A Graph Meta-Network for Learning on Kolmogorov-Arnold Networks
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914361087361024 |
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| author | Bar-Shalom, Guy Tavory, Ami Evron, Itay Bechler-Speicher, Maya Guy, Ido Maron, Haggai |
| author_facet | Bar-Shalom, Guy Tavory, Ami Evron, Itay Bechler-Speicher, Maya Guy, Ido Maron, Haggai |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16316 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Graph Meta-Network for Learning on Kolmogorov-Arnold Networks Bar-Shalom, Guy Tavory, Ami Evron, Itay Bechler-Speicher, Maya Guy, Ido Maron, Haggai Machine Learning Artificial Intelligence 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. |
| title | A Graph Meta-Network for Learning on Kolmogorov-Arnold Networks |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2602.16316 |