adopting Structural Kolmogorov-Arnold Networks (KANs). These models, particularly RF-KAN and SV-KAN, offer competitive accuracy on datasets like CIFAR-10 and CIFAR-100 while drastically reducing parameter counts to about 0.4M. You can achieve strong performance at roughly a fifth of the parameters compared to traditional per-edge KANs, making them ideal for resource-constrained environments or large-scale deployments.

Key insights

Learnable functions in convolutional KANs are more efficient when applied to filter structure or shared values, not individual kernel entries.

Principles

• Structural KANs reduce parameters significantly.
• Localized oscillatory bases enhance performance.
• Content adaptivity improves model accuracy.

Method

The paper explores three realizations: SV-KAN (shared univariate function on values), AG-KAN (shared value function with Gaussian gate), and RF-KAN (learnable functions on filter shape using Morlet wavelet basis).

In practice

• Implement KANs with structural function placement.
• Explore Morlet wavelet bases for filter shapes.
• Integrate content-adaptive mechanisms.

Topics

• Kolmogorov-Arnold Networks
• Convolutional Neural Networks
• Parameter Efficiency
• Neural Network Architectures
• Image Classification
• Wavelet Basis Functions

Code references

• hoangthangta/All-KAN

Best for: Research Scientist, Computer Vision Engineer, AI Scientist, Machine Learning Engineer, AI Architect

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Editorial summary, takeaway, and curation by AIssential. Original article published by Takara TLDR - Daily AI Papers.