一种用于Kolmogorov-Arnold网络学习的图元网络
A Graph Meta-Network for Learning on Kolmogorov-Arnold Networks
AI总结：
本文提出WS-KAN，一种用于Kolmogorov-Arnold网络学习的图元网络，通过利用其排列对称性提升模型表达能力，并在多种任务中超越基线模型。
摘要：
权重空间模型直接从神经网络的参数学习，使预测其在新数据集上的准确性成为可能。 naive方法--如将MLP应用于扁平化参数--表现不佳，使设计更好的权重空间架构成为核心挑战。尽管先前工作利用标准网络中的排列对称性来指导此类设计，但尚无类似的分析或针对Kolmogorov-Arnold网络（KANs）的定制架构。在本工作中，我们证明KANs与MLP具有相同的排列对称性，并提出KAN图，作为其计算的图表示。在此基础上，我们开发了WS-KAN，这是首个在KAN上学习的权重空间架构，能够自然地考虑其对称性。我们分析了WS-KAN的表达能力，证明其可以复制输入KAN的正向传递--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任务的全面的"动物园"训练好的KANs，用于作为基准来经验性评估WS-KAN。在所有任务中，WS-KAN在结构无关的基线模型上表现一致优于，经常以显著的幅度。我们的代码可在https://github.com/BarSGuy/KAN-Graph-Metanetwork获得。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
