# On Large Batch Training and Sharp Minima: A Fokker–Planck Perspective

@article{Dai2020OnLB, title={On Large Batch Training and Sharp Minima: A Fokker–Planck Perspective}, author={Xiaowu Dai and Yuhua Zhu}, journal={Journal of Statistical Theory and Practice}, year={2020}, volume={14}, pages={1-31} }

We study the statistical properties of the dynamic trajectory of stochastic gradient descent (SGD). We approximate the mini-batch SGD and the momentum SGD as stochastic differential equations. We exploit the continuous formulation of SDE and the theory of Fokker–Planck equations to develop new results on the escaping phenomenon and the relationship with large batch and sharp minima. In particular, we find that the stochastic process solution tends to converge to flatter minima regardless of the…

## 2 Citations

### A sharp convergence rate for a model equation of the asynchronous stochastic gradient descent

- Computer Science, MathematicsCommunications in Mathematical Sciences
- 2021

It is proved that when the number of local workers is larger than the expected staleness, then ASGD is morecient than stochastic gradient descent, and the theoretical result suggests that longer delays result in slower convergence rate.

### Bayesian mechanics for stationary processes

- Computer ScienceProceedings of the Royal Society A
- 2021

It follows that active states can be seen as performing active inference and well-known forms of stochastic control, which are prominent formulations of adaptive behaviour in theoretical biology and engineering.

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