Universal characteristics of deep neural network loss surfaces from random matrix theory

@article{Baskerville2022UniversalCO,
  title={Universal characteristics of deep neural network loss surfaces from random matrix theory},
  author={Nicholas P Baskerville and Jonathan P. Keating and Francesco Mezzadri and Joseph Najnudel and Diego Granziol},
  journal={ArXiv},
  year={2022},
  volume={abs/2205.08601}
}
This paper considers several aspects of random matrix universality in deep neural networks. Motivated by recent experimental work, we use universal properties of random matrices related to local statistics to derive practical implications for deep neural networks based on a realistic model of their Hessians. In particular we derive universal aspects of outliers in the spectra of deep neural networks and demonstrate the important role of random matrix local laws in popular pre-conditioning… 

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