Incorporating Arbitrary Matrix Group Equivariance into KANs
Authors: Lexiang Hu, Yisen Wang, Zhouchen Lin
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In Section 6, we evaluate EKAN on tasks with known symmetries. We show that EKAN can achieve higher accuracy than baseline models with smaller datasets or fewer parameters. ... In this section, we evaluate the performance of EKAN on regression and classification tasks with known symmetries. Compared with general models such as MLPs, KANs, and equivariant architectures like EMLP (Finzi et al., 2021) and CGENN (Ruhe et al., 2023), EKAN achieves lower test loss and higher test accuracy with smaller datasets or fewer parameters. |
| Researcher Affiliation | Academia | 1State Key Lab of General AI, School of Intelligence Science and Technology, Peking University 2Institute for Artificial Intelligence, Peking University 3Pazhou Laboratory (Huangpu), Guangzhou, Guangdong, China. Correspondence to: Zhouchen Lin <EMAIL>. |
| Pseudocode | No | The paper describes methods using mathematical equations and text, but does not include any clearly labeled pseudocode blocks or algorithms. |
| Open Source Code | Yes | Code and data are available at https://github.com/hulx2002/EKAN. |
| Open Datasets | Yes | The data generation process for particle scattering is entirely consistent with that in EMLP (Finzi et al., 2021). ... The dataset for the three-body problem comes from HNN (Greydanus et al., 2019)... The top quark tagging dataset is sourced from Kasieczka et al. (2019) |
| Dataset Splits | Yes | We embed the group O(1, 3) and its subgroups SO+(1, 3) and SO(1, 3) equivariance into EKAN. Models are evaluated on synthetic datasets with different training set sizes, which are generated by sampling qµ, pµ, qµ, pµ N(0, 1 42 ). ... The dataset contains 30k training samples and 30k test samples. ... We sample training sets of different sizes from the original dataset for evaluation. |
| Hardware Specification | Yes | We perform this experiment on a single-core NVIDIA Ge Force RTX 3090 GPU with available memory of 24576 Mi B. |
| Software Dependencies | No | We train EKAN using the Adan optimizer (Xie et al., 2024)... No specific versions for other software dependencies (e.g., Python, PyTorch) are mentioned. |
| Experiment Setup | Yes | Both EKAN and KAN have the depth of L = 2, the spline order of k = 3, and grid intervals of G = 3. ... We train EKAN using the Adan optimizer (Xie et al., 2024) with the learning rate of 3 10 3 and the batch size of 500. For datasets with the training set size < 1000, we set the number of epochs to 7000, while for datasets with the training set size 1000, we set the number of epochs to 15000... The grids of EKAN and KAN are updated every 5 epochs and stop updating at the 50th epoch. |