Statistical physics has long explained how networks of simple interacting neurons can act as associative memories, as in the Hopfield model. The more neurons a network has, the more memories it can store, up to a critical load beyond which recall collapses. But brains do not only store static memories. They generate rhythms, sequences and other activity patterns that unfold in time, and many such rhythms coexist in the same neural circuits. Classical theories, which assume symmetric interactions and memories that are static snapshots, cannot capture this. What happens when interactions are nonreciprocal (neuron A influences B differently than B influences A), so that a network can store many dynamical memories, each a different rhythm or even a chaotic trajectory?

In this talk I will present an analytical theory that answers this question for large neural networks storing infinitely many memories. Borrowing tools from the physics of disordered systems, we treat all memories except the one being recalled as structured noise. A path-integral calculation averages over this noise and reduces the whole network to a single neuron driven by self-consistent fluctuations, a dynamical mean-field theory. The theory shows that capacity depends on the characteristic frequencies encoded in the couplings (the eigenphases of the matrices encoding each memory). When all memories share the same eigenphases, their interference builds up and recall fails early. When eigenphases are diverse, much of the interference cancels, and the network can store up to about twice as many memories as a classical Hopfield network. I will discuss what this suggests about the coexistence of brain rhythms, and how diversity can act as a stabilising force in large interacting systems.

If you wish to attend this seminar online, please send an email to m.t.pham@uva.nl to receive the zoom-link.