Multilevel Artificial Neural Network Training for Spatially Correlated Learning
This addresses the issue of training efficiency for neural networks, particularly in spatially correlated learning tasks, though it appears incremental as it builds on existing multiscale modeling techniques.
The paper tackles the problem of slow neural network training by introducing Multiscale Artificial Neural Network (MsANN) training, which uses multilevel methods to simultaneously train a hierarchy of models at varying spatial resolutions, resulting in learning that is an order of magnitude faster with comparable error levels.
Multigrid modeling algorithms are a technique used to accelerate relaxation models running on a hierarchy of similar graphlike structures. We introduce and demonstrate a new method for training neural networks which uses multilevel methods. Using an objective function derived from a graph-distance metric, we perform orthogonally-constrained optimization to find optimal prolongation and restriction maps between graphs. We compare and contrast several methods for performing this numerical optimization, and additionally present some new theoretical results on upper bounds of this type of objective function. Once calculated, these optimal maps between graphs form the core of Multiscale Artificial Neural Network (MsANN) training, a new procedure we present which simultaneously trains a hierarchy of neural network models of varying spatial resolution. Parameter information is passed between members of this hierarchy according to standard coarsening and refinement schedules from the multiscale modelling literature. In our machine learning experiments, these models are able to learn faster than default training, achieving a comparable level of error in an order of magnitude fewer training examples.