Kolmogorov-Arnold Energy Models: Fast, Interpretable Generative Modeling

arXiv:2506.14167 · cs.LG · Submitted 2025-06-17 · Read on arXiv

cs.LG

Submitted: 2025-06-17

Updated: 2026-09-16

Code: https://github.com/EnzymeAD/Reactant.jl

License: http://creativecommons.org/licenses/by/4.0/

The gist: Generative models typically rely on either simple latent priors (e.g., Variational Autoencoders, VAEs), which are efficient but limited, or expressive iterative samplers (e.g., Diffusion and

Terminology

Abstract

Generative models typically rely on either simple latent priors (e.g., Variational Autoencoders, VAEs), which are efficient but limited, or expressive iterative samplers (e.g., Diffusion and Energy-based Models), which are costly and opaque. We introduce a new unsupervised model, the Kolmogorov-Arnold Energy Model (KAEM), to bridge this trade-off and provide new opportunities for interpretability. Based on a novel adaptation of the Kolmogorov-Arnold Representation Theorem, KAEM imposes a univariate latent prior, enabling fast and exact inference via the inverse transform method. On small datasets, we show that importance sampling becomes a tractable, unbiased, and single-pass posterior inference method. For settings requiring exploration, we propose a population-based strategy that decomposes the posterior into a sequence of annealed distributions, serving as a new remedy for poor mixing in Energy-based Models. KAEM attains competitive Fréchet Inception Distance among latent-prior models on SVHN, CIFAR10, and CelebA while sampling in a single forward pass at lower cost than iterative EBMs, and exposing an interpretable prior built from 1D densities.

Sources

Related papers