Reviews: Langevin Dynamics with Continuous Tempering for Training Deep Neural Networks

The paper proposes a new method to optimize deep neural networks, starting with a stochastic search using'original' Langevin (where the temperature appears as a function of an auxiliary variable), then transitioning to more classical, deterministic algorithm. I enjoyed reading the paper - I am not an expert in the field but as far as I could tell the methods are novel, and the idea of treating the temperature as a function of an augmented variable seems elegant; since one can then change the landscape for temperature (tweaking g(\alpha) and \phi(\alpha)) without changing the optimum of the function. The numerical experiments seem to indicate that the method is not more computationally demand but improves optimization. I recommend acceptance, with minor caveats below. However they don't explicitly investigate the ability of the algorithm to jump between modes, a property frequently mentioned in the body of the text.