Summary of Generalization Bounds and Model Complexity For Kolmogorov-arnold Networks, by Xianyang Zhang and Huijuan Zhou
Generalization Bounds and Model Complexity for Kolmogorov-Arnold Networks
by Xianyang Zhang, Huijuan Zhou
First submitted to arxiv on: 10 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Neural and Evolutionary Computing (cs.NE); Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The proposed Kolmogorov-Arnold Network (KAN) offers improved interpretability and a more parsimonious design compared to multi-layer perceptrons in various science-oriented tasks. This paper provides a rigorous theoretical analysis of KAN by establishing generalization bounds for KAN equipped with activation functions that are either represented by linear combinations of basis functions or lying in a low-rank Reproducing Kernel Hilbert Space (RKHS). The bounds scale with the l1 norm of coefficient matrices, Lipschitz constants, and combinatorial parameters. These results are empirically investigated on simulated and real datasets using stochastic gradient descent. The numerical results demonstrate the practical relevance of these bounds. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Kolmogorov-Arnold Network (KAN) is a new way to make computers learn. It’s better than old methods because it’s easier to understand how KAN works, and it uses fewer parts. This paper helps us understand how well KAN will do on different tasks by setting limits for what it can do. These limits depend on things like the complexity of the task and how well the computer is trained. The results are tested using real and made-up data and show that this new way works. |
Keywords
» Artificial intelligence » Generalization » Stochastic gradient descent
