THE DYNAMIC OF ARITHMETIC - RICHARD DALLAWAY


Chatper 5

A CONNECTIONIST MODEL OF MULTICOLUMN ARITHMETIC

Before detailing the connectionist network used to model arithmetic, this chapter first outlines the known features of arithmetic that constrain the model. The architecture, input and output representations and training environment are then described. The results of simulations---the errors the network makes when solving multicolumn problems---are presented, and the network's behaviour is analysed. Finally there is a discussion of how the network relates to Sierra, and how notions like bug migration and impasses can be accommodated.

  • Constraints on the model
  • What we know about multicolumn arithmetic
  • What we don't know about multicolumn arithmetic
  • Architecture of the model
  • Input and output representations
  • Training
  • Results
  • Analysis
  • Finite state machines
  • Graded state machines
  • Repairs
  • Accuracy of transitions
  • Development of trajectories
  • Summary
  • Bug migration
  • Bug migration as noise
  • Bug migration as learning
  • Impasses
  • The importance of impasses
  • Summary

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