The learning dynamics of a universal approximator

The learning properties of a universal approximator, a normalized committee machine with adjustable biases, are studied for on-line back-propagation learning. Within a statistical mechanics framework, numerical studies show that this model has features which do not exist in previously studied two-layer network models without adjustable biases, e.g., attractive suboptimal symmetric phases even for realizable cases and noiseless data.

Learning with regularizers in multilayer neural networks

We study the effect of regularization in an on-line gradient-descent learning scenario for a general two-layer student network with an arbitrary number of hidden units. Training examples are randomly drawn input vectors labelled by a two-layer teacher network with an arbitrary number of hidden units which may be corrupted by Gaussian output noise. We examine the effect of weight decay regularization on the dynamical evolution of the order parameters and generalization error in various phases of the learning process, in both noiseless and noisy scenarios.

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.

Noise, regularizers, and unrealizable scenarios in online learning from restricted training sets

We study the dynamics of on-line learning in multilayer neural networks where training examples are sampled with repetition and where the number of examples scales with the number of network weights. The analysis is carried out using the dynamical replica method aimed at obtaining a closed set of coupled equations for a set of macroscopic variables from which both training and generalization errors can be calculated. We focus on scenarios whereby training examples are corrupted by additive Gaussian output noise and regularizers are introduced to improve the network performance. The dependence of the dynamics on the noise level, with and without regularizers, is examined, as well as that of the asymptotic values obtained for both training and generalization errors. We also demonstrate the ability of the method to approximate the learning dynamics in structurally unrealizable scenarios. The theoretical results show good agreement with those obtained by computer simulations.

Organisational learning - a critical systems thinking discipline

Original Paper European Journal of Information Systems (2001) 10, 135–146; doi:10.1057/palgrave.ejis.3000394 Organisational learning—a critical systems thinking discipline P Panagiotidis1,3 and J S Edwards2,4 1Deloitte and Touche, Athens, Greece 2Aston Business School, Aston University, Aston Triangle, Birmingham, B4 7ET, UK Correspondence: Dr J S Edwards, Aston Business School, Aston University, Aston Triangle, Birmingham, B4 7ET, UK. E-mail: j.s.edwards@aston.ac.uk 3Petros Panagiotidis is Manager responsible for the Process and Systems Integrity Services of Deloitte and Touche in Athens, Greece. He has a BSc in Business Administration and an MSc in Management Information Systems from Western International University, Phoenix, Arizona, USA; an MSc in Business Systems Analysis and Design from City University, London, UK; and a PhD degree from Aston University, Birmingham, UK. His doctorate was in Business Systems Analysis and Design. His principal interests now are in the ERP/DSS field, where he serves as project leader and project risk managment leader in the implementation of SAP and JD Edwards/Cognos in various major clients in the telecommunications and manufacturing sectors. In addition, he is responsible for the development and application of knowledge management systems and activity-based costing systems. 4John S Edwards is Senior Lecturer in Operational Research and Systems at Aston Business School, Birmingham, UK. He holds MA and PhD degrees (in mathematics and operational research respectively) from Cambridge University. His principal research interests are in knowledge management and decision support, especially methods and processes for system development. He has written more than 30 research papers on these topics, and two books, Building Knowledge-based Systems and Decision Making with Computers, both published by Pitman. Current research work includes the effect of scale of operations on knowledge management, interfacing expert systems with simulation models, process modelling in law and legal services, and a study of the use of artifical intelligence techniques in management accounting. Top of pageAbstract This paper deals with the application of critical systems thinking in the domain of organisational learning and knowledge management. Its viewpoint is that deep organisational learning only takes place when the business systems' stakeholders reflect on their actions and thus inquire about their purpose(s) in relation to the business system and the other stakeholders they perceive to exist. This is done by reflecting both on the sources of motivation and/or deception that are contained in their purpose, and also on the sources of collective motivation and/or deception that are contained in the business system's purpose. The development of an organisational information system that captures, manages and institutionalises meaningful information—a knowledge management system—cannot be separated from organisational learning practices, since it should be the result of these very practices. Although Senge's five disciplines provide a useful starting-point in looking at organisational learning, we argue for a critical systems approach, instead of an uncritical Systems Dynamics one that concentrates only on the organisational learning practices. We proceed to outline a methodology called Business Systems Purpose Analysis (BSPA) that offers a participatory structure for team and organisational learning, upon which the stakeholders can take legitimate action that is based on the force of the better argument. In addition, the organisational learning process in BSPA leads to the development of an intrinsically motivated information organisational system that allows for the institutionalisation of the learning process itself in the form of an organisational knowledge management system. This could be a specific application, or something as wide-ranging as an Enterprise Resource Planning (ERP) implementation. Examples of the use of BSPA in two ERP implementations are presented.

The evolution of learning systems:to Bayes or not to be

Bayesian algorithms pose a limit to the performance learning algorithms can achieve. Natural selection should guide the evolution of information processing systems towards those limits. What can we learn from this evolution and what properties do the intermediate stages have? While this question is too general to permit any answer, progress can be made by restricting the class of information processing systems under study. We present analytical and numerical results for the evolution of on-line algorithms for learning from examples for neural network classifiers, which might include or not a hidden layer. The analytical results are obtained by solving a variational problem to determine the learning algorithm that leads to maximum generalization ability. Simulations using evolutionary programming, for programs that implement learning algorithms, confirm and expand the results. The principal result is not just that the evolution is towards a Bayesian limit. Indeed it is essentially reached. In addition we find that evolution is driven by the discovery of useful structures or combinations of variables and operators. In different runs the temporal order of the discovery of such combinations is unique. The main result is that combinations that signal the surprise brought by an example arise always before combinations that serve to gauge the performance of the learning algorithm. This latter structures can be used to implement annealing schedules. The temporal ordering can be understood analytically as well by doing the functional optimization in restricted functional spaces. We also show that there is data suggesting that the appearance of these traits also follows the same temporal ordering in biological systems. © 2006 American Institute of Physics.