arXiv:2512.12448v2 Announce Type: replace-cross Abstract: Efforts to improve Kolmogorov--Arnold networks (KANs) with architectural enhancements have been stymied by the complexity those enhancements bring, undermining the interpretability that makes KANs attractive in the first place. Here we study overprovisioned architectures combined with sparsification, deep supervision, and depth selection, to learn compact, interpretable KANs without sacrificing accuracy. Crucially, we focus on differentiable mechanisms under a principled minimum description length objective, jointly optimizing activations, structure, and depth end-to-end. Experiments across function approximation benchmarks, dynamical systems forecasting, and real-world prediction tasks demonstrate that sparsification alone is insufficient, but the combination with depth selection achieves competitive or superior accuracy while discovering substantially smaller models. The result is a principled path toward models that are both more expressive and more interpretable, addressing a key tension in scientific machine learning.