Year: 2018
Type: preprint
Abstract: Recent work has argued that stochastic gradient descent can approximate the Bayesian uncertainty in model parameters near local minima. In this work we develop a similar correspondence for minibatch natural gradient descent (NGD). We prove that for sufficiently small learning rates, if the model predictions on the training set approach the true conditional distribution of labels given inputs, the stationary distribution of minibatch NGD approaches a Bayesian posterior near local minima. The temperature $T = εN / (2B)$ is controlled by the learning rate $ε$, training set size $N$ and batch size $B$. However minibatch NGD is not parameterisation invariant and it does not sample a valid posterior away from local minima. We therefore propose a novel optimiser, "stochastic NGD", which introduces the additional correction terms required to preserve both properties.
Source: arXiv (Cornell University)
Authors: Smith, Samuel L., Duckworth, Daniel, Rezchikov, Semon, Le, Quoc V., Sohl-Dickstein, Jascha
Institutions: Google (United States), Google DeepMind (United Kingdom)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2861280779