A continuous two-dimensional model of discrete one-dimensional threshold learning

We present a model of threshold learning that represents discrete one-dimensional processes by a continuous two-dimensional process. The model gives us an overall view of the learning dynamics of an expanded range of training procedures, and provides insight for expansion to multidimensional threshold logic gates. The expected performance is measured by learning curves, while the confidence in this expected performance is measured by variance curves. Previous work on the continuous approximation has been restricted to single-dimensional processes. We believe this theory will provide the designer of trainable pattern classifiers with tools for deciding when to stop training.