Abstract for With_PhD_thesis_97.ps:
The present thesis is about optimization of recurrent neural networks applied to
time series modeling. In particular is considered fully recurrent networks working
from only a single external input, one layer of nonlinear hidden units and a linear
output unit applied to prediction of discrete time series. The overall objectives
are to improve training by application of second-order methods and to improve
generalization ability by architecture optimization accomplished by pruning. The
major topics covered in the thesis are:
* The problem of training recurrent networks is analyzed from a numerical point of
view. Especially it is analyzed how numerical ill-conditioning of the Hessian
matrix might arise.
* Training is significantly improved by application of the damped Gauss-Newton
method, involving the {\em full} Hessian. This method is found to outperform
gradient descent in terms of both quality of solution obtained as well as
computation time required.
* A theoretical definition of the generalization error for recurrent networks
is provided. This definition justifies a commonly adopted approach for estimating
generalization ability.
* The viability of pruning recurrent networks by the Optimal Brain Damage (OBD) and
Optimal Brain Surgeon (OBS) pruning schemes is investigated. OBD is found to be
very effective whereas OBS is severely influenced by numerical problems which
leads to pruning of important weights.
* A novel operational tool for examination of the internal memory of recurrent
networks is proposed. The tool allows for assessment of the length of the effective
memory of previous inputs built up in the recurrent network during application.
Time series modeling is also treated from a more general point of view, namely
modeling of the joint probability distribution function of the observed series. Two
recurrent models rooted in statistical physics are considered in this respect,
namely the ``Boltzmann chain'' and the ``Boltzmann zipper'' and a comprehensive
tutorial on these models is provided. Boltzmann chains and zippers are found to
benefit as well from second-order training and architecture optimization by pruning
which is illustrated on artificial problems and a small speech recognition problem.