A category theory approach to the semiotics of machine learning

The successes of Machine Learning, and in particular of Deep Learning systems, have led to a reformulation of the Artificial Intelligence agenda. One of the pressing issues in the field is the extraction of knowledge out of the behavior of those systems. In this paper we propose a semiotic analysis of that behavior, based on the formal model of learners. We analyze the topos-theoretic properties that ensure the logical expressivity of the knowledge embodied by learners. Furthermore, we show that there exists an ideal universal learner, able to interpret the knowledge gained about any possible function as well as about itself, which can be monotonically approximated by networks of increasing size.