Differentiable Image Compression via KAN-Driven Dynamic Quantization

The rapid evolution of visual data demands compression technologies that balance theoretical expressiveness with practical deployment constraints. Current learning-based approaches face dual challenges: non-differentiable quantization operations that hinder end-to-end optimization, and rigid architectural components limiting adaptability to diverse content characteristics. This paper introduces a novel neural compression framework that integrates principles from Kolmogorov-Arnold Networks (KANs) with dynamic quantization mechanisms. Our threefold contribution addresses these limitations through: (1) A spline-enhanced hybrid architecture combining KAN's adaptive nonlinearities with convolutional feature extraction, theoretically grounded in function decomposition theory; (2) A trainable quantization process employing content-dependent step sizes with bounded gradient approximation errors; (3) An autonomous rate control system that dynamically balances distortion and entropy constraints. Extensive evaluations demonstrate the framework's superiority in rate-distortion performance compared to state-of-the-art codecs, particularly in preserving high-frequency components critical for perceptual quality. Practical implementations reveal robust performance across standard benchmarks and emerging multimedia formats. Beyond immediate compression applications, this work establishes foundational insights for developing explainable neural codecs, suggesting promising extensions to video and volumetric data compression through adaptive basis function learning.