Globally optimal parameters for on-line learning in multilayer neural networks

We present a framework for calculating globally optimal parameters, within a given time frame, for on-line learning in multilayer neural networks. We demonstrate the capability of this method by computing optimal learning rates in typical learning scenarios. A similar treatment allows one to determine the relevance of related training algorithms based on modifications to the basic gradient descent rule as well as to compare different training methods.

Noisy fitness evaluation in genetic algorithms and the dynamics of learning

A theoretical model is presented which describes selection in a genetic algorithm (GA) under a stochastic fitness measure and correctly accounts for finite population effects. Although this model describes a number of selection schemes, we only consider Boltzmann selection in detail here as results for this form of selection are particularly transparent when fitness is corrupted by additive Gaussian noise. Finite population effects are shown to be of fundamental importance in this case, as the noise has no effect in the infinite population limit. In the limit of weak selection we show how the effects of any Gaussian noise can be removed by increasing the population size appropriately. The theory is tested on two closely related problems: the one-max problem corrupted by Gaussian noise and generalization in a perceptron with binary weights. The averaged dynamics can be accurately modelled for both problems using a formalism which describes the dynamics of the GA using methods from statistical mechanics. The second problem is a simple example of a learning problem and by considering this problem we show how the accurate characterization of noise in the fitness evaluation may be relevant in machine learning. The training error (negative fitness) is the number of misclassified training examples in a batch and can be considered as a noisy version of the generalization error if an independent batch is used for each evaluation. The noise is due to the finite batch size and in the limit of large problem size and weak selection we show how the effect of this noise can be removed by increasing the population size. This allows the optimal batch size to be determined, which minimizes computation time as well as the total number of training examples required.

Dynamics of on-line learning in radial basis function networks

On-line learning is examined for the radial basis function network, an important and practical type of neural network. The evolution of generalization error is calculated within a framework which allows the phenomena of the learning process, such as the specialization of the hidden units, to be analyzed. The distinct stages of training are elucidated, and the role of the learning rate described. The three most important stages of training, the symmetric phase, the symmetry-breaking phase, and the convergence phase, are analyzed in detail; the convergence phase analysis allows derivation of maximal and optimal learning rates. As well as finding the evolution of the mean system parameters, the variances of these parameters are derived and shown to be typically small. Finally, the analytic results are strongly confirmed by simulations.

On-line learning with adaptive back-propagation in two-layer networks

An adaptive back-propagation algorithm parameterized by an inverse temperature 1/T is studied and compared with gradient descent (standard back-propagation) for on-line learning in two-layer neural networks with an arbitrary number of hidden units. Within a statistical mechanics framework, we analyse these learning algorithms in both the symmetric and the convergence phase for finite learning rates in the case of uncorrelated teachers of similar but arbitrary length T. These analyses show that adaptive back-propagation results generally in faster training by breaking the symmetry between hidden units more efficiently and by providing faster convergence to optimal generalization than gradient descent.

On-line learning in radial basis functions networks

An analytic investigation of the average case learning and generalization properties of Radial Basis Function Networks (RBFs) is presented, utilising on-line gradient descent as the learning rule. The analytic method employed allows both the calculation of generalization error and the examination of the internal dynamics of the network. The generalization error and internal dynamics are then used to examine the role of the learning rate and the specialization of the hidden units, which gives insight into decreasing the time required for training. The realizable and over-realizable cases are studied in detail; the phase of learning in which the hidden units are unspecialized (symmetric phase) and the phase in which asymptotic convergence occurs are analyzed, and their typical properties found. Finally, simulations are performed which strongly confirm the analytic results.

Globally optimal learning rates in multilayer neural networks

A method for calculating the globally optimal learning rate in on-line gradient-descent training of multilayer neural networks is presented. The method is based on a variational approach which maximizes the decrease in generalization error over a given time frame. We demonstrate the method by computing optimal learning rates in typical learning scenarios. The method can also be employed when different learning rates are allowed for different parameter vectors as well as to determine the relevance of related training algorithms based on modifications to the basic gradient descent rule.

