Convergence rates of Gibbs measures with degenerate minimum

arXiv link, Bernoulli Journal link

This repository contains a notebook showing how we can compute the higher order nested expansion of some objective function to be minimized in problems where the Hessian matrix at the minimum is singular. In this example, we train a neural network and study the behaviour of the loss function in the neighbourhood of the (empirical) minimum.

The machine learning library that is used is TensorFlow.

Citation

Please cite our paper if it helps your research (only arXiv for now):

@ARTICLE{2021arXiv210111557B,
       author = {{Bras}, Pierre},
        title = "{Convergence rates of Gibbs measures with degenerate minimum}",
      journal = {arXiv e-prints},
     keywords = {Mathematics - Probability},
         year = 2021,
        month = jan,
          eid = {arXiv:2101.11557},
        pages = {arXiv:2101.11557},
archivePrefix = {arXiv},
       eprint = {2101.11557},
 primaryClass = {math.PR},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2021arXiv210111557B},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}