Book contents
- Frontmatter
- Contents
- Acknowledgements
- List of contributors
- Foreword
- 1 Introduction
- 2 On-line Learning and Stochastic Approximations
- 3 Exact and Perturbation Solutions for the Ensemble Dynamics
- 4 A Statistical Study of On-line Learning
- 5 On-line Learning in Switching and Drifting Environments with Application to Blind Source Separation
- 6 Parameter Adaptation in Stochastic Optimization
- 7 Optimal On-line Learning in Multilayer Neural Networks
- 8 Universal Asymptotics in Committee Machines with Tree Architecture
- 9 Incorporating Curvature Information into On-line Learning
- 10 Annealed On-line Learning in Multilayer Neural Networks
- 11 On-line Learning of Prototypes and Principal Components
- 12 On-line Learning with Time-Correlated Examples
- 13 On-line Learning from Finite Training Sets
- 14 Dynamics of Supervised Learning with Restricted Training Sets
- 15 On-line Learning of a Decision Boundary with and without Queries
- 16 A Bayesian Approach to On-line Learning
- 17 Optimal Perceptron Learning: an On-line Bayesian Approach
14 - Dynamics of Supervised Learning with Restricted Training Sets
Published online by Cambridge University Press: 28 January 2010
- Frontmatter
- Contents
- Acknowledgements
- List of contributors
- Foreword
- 1 Introduction
- 2 On-line Learning and Stochastic Approximations
- 3 Exact and Perturbation Solutions for the Ensemble Dynamics
- 4 A Statistical Study of On-line Learning
- 5 On-line Learning in Switching and Drifting Environments with Application to Blind Source Separation
- 6 Parameter Adaptation in Stochastic Optimization
- 7 Optimal On-line Learning in Multilayer Neural Networks
- 8 Universal Asymptotics in Committee Machines with Tree Architecture
- 9 Incorporating Curvature Information into On-line Learning
- 10 Annealed On-line Learning in Multilayer Neural Networks
- 11 On-line Learning of Prototypes and Principal Components
- 12 On-line Learning with Time-Correlated Examples
- 13 On-line Learning from Finite Training Sets
- 14 Dynamics of Supervised Learning with Restricted Training Sets
- 15 On-line Learning of a Decision Boundary with and without Queries
- 16 A Bayesian Approach to On-line Learning
- 17 Optimal Perceptron Learning: an On-line Bayesian Approach
Summary
Abstract
We study the dynamics of supervised learning in layered neural networks, in the regime where the size p of the training set is proportional to the number N of inputs. Here the local fields are no longer described by Gaussian distributions. We show how dynamical replica theory can be used to predict the evolution of macroscopic observables, including the relevant performance measures, incorporating the theory of complete training sets in the limit p/N → ∞ as a special case. For simplicity we restrict ourselves here to single-layer networks and realizable tasks.
Introduction
In the last few years much progress has been made in the analysis of the dynamics of supervised learning in layered neural networks, using the strategy of statistical mechanics: by deriving from the microscopic dynamical equations a set of closed laws describing the evolution of suitably chosen macroscopic observables (dynamic order parameters) in the limit of an infinite system size [e.g. Kinzel & Rujan (1990), Kinouchi & Caticha (1992), Biehl & Schwarze (1992, 1995), Saad & Solla (1995)]. A recent review and more extensive guide to the relevant references can be found in Mace & Coolen (1998a).
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- On-Line Learning in Neural Networks , pp. 303 - 344Publisher: Cambridge University PressPrint publication year: 1999