Recursive Kolmogorov-Arnold Flows for Adaptive Representation Learning

Contemporary deep learning relies on the discrete stacking of layers to increase model capacity, a paradigm that leads to linear parameter growth and rigid inference latency. This work investigates the Recursive Kolmogorov-Arnold Flow (RKAF), an architecture designed to achieve variable depth through a single, shared recursive cell. The proposed method departs from standard layer-stacking by integrating learnable non-linear basis functions (inspired by the Kolmogorov-Arnold representation theorem) with a "pondering" mechanism. This allows the model to dynamically allocate computational resources—iterating deeper on complex samples and exiting early on simple ones. We benchmark RKAF against standard 3-layer Multi-Layer Perceptrons (MLPs) on five diverse datasets (Breast Cancer, Wine, Digits, Diabetes, and California Housing). Results demonstrate that RKAF maintains high classification accuracy while achieving substantial gains in regression tasks. Specifically, on the Diabetes dataset, RKAF improved the R2 score from 0.04 to 0.46. Overall, the architecture achieved an average parameter reduction of 41%, proving that models do not need to be physically deep to be computationally expressive.