Phase Transitions in Connectionist Models Having Rapidly Varying Connection Strengths

A phase transition in a connectionist model refers to a qualitative change in the model's behavior as parameters determining the spread of activation (gain, decay rate, etc.) pass through certain critical values. As connectionist methods have been increasingly adopted to model various problems in neuroscience, artificial intelligence, and cognitive science, there has been an increased need to understand and predict these phase transitions to assure meaningful model behavior. This paper extends previous results on phase transitions to encompass a class of connectionist models having rapidly varying connection strengths (fast weights). Phase transitions are predicted theoretically and then verified through a series of computer simulations. These results broaden the range of connectionist models for which phase transitions are identified and lay the foundation for future studies comparing models with rapidly varying and slowly varying connection strengths.