  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 differential equations for a defined 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 differential equations, which are adapted to
feed-forward neural networks, including a multi-layer Langevin algorithm,
AdLaLa (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.
