Concentration of measure in "low-rank" biological neural networks
Recurrent neural networks with low-rank connectivity matrices are general and tractable models of collective dynamics in large networks. This class of models dates back to the seminal works of J. Hopfield (1982) and S. Amari (1972), and it still plays an instrumental role in computational neuroscience today. To highlight the analytical tractability of these models, I will first review some recent theoretical results concerning the case where the low-rank connectivity is random, the rank is kept fixed, and the number of neurons tends to infinity.


