Stochastic Thermodynamics of Learning
  Virtually every organism gathers information about its noisy environment and builds models from that data, mostly using neural networks. Here, we use stochastic thermodynamics to analyse the learning of a classification rule by a neural network. We show that the information acquired by the network is bounded by the thermodynamic cost of learning and introduce a learning efficiency $\eta\le1$. We discuss the conditions for optimal learning and analyse Hebbian learning in the thermodynamic limit. 
Sebastian Goldt and Udo Seifert
cond-mat.stat-mech cond-mat.dis-nn physics.bio-ph