Partitioned integrators for thermodynamic parameterization of neural networks

Benedict Leimkuhler, Charles Matthews, Tiffany Vlaar

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

Traditionally, neural networks are parameterized using optimization procedures such as stochastic gradient descent, RMSProp and ADAM.
These procedures tend to drive the parameters of the network toward a local minimum. In this article, we employ alternative \sampling" algorithms (referred to here as \thermodynamic parameterization methods") which rely on discretized stochastic dierential equations for a dened target distribution on parameter space. We show that the thermodynamic perspective already
improves neural network training. Moreover, by partitioning the parameters based on natural layer structure we obtain schemes with very rapid convergence for data sets with complicated loss landscapes.
We describe easy-to-implement hybrid partitioned numerical algorithms, based on discretized stochastic dierential equations, which are adapted to feed-forward neural networks, including a multi-layer Langevin algorithm, Ad-LaLa (combining the adaptive Langevin and Langevin algorithms) and LOL (combining Langevin and Overdamped Langevin); we examine the convergence
of these methods using numerical studies and compare their performance among themselves and in relation to standard alternatives such as stochastic gradient descent and ADAM. We present evidence that thermodynamic parameterization
methods can be (i) faster, (ii) more accurate, and (iii) more
robust than standard algorithms used within machine learning frameworks.
Original languageEnglish
Pages (from-to)457-489
JournalFoundations of Data Science
Issue number4
Publication statusPublished - 31 Dec 2019


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