Incorporating curvature information into on-line learning

We analyse the dynamics of a number of second order on-line learning algorithms training multi-layer neural networks, using the methods of statistical mechanics. We first consider on-line Newton's method, which is known to provide optimal asymptotic performance. We determine the asymptotic generalization error decay for a soft committee machine, which is shown to compare favourably with the result for standard gradient descent. Matrix momentum provides a practical approximation to this method by allowing an efficient inversion of the Hessian. We consider an idealized matrix momentum algorithm which requires access to the Hessian and find close correspondence with the dynamics of on-line Newton's method. In practice, the Hessian will not be known on-line and we therefore consider matrix momentum using a single example approximation to the Hessian. In this case good asymptotic performance may still be achieved, but the algorithm is now sensitive to parameter choice because of noise in the Hessian estimate. On-line Newton's method is not appropriate during the transient learning phase, since a suboptimal unstable fixed point of the gradient descent dynamics becomes stable for this algorithm. A principled alternative is to use Amari's natural gradient learning algorithm and we show how this method provides a significant reduction in learning time when compared to gradient descent, while retaining the asymptotic performance of on-line Newton's method.

Training Bayesian networks for image segmentation

We are concerned with the problem of image segmentation in which each pixel is assigned to one of a predefined finite number of classes. In Bayesian image analysis, this requires fusing together local predictions for the class labels with a prior model of segmentations. Markov Random Fields (MRFs) have been used to incorporate some of this prior knowledge, but this not entirely satisfactory as inference in MRFs is NP-hard. The multiscale quadtree model of Bouman and Shapiro (1994) is an attractive alternative, as this is a tree-structured belief network in which inference can be carried out in linear time (Pearl 1988). It is an hierarchical model where the bottom-level nodes are pixels, and higher levels correspond to downsampled versions of the image. The conditional-probability tables (CPTs) in the belief network encode the knowledge of how the levels interact. In this paper we discuss two methods of learning the CPTs given training data, using (a) maximum likelihood and the EM algorithm and (b) emphconditional maximum likelihood (CML). Segmentations obtained using networks trained by CML show a statistically-significant improvement in performance on synthetic images. We also demonstrate the methods on a real-world outdoor-scene segmentation task.

On-line learning of unrealizable tasks

The dynamics of on-line learning is investigated for structurally unrealizable tasks in the context of two-layer neural networks with an arbitrary number of hidden neurons. Within a statistical mechanics framework, a closed set of differential equations describing the learning dynamics can be derived, for the general case of unrealizable isotropic tasks. In the asymptotic regime one can solve the dynamics analytically in the limit of large number of hidden neurons, providing an analytical expression for the residual generalization error, the optimal and critical asymptotic training parameters, and the corresponding prefactor of the generalization error decay.

On-line learning in neural networks

On-line learning is one of the most powerful and commonly used techniques for training large layered networks and has been used successfully in many real-world applications. Traditional analytical methods have been recently complemented by ones from statistical physics and Bayesian statistics. This powerful combination of analytical methods provides more insight and deeper understanding of existing algorithms and leads to novel and principled proposals for their improvement. This book presents a coherent picture of the state-of-the-art in the theoretical analysis of on-line learning. An introduction relates the subject to other developments in neural networks and explains the overall picture. Surveys by leading experts in the field combine new and established material and enable non-experts to learn more about the techniques and methods used. This book, the first in the area, provides a comprehensive view of the subject and will be welcomed by mathematicians, scientists and engineers, whether in industry or academia.

The theory of on-line learning: a statistical physics approach

In this paper we review recent theoretical approaches for analysing the dynamics of on-line learning in multilayer neural networks using methods adopted from statistical physics. The analysis is based on monitoring a set of macroscopic variables from which the generalisation error can be calculated. A closed set of dynamical equations for the macroscopic variables is derived analytically and solved numerically. The theoretical framework is then employed for defining optimal learning parameters and for analysing the incorporation of second order information into the learning process using natural gradient descent and matrix-momentum based methods. We will also briefly explain an extension of the original framework for analysing the case where training examples are sampled with repetition.

Challenges for expatriate managers:an exploration of cross-cultural management, adjustment, and training issues faced by Anglo-American managers in Hong Kong

