首个专为KAN设计的权重空间模型，能高效预测其性能。
A Graph Meta-Network for Learning on Kolmogorov-Arnold Networks
- 构建KAN图结构，利用其对称性设计新模型
- 在多个任务上超越传统方法，提升显著
- 适合研究KAN性能预测与模型分析者
权重空间模型直接从神经网络参数中学习，可预测其在新数据集上的表现。简单方法（如将参数展平后输入MLP）效果差，因此设计更优的权重空间架构成为关键挑战。以往工作利用标准网络的置换对称性指导设计，但对柯尔莫戈罗夫-阿诺德网络（KANs）尚无类似分析或专用架构。本文证明KANs与MLPs共享相同的置换对称性，并提出KAN图，作为其计算的图表示。基于此，我们开发了首个针对KAN的权重空间模型WS-KAN，自然体现其对称性。我们分析了WS-KAN的表达能力，表明其可复现输入KAN的前向传播——这是评估权重空间架构表达力的标准方法。我们构建了一个涵盖多种任务的训练好的KAN“动物园”，用作基准，实证评估WS-KAN。在所有任务中，WS-KAN均持续优于结构无关基线，差距明显。代码已开源：https://github.com/BarSGuy/KAN-Graph-Metanetwork。
原文摘要 · Abstract (English)
Weight-space models learn directly from the parameters of neural networks, enabling tasks such as predicting their accuracy on new datasets. Naive methods -- like applying MLPs to flattened parameters -- perform poorly, making the design of better weight-space architectures a central challenge. While prior work leveraged permutation symmetries in standard networks to guide such designs, no analogous analysis or tailored architecture yet exists for Kolmogorov-Arnold Networks (KANs). In this work, we show that KANs share the same permutation symmetries as MLPs, and propose the KAN-graph, a graph representation of their computation. Building on this, we develop WS-KAN, the first weight-space architecture that learns on KANs, which naturally accounts for their symmetry. We analyze WS-KAN's expressive power, showing it can replicate an input KAN's forward pass - a standard approach for assessing expressiveness in weight-space architectures. We construct a comprehensive ``zoo'' of trained KANs spanning diverse tasks, which we use as benchmarks to empirically evaluate WS-KAN. Across all tasks, WS-KAN consistently outperforms structure-agnostic baselines, often by a substantial margin. Our code is available at https://github.com/BarSGuy/KAN-Graph-Metanetwork.
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