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.

翻译：旨在通过架构增强改进科尔莫戈罗夫-阿诺德网络（KANs）的研究工作，常因这些增强带来的复杂性而受阻，进而削弱了KANs最初吸引人的可解释性。本文研究了过度配置架构与稀疏化、深度监督及深度选择相结合的方法，以学习紧凑且可解释的KANs，同时不牺牲准确性。关键之处在于，我们聚焦于在原则性最小描述长度目标下的可微机制，通过端到端方式联合优化激活函数、网络结构与深度。在函数逼近基准、动力系统预测及实际预测任务中的实验表明，仅依赖稀疏化效果有限，但结合深度选择后，能在发现显著更小模型的同时实现具有竞争性或更优的准确性。这为构建既更具表达能力又更可解释的模型提供了原则性路径，回应了科学机器学习领域中的关键矛盾。