This field work study furthers understanding about expatriate management, in particular, the nature of cross-cultural management in Hong Kong involving Anglo-American expatriate and Chinese host national managers, the important features of adjustment for expatriates living and working there, and the type of training which will assist them to adjust and to work successfully in this Asian environment. Qualitative and quantitative data on each issue was gathered during in-depth interviews in Hong Kong, using structured interview schedules, with 39 expatriate and 31 host national managers drawn from a cross-section of functional areas and organizations. Despite the adoption of Western technology and the influence of Western business practices, micro-level management in Hong Kong retains a cultural specificity which is consistent with the norms and values of Chinese culture. There are differences in how expatriates and host nationals define their social roles, and Hong Kong's recent colonial history appears to influence cross-cultural interpersonal interactions. The inability of the spouse and/or family to adapt to Hong Kong is identified as a major reason for expatriate assignments to fail, though the causes have less to do with living away from family and friends, than with Hong Kong's highly urbanized environment and the heavy demands of work. Culture shock is not identified as a major problem, but in Hong Kong micro-level social factors require greater adjustment than macro-level societal factors. The adjustment of expatriate managers is facilitated by a strong orientation towards career development and hard work, possession of technical/professional expertise, and a willingness to engage in a process of continuous 'active learning' with respect to the host national society and culture. A four-part model of manager training suitable for Hong Kong is derived from the study data. It consists of a pre-departure briefing, post-arrival cross-cultural training, language training in basic Cantonese and in how to communicate more effectively in English with non-native speakers, and the assignment of a mentor to newly arrived expatriate managers.

Mapping teaching, learning and assessment in the MPharm in UK schools of pharmacy

Aim To undertake a national study of teaching, learning and assessment in UK schools of pharmacy. Design Triangulation of course documentation, 24 semi-structured interviews undertaken with 29 representatives from the schools and a survey of all final year students (n=1,847) in the 15 schools within the UK during 2003–04. Subjects and setting All established UK pharmacy schools and final year MPharm students. Outcome measures Data were combined and analysed under the topics of curriculum, teaching and learning, assessment, multi-professional teaching and learning, placement education and research projects. Results Professional accreditation was the main driver for curriculum design but links to preregistration training were poor. Curricula were consistent but offered little student choice. On average half the curriculum was science-based. Staff supported the science content but students less so. Courses were didactic but schools were experimenting with new methods of learning. Examinations were the principal form of assessment but the contribution of practice to the final degree ranged considerably (21–63%). Most students considered the assessment load to be about right but with too much emphasis upon knowledge. Assessment of professional competence was focused upon dispensing and pharmacy law. All schools undertook placement teaching in hospitals but there was little in community/primary care. There was little inter-professional education. Resources and logistics were the major limiters. Conclusions There is a need for an integrated review of the accreditation process for the MPharm and preregistration training and redefinition of professional competence at an undergraduate level.

Mirror-image relations in category learning

The discrimination of patterns that are mirror-symmetric counterparts of each other is difficult and requires substantial training. We explored whether mirror-image discrimination during expertise acquisition is based on associative learning strategies or involves a representational shift towards configural pattern descriptions that permit resolution of symmetry relations. Subjects were trained to discriminate between sets of unfamiliar grey-level patterns in two conditions, which either required the separation of mirror images or not. Both groups were subsequently tested in a 4-class category-learning task employing the same set of stimuli. The results show that subjects who had successfully learned to discriminate between mirror-symmetric counterparts were distinctly faster in the categorization task, indicating a transfer of conceptual knowledge between the two tasks. Additional computer simulations suggest that the development of such symmetry concepts involves the construction of configural, protoholistic descriptions, in which positions of pattern parts are encoded relative to a spatial frame of reference.

The development and evaluation of distance learning materials for administrative personnel in a multi-national company

There has been substantial research into the role of distance learning in education. Despite the rise in the popularity and practice of this form of learning in business, there has not been a parallel increase in the amount of research carried out in this field. An extensive investigation was conducted into the entire distance learning system of a multi-national company with particular emphasis on the design, implementation and evaluation of the materials. In addition, the performance and attitudes of trainees were examined. The results of a comparative study indicated that trainees using distance learning had significantly higher test scores than trainees using conventional face-to-face training. The influence of the previous distance learning experience, educational background and selected study environment of trainees was investigated. Trainees with previous experience of distance learning were more likely to complete the course and with significantly higher test scores than trainees with no previous experience. The more advanced the educational background of trainees, the greater the likelihood of their completing the course, although there was no significant difference in the test scores achieved. Trainees preferred to use the materials at home and those opting to study in this environment scored significantly higher than those studying in the office, the study room at work or in a combination of environments. The influence of learning styles (Kolb, 1976) was tested. The results indicated that the convergers had the greatest completion rates and scored significantly higher than trainees with the assimilator, accommodator and diverger learning styles. The attitudes of the trainees, supervisors and trainers were examined using questionnaire, interview and discussion techniques. The findings highlighted the potential problems of lack of awareness and low motivation which could prove to be major obstacles to the success of distance learning in business.