Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
From Kolmogorov to Cauchy: Shallow XNet Surpasses KANs
Authors: Xin Li, Xiaotao Zheng, Zhihong Xia
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Empirical results: Across three domains, XNet outperforms strong baselines: Function approximation: over 600 lower MSE on discontinuous targets. PDE solving: over 10,000 lower error than deep MLPs in PINN settings. Reinforcement learning: faster convergence and higher rewards under PPO. |
| Researcher Affiliation | Academia | Xin Li College of Computer Science and Technology Dongguan University of Technology, China Institute for Advanced Research Great Bay University, Dongguan, Guangdong, China EMAIL Xiaotao Zheng Center for Financial Engineering Soochow University, Suzhou, China EMAIL Zhihong Xia Institute for Advanced Research Great Bay University, Dongguan, Guangdong, China Department of Mathematics Northwestern University, Evanston, IL, USA EMAIL |
| Pseudocode | No | The paper describes methods and procedures in prose within sections like '3 Theoretical Foundations of XNet' and '4 Experimental Setup and Results' but does not include any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | Yes | We provide the full code and reproduction instructions in the Supplementary Material (see supplementary.zip ). |
| Open Datasets | Yes | Dataset and Implementation Details. We collect several special functions common in math and physics, summarized in Table 4. For neural network architectures, we implemented consistent parameter configurations following [19]. |
| Dataset Splits | Yes | Each experiment utilized 8000 training points and 1000 test points. |
| Hardware Specification | Yes | The numerical experiments presented below were performed in Python using the Tensorflow-CPU processor on a Dell computer equipped with a 3.00 Gigahertz (GHz) Intel Core i9-13900KF. |
| Software Dependencies | No | The paper mentions 'Python' and 'Tensorflow-CPU' in section B.1 'Implementation Environment' but does not specify exact version numbers for these software components, which is required for a reproducible description. |
| Experiment Setup | Yes | Both models were trained using the Adam optimizer [12] under identical conditions. MLPs are configured with fixed widths of 5 or 100, with depths varying across {2, 3, 4, 5, 6}. KANs maintain a fixed width of 5 with depths similarly swept through {2, 3, 4, 5, 6}. XNet was constructed as a single-layer architecture with either 500 or 5000 basis functions. All models were trained using the Adam optimizer, implementing identical hyperparameters across architectures to isolate the effects of the function approximator choice. |