让KAN网络自动发现可解释的数学表达式
Softly Symbolifying Kolmogorov-Arnold Networks
- 在训练中引入符号项字典，用可微门控实现稀疏化
- 模型更小但精度更高，在符号任务和真实预测中表现优异
- 无需额外正则化也能自发产生简洁表达，适合需要可解释性的场景
Kolmogorov-Arnold Networks（KAN）为可解释机器学习提供了新路径：其可学习激活函数可独立分析，同时整体能精准拟合复杂数据。但实践中，训练后的激活常缺乏符号保真度，学习到无意义的病态分解。我们提出软符号化KAN（S2KAN），将符号基元直接融入训练过程。每个激活从符号项与密集项组成的字典中选取，通过可学习门控实现表示稀疏化。关键在于该稀疏化过程可微，支持端到端优化，并由最小描述长度目标引导。当符号项足够时，S2KAN发现可解释形式；不足时则自然退化为密集样条。我们在符号基准、动力系统预测及真实世界预测任务中验证了其竞争力或优越性，且模型在无显式正则化下仍表现出自发稀疏化现象。
原文摘要 · Abstract (English)
Kolmogorov-Arnold Networks (KANs) offer a promising path toward interpretable machine learning: their learnable activations can be studied individually, while collectively fitting complex data accurately. In practice, however, trained activations often lack symbolic fidelity, learning pathological decompositions with no meaningful correspondence to interpretable forms. We propose Softly Symbolified Kolmogorov-Arnold Networks (S2KAN), which integrate symbolic primitives directly into training. Each activation draws from a dictionary of symbolic and dense terms, with learnable gates that sparsify the representation. Crucially, this sparsification is differentiable, enabling end-to-end optimization, and is guided by a principled Minimum Description Length objective. When symbolic terms suffice, S2KAN discovers interpretable forms; when they do not, it gracefully degrades to dense splines. We demonstrate competitive or superior accuracy with substantially smaller models across symbolic benchmarks, dynamical systems forecasting, and real-world prediction tasks, and observe evidence of emergent self-sparsification even without regularization pressure.
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