Autoencoder–Based Image Representation Learning with Kolmogorov–Arnold Networks

Autoencoders are widely used for learning compact latent representations of images. While convolutional architectures dominate this area due to their ability to exploit spatial locality, recent developments in neural network design have introduced Kolmogorov–Arnold networks (KANs), which replace fixed activation functions with learnable univariate mappings derived from the Kolmogorov–Arnold superposition theorem. Although KAN-based autoencoders have recently been explored for image representation tasks, existing studies typically focus on limited datasets, fixed KAN formulations, or reconstruction accuracy solely. In this work, we present a KAN-based image autoencoder model that emphasizes representation quality, model complexity, and computational cost. We design and evaluate KAN-based and FastKAN-based autoencoders under strictly matched latent dimensionality constraints and compare them with a convolutional autoencoder baseline across multiple image datasets. Reconstruction quality is assessed using the mean squared error (MSE), which quantifies pixel-wise reconstruction errors, the peak signal-to-noise ratio (PSNR), which measures signal fidelity on a logarithmic scale, and the structural similarity index (SSIM), which reflects perceptual structural similarity. Experimental results demonstrate that KAN-based autoencoders achieve reconstruction quality comparable to convolutional autoencoders of the same representation size, with statistically significant improvements in the PSNR observed in several scenarios, while exhibiting distinct efficiency trade-offs. These findings clarify the practical role of Kolmogorov–Arnold networks in image autoencoder representation learning and highlight them as an alternative to convolutional architectures in low-resolution image settings.