SAGRAD: A Program for Neural Network Training with Simulated Annealing and the Conjugate Gradient Method
Javier Bernal, Jose Torres-Jimenez
TL;DR
SAGRAD presents a Fortran 77 framework for classification neural networks trained by batch learning, integrating simulated annealing with Møller's scaled conjugate gradient algorithm to navigate nonquadratic loss landscapes. It provides detailed implementations for efficient gradient computation via backpropagation and exact Hessian-vector products using the $\mathcal{R}$ operator, enabling effective second-order information without forming the full Hessian. The paper introduces two SA variants (low- and high-intensity) and a three-step training process that combines initialization, optimization, and optional global-search phases, with empirical validation on Cushing syndrome and wine datasets showing high accuracy and agreement with prior work. The contribution lies in a cohesive, publicly available, Fortran-based system that demonstrates robust training of multi-layer networks for classification using a principled hybrid optimization strategy.
Abstract
SAGRAD (Simulated Annealing GRADient), a Fortran 77 program for computing neural networks for classification using batch learning, is discussed. Neural network training in SAGRAD is based on a combination of simulated annealing and Møller's scaled conjugate gradient algorithm, the latter a variation of the traditional conjugate gradient method, better suited for the nonquadratic nature of neural networks. Different aspects of the implementation of the training process in SAGRAD are discussed, such as the efficient computation of gradients and multiplication of vectors by Hessian matrices that are required by Møller's algorithm; the (re)initialization of weights with simulated annealing required to (re)start Møller's algorithm the first time and each time thereafter that it shows insufficient progress in reaching a possibly local minimum; and the use of simulated annealing when Møller's algorithm, after possibly making considerable progress, becomes stuck at a local minimum or flat area of weight space. Outlines of the scaled conjugate gradient algorithm, the simulated annealing procedure and the training process used in SAGRAD are presented together with results from running SAGRAD on two examples of training data.