4 research outputs found
Multilevel Artificial Neural Network Training for Spatially Correlated Learning
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.Comment: Manuscript (24 pages) and Supplementary Material (4 pages). Updated
January 2019 to reflect new formulation of MsANN structure and new training
procedur