Soft Mode in the Dynamics of Over-realizable On-line Learning for Soft Committee Machines
This addresses the problem of understanding learning dynamics in over-parametrized neural networks for researchers in machine learning theory, though it is incremental as it builds on prior student-teacher scenarios.
The paper investigates the dynamics of over-realizable on-line learning in two-layer soft committee machines, finding that the approach to perfect learning follows a power-law decay instead of exponential decay as in the realizable case, with all student nodes replicating teacher nodes under appropriate rescaling.
Over-parametrized deep neural networks trained by stochastic gradient descent are successful in performing many tasks of practical relevance. One aspect of over-parametrization is the possibility that the student network has a larger expressivity than the data generating process. In the context of a student-teacher scenario, this corresponds to the so-called over-realizable case, where the student network has a larger number of hidden units than the teacher. For on-line learning of a two-layer soft committee machine in the over-realizable case, we find that the approach to perfect learning occurs in a power-law fashion rather than exponentially as in the realizable case. All student nodes learn and replicate one of the teacher nodes if teacher and student outputs are suitably rescaled.