Partitioned integrators for thermodynamic parameterization of neural networks

TL;DR

This paper introduces partitioned thermodynamic sampling algorithms for neural network training, which improve convergence speed, accuracy, and robustness compared to traditional optimization methods like SGD and ADAM.

Contribution

It proposes novel hybrid partitioned stochastic differential equation-based algorithms tailored for neural networks, demonstrating their advantages over standard optimization techniques.

Findings

Partitioned thermodynamic methods converge faster.

These methods are more accurate than SGD and ADAM.

Thermodynamic approaches are more robust in complex landscapes.

Abstract

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.