|InterJournal Complex Systems, 246
|Manuscript Number: |
Submission Date: 981215
|What Can We Learn From Learning Curves?|
Subject(s): CX.16, CX.41, CX.65, CX.66
Category: Brief Article
One of the universal characteristic features of complex adaptive systems is their capability to learn in the sense of exhibiting persistent change of behavior in response to changing external conditions. This applies to natural as well as artificial complex systems across different levels of complexity. There exists a vast amount of literature that deals with specifics of how learning takes place and how it can be accelerated or made more robust to external perturbations. Since the early years of systematic studies of motor learning a number of different types of functional forms have been proposed to describe the shape of these learning curves. In many publications this description was based purely on curve fitting without much theoretical foundation. Others are dealing with models for learning in an artificial intelligence context (for instance the "chunking model" of Newell and Rosenbloom) as a theoretical basis for general learning behavior. The recent interest in a dynamical systems approach to motor behavior provided the interpretation of learning as transient approach of state space trajectories to attractors that correspond to the behavioral pattern that needs to be learned. This is closely related to hill climbing methods in neural network learning. The corresponding learning curves therefor would be expected to show an exponential characteristics. Other interpretations associated learning with non-equilibrium phase-transitions which would imply power-law behavior with critical exponents. In this report we describe conditions for motor learning for which we would expect exponential or power law behavior. We fit both learning curve representations to empirical data-sets from motor tasks. We present simulations that demonstrate how observed learning curves can be reproduced by a number of different methods that can lead to testable hypotheses about the learning mechanism.
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