Information theoretic study of the neural geometry induced by category
  learning
Laurent Bonnasse-Gahot Jean-Pierre Nadal
Categorization is an important topic both for biological and artificial
neural networks. Here, we take an information theoretic approach to assess the
efficiency of the representations induced by category learning. We show that
one can decompose the relevant Bayesian cost into two components, one for the
coding part and one for the decoding part. Minimizing the coding cost implies
maximizing the mutual information between the set of categories and the neural
activities. We analytically show that this mutual information can be written as
the sum of two terms that can be interpreted as (i) finding an appropriate
representation space, and, (ii) building a representation with the appropriate
metrics, based on the neural Fisher information on this space. One main
consequence is that category learning induces an expansion of neural space near
decision boundaries. Finally, we provide numerical illustrations that show how
Fisher information of the coding neural population aligns with the boundaries
between categories.