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Categorization is an important topic both for biological and artificialneural networks. Here, we take an information theoretic approach to assess theefficiency of the representations induced by category learning. We show thatone can decompose the relevant Bayesian cost into two components, one for thecoding part and one for the decoding part. Minimizing the coding cost impliesmaximizing the mutual information between the set of categories and the neuralactivities. We analytically show that this mutual information can be written asthe sum of two terms that can be interpreted as (i) finding an appropriaterepresentation space, and, (ii) building a representation with the appropriatemetrics, based on the neural Fisher information on this space. One mainconsequence is that category learning induces an expansion of neural space neardecision boundaries. Finally, we provide numerical illustrations that show howFisher information of the coding neural population aligns with the boundariesbetween categories.

Information theoretic study of the neural geometry induced by category learning