Description and training of neural network dynamics

Attractor properties of a popular discrete-time neural network model are illustrated through numerical simulations. The most complex dynamics is found to occur within particular ranges of parameters controlling the symmetry and magnitude of the weight matrix. A small network model is observed to produce fixed points, limit cycles, mode-locking, the Ruelle-Takens route to chaos, and the period-doubling route to chaos. Training algorithms for tuning this dynamical behaviour are discussed. Training can be an easy or difficult task, depending whether the problem requires the use of temporal information distributed over long time intervals. Such problems require training algorithms which can handle hidden nodes. The most prominent of these algorithms, back propagation through time, solves the temporal credit assignment problem in a way which can work only if the relevant information is distributed locally in time. The Moving Targets algorithm works for the more general case, but is computationally intensive, and prone to local minima.

Efficient training of RBF networks for classification.

Radial Basis Function networks with linear outputs are often used in regression problems because they can be substantially faster to train than Multi-layer Perceptrons. For classification problems, the use of linear outputs is less appropriate as the outputs are not guaranteed to represent probabilities. We show how RBFs with logistic and softmax outputs can be trained efficiently using the Fisher scoring algorithm. This approach can be used with any model which consists of a generalised linear output function applied to a model which is linear in its parameters. We compare this approach with standard non-linear optimisation algorithms on a number of datasets.

Bayesian training of mixture density networks

Mixture Density Networks (MDNs) are a well-established method for modelling the conditional probability density which is useful for complex multi-valued functions where regression methods (such as MLPs) fail. In this paper we extend earlier research of a regularisation method for a special case of MDNs to the general case using evidence based regularisation and we show how the Hessian of the MDN error function can be evaluated using R-propagation. The method is tested on two data sets and compared with early stopping.

Efficient training of RBF networks for classification

Radial Basis Function networks with linear outputs are often used in regression problems because they can be substantially faster to train than Multi-layer Perceptrons. For classification problems, the use of linear outputs is less appropriate as the outputs are not guaranteed to represent probabilities. In this paper we show how RBFs with logistic and softmax outputs can be trained efficiently using algorithms derived from Generalised Linear Models. This approach is compared with standard non-linear optimisation algorithms on a number of datasets.

Discriminative training of the hidden vector state model for semantic parsing

In this paper, we discuss how discriminative training can be applied to the hidden vector state (HVS) model in different task domains. The HVS model is a discrete hidden Markov model (HMM) in which each HMM state represents the state of a push-down automaton with a finite stack size. In previous applications, maximum-likelihood estimation (MLE) is used to derive the parameters of the HVS model. However, MLE makes a number of assumptions and unfortunately some of these assumptions do not hold. Discriminative training, without making such assumptions, can improve the performance of the HVS model by discriminating the correct hypothesis from the competing hypotheses. Experiments have been conducted in two domains: the travel domain for the semantic parsing task using the DARPA Communicator data and the Air Travel Information Services (ATIS) data and the bioinformatics domain for the information extraction task using the GENIA corpus. The results demonstrate modest improvements of the performance of the HVS model using discriminative training. In the travel domain, discriminative training of the HVS model gives a relative error reduction rate of 31 percent in F-measure when compared with MLE on the DARPA Communicator data and 9 percent on the ATIS data. In the bioinformatics domain, a relative error reduction rate of 4 percent in F-measure is achieved on the GENIA corpus.