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.

翻译：权重空间模型直接从神经网络的参数中学习，使其能够执行诸如预测在新数据集上的准确性等任务。简单方法——例如将多层感知器应用于展平的参数——表现不佳，因此设计更好的权重空间架构成为一个核心挑战。虽然先前的研究利用标准网络中的置换对称性来指导此类设计，但针对Kolmogorov-Arnold网络（KANs）尚未有类似的分析或定制架构。在本工作中，我们证明KANs与多层感知器具有相同的置换对称性，并提出了KAN图——一种其计算过程的图表示。在此基础上，我们开发了WS-KAN，首个在KANs上学习的权重空间架构，该架构自然地考虑了其对称性。我们分析了WS-KAN的表达能力，证明其能够复现输入KAN的前向传播过程——这是评估权重空间架构表达能力的标准方法。我们构建了一个涵盖多样化任务的训练KAN综合“动物园”，并将其作为基准对WS-KAN进行实证评估。在所有任务中，WS-KAN始终优于结构无关的基线方法，且通常优势显著。我们的代码可在 https://github.com/BarSGuy/KAN-Graph-Metanetwork 获取。