多出口架构让KAN自动找到最简有效模型，兼顾精度与可解释性。
Multi-Exit Kolmogorov-Arnold Networks: enhancing accuracy and parsimony
- 每层设独立预测分支，实现多深度输出与深层监督
- 多数任务中早期出口即达最优精度，模型更简洁
- 可自动学习退出策略，适合科学建模场景
Kolmogorov-Arnold Networks（KANs）以高精度与可解释性结合著称，适用于科学建模。然而，任务所需的网络深度难以预判，更深的KAN优化困难且难以解释。本文提出多出口KAN，每个层均含独立预测分支，使网络能在多个深度同时做出准确预测。该结构提供深层监督，提升训练效果，并自动发现任务所需的最佳模型复杂度。在合成函数、动力系统及真实数据集上，多出口KAN始终优于标准单出口版本。令人惊讶的是，最佳预测常来自早期、更简单的出口，表明网络能自然识别出更小、更简洁且可解释的模型，而无需牺牲精度。为此，我们设计了一种可微的“学习退出”算法，在训练中动态平衡各出口贡献。本方法为科学发现中的机器学习提供了一种兼顾高性能与可解释性的实用路径。
原文摘要 · Abstract (English)
Kolmogorov-Arnold Networks (KANs) uniquely combine high accuracy with interpretability, making them valuable for scientific modeling. However, it is unclear a priori how deep a network needs to be for any given task, and deeper KANs can be difficult to optimize and interpret. Here we introduce multi-exit KANs, where each layer includes its own prediction branch, enabling the network to make accurate predictions at multiple depths simultaneously. This architecture provides deep supervision that improves training while discovering the right level of model complexity for each task. Multi-exit KANs consistently outperform standard, single-exit versions on synthetic functions, dynamical systems, and real-world datasets. Remarkably, the best predictions often come from earlier, simpler exits, revealing that these networks naturally identify smaller, more parsimonious and interpretable models without sacrificing accuracy. To automate this discovery, we develop a differentiable "learning-to-exit" algorithm that balances contributions from exits during training. Our approach offers scientists a practical way to achieve both high performance and interpretability, addressing a fundamental challenge in machine learning for scientific discovery.
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