Neural coding and information geometry

Crudely stated, a central issue in computational neuroscience is to gain insight into how interactions of neural activities carry and process, or encode and decode, information of the outside world. Once neural activities are considered samples of statistical variables, it becomes obvious that research into this neural coding has various connections with the issues investigated by information geometry, and it thus benefits from the perspectives and tools of information geometry. In my talk, I first provide a general overview, to introduce the audience to this subject, and then present some of our relevant work. For example, several previous studies have suggested that a pairwise interaction model (equivalent to so-called Ising models) is sufficient for describing neural activity patterns. In contrast, we recently demonstrated that a hierarchical model of the pairwise models on different scales is more accurate for describing neural data, despite its relative parsimony compared with ordinary pairwise models. The hierarchical model embeds higher-than-pairwise interactions as constraints and has an interesting relation to the generalized Pythagorean theorem or decompositions of different order interactions of discrete variables.