Exponential Transitions: Telltale Sign of Consistency in Learning Systems

This work proves the existence of observable exponential transitions in all learning processes, exponential transitions that can be used to tell when a sample performance index faithfully represents the true average performance index. The existence of this critical behavior in every learning problem allows to subsume the conditions imposed by statistical learning theory to ensure the consistency of a Learning Machine (LM). This fact is used to design an algorithm that easily permits to determine whether an arbitrary LM has achieved consistency or not. The algorithm is tested with classification and regression problems.