All you need is relative information#


SLT has taught me that relative information (or Kullback-Leibler divergence) is all you need. For instance, the level sets of relative information give us state density functions, whose Fourier, Laplace and Mellin transforms reveal different facets of learning algorithms and their ability to generalize. In this talk, I will outline two ongoing projects involving relative information. The first project explores the information theory of time series, for the purpose of understanding language models and reinforcement learning. Using relative information rate, we derive stochastic learning algorithms for spiking neural networks with memory. The second project explores cohomological generalizations of relative information, building on recent work by Pierre Baudot and Daniel Bennequin and by Tai-Danae Bradley. The hope is to uncover new tools for studying non-statistical spaces, by analyzing the level sets of generalized relative information and their transforms.