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: Artificial Intelligence · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Computer Vision & Pattern Recognition · Depth: Expert, quick

Summary

Structural Kolmogorov-Arnold Convolutions (KANs) offer a parameter-efficient alternative to traditional per-edge Convolutional KANs, which are expressive but parameter-heavy. This approach places learnable univariate functions within the convolution's structure, acting on either pixel values or the filter shape. Three realisations are explored: SV-KAN, applying a shared univariate function to values with a static spatial filter; AG-KAN, adding a content-adaptive Gaussian gate; and RF-KAN, building filters from oriented ridge profiles using a localized oscillatory wavelet basis with content-adaptive amplitudes. Under a four-layer protocol, RF-KAN and SV-KAN achieved 88.47±0.10% and 88.20±0.31% on CIFAR-10, and 64.40±0.19% and 64.57±0.30% on CIFAR-100, with approximately 0.4M parameters. These models outperformed plain convolutions and per-edge KANs, including the official Gram variant, using about a fifth of the parameters. RF-KAN's gain is attributed to its localized oscillatory basis and content adaptivity, with the learned shape being a critical component.

Key takeaway

For AI Scientists and Machine Learning Engineers optimizing model efficiency in computer vision, Structural KANs present a compelling alternative. You should evaluate RF-KAN and SV-KAN for your next image classification project, especially when parameter count is a critical constraint. These models demonstrate superior performance on CIFAR-10 and CIFAR-100 with roughly a fifth of the parameters compared to per-edge KANs, indicating a significant advantage for deploying efficient, high-accuracy solutions.

Key insights

Structural KANs achieve parameter efficiency and strong performance by applying learnable functions to convolution structure or filter shape.

Principles

• Learnable functions in convolution structure reduce parameters.
• Content adaptivity enhances model performance.
• Localized oscillatory bases are effective for filter shapes.

Method

Design KANs by placing learnable univariate functions on pixel values (SV-KAN, AG-KAN) or filter shape (RF-KAN) within the convolutional structure.

In practice

• Consider structural KANs for efficient image classification.
• Explore content-adaptive filter designs for improved accuracy.
• Investigate oscillatory bases for convolutional kernel construction.

Topics

• Kolmogorov-Arnold Networks
• Convolutional Neural Networks
• Parameter Efficiency
• Image Classification
• Model Architecture
• Computer Vision

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

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Editorial summary, takeaway, and curation by AIssential. Original article published by Artificial Intelligence.