标题： 多出口科尔莫戈罗夫-阿诺德网络：提高准确性和简洁性 显示英文标题

标题： Multi-Exit Kolmogorov-Arnold Networks: enhancing accuracy and parsimony

摘要： Kolmogorov-Arnold网络（KANs）独特地结合了高精度与可解释性，使其在科学建模中具有重要价值。然而，在任何特定任务中，网络需要多深尚不清楚，并且较深的KANs可能难以优化。 在此，我们引入了多出口KANs，其中每一层都包含自己的预测分支，从而使网络能够在多个深度上同时做出准确预测。该架构通过提供深层监督来改进训练，同时为每个任务发现适当的模型复杂度级别。 在合成函数、动态系统和现实世界数据集上，多出口KANs始终优于标准的单出口版本。令人惊讶的是，最佳预测往往来自较早、更简单的出口，这表明这些网络自然识别出更小、更简洁且可解释的模型，而不会牺牲准确性。 为了自动化这一发现过程，我们开发了一种可微分的“学习退出”算法，该算法在训练期间平衡了各出口的贡献。我们的方法为科学家提供了一种实现高性能和可解释性的实用方式，解决了科学发现领域机器学习中的一个基本挑战。 显示英文摘要

摘要： 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. 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.