References
Neyshabur B, Tomioka R, Srebro N. Norm-based capacity control in neural networks. In: Proceedings of the 28th Conference on Learing Theory, Paris, 2015. 1376–1401
Zhang C Y, Bengio S, Hardt M, et al. Understanding deep learning requires rethinking generalization. In: Proceedings of the 5th International Conference on Learning Representation, Toulon, 2017
Nagarajan V, Kolter J Z. Uniform convergence may be unable to explain generalization in deep learning. In: Proceedins of Advances in Neural Information Processing Systems, 2019. 11615–11626
Lawrence S, Giles C L, Tsoi A C. Lessons in neural network training: overfitting may be harder than expected. In: Proceedings of the 14th National Conference on Artificial Intelligence, Providence, 1997. 540–545
Liu Y Y, Starzyk J A, Zhu Z. Optimized approximation algorithm in neural networks without overfitting. IEEE Trans Neural Netw, 2008, 19: 983–995
Kulis B. Metric learning: a survey. Found Trends Mach Learn, 2013, 5: 287–363
Davis J V, Kulis B, Jain P, et al. Information-theoretic metric learning. In: Proceedings of the 24th International Conference on Machine Learning, Corvalis, 2007. 209–216
Acknowledgements
This work was supported by National Natural Science Foundation of China (NSFC) (Grant Nos. 61751306, 61921006). The author wants to thank Shen-Huan LYU and Zhi-Hao TAN for discussion and help in figures.
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Zhou, ZH. Why over-parameterization of deep neural networks does not overfit?. Sci. China Inf. Sci. 64, 116101 (2021). https://doi.org/10.1007/s11432-020-2885-6
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DOI: https://doi.org/10.1007/s11432-020-2885-6