通过结构稀疏与深度选择，让可解释的KAN网络更小更强
Optimized Architectures for Kolmogorov-Arnold Networks
- 用可微稀疏化+深度选择联合优化网络结构
- 在函数逼近等任务上精度不降反升，模型大幅缩小
- 适合追求可解释性与效率的科学机器学习研究者
为提升柯尔莫戈洛夫-阿诺德网络（KAN）的性能而进行的架构改进，常因复杂性破坏其可解释性。本文研究过参数化架构结合稀疏化、深度监督与深度选择，以学习紧凑且可解释的KAN，同时保持精度。关键在于基于最小描述长度原则的可微机制，端到端联合优化激活值、结构与深度。在函数逼近基准、动力系统预测及真实世界预测任务上的实验表明，仅稀疏化不足以为继，但结合深度选择后，在保持或超越现有精度的同时显著减小模型规模。该方法为科学机器学习中表达力与可解释性之间的权衡提供了可遵循的路径。
原文摘要 · Abstract (English)
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.
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