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Structured connectivity as a source of slow dynamics in randomly connected networks
Daniel Martí1, Nicolas Brunel2, Srdjan Ostojic1
1Group for Neural Theory, École Normale Supérieure, Paris, France 2Department of Statistics and Neurobiology, The University of Chicago, IL, USA

Cortical networks exhibit dynamics on a range of timescales. Slow dynamics at the timescale of hundreds of milliseconds to seconds carry information about the recent history of the stimulus, and can therefore act as a substrate for short-term memory. How networks composed of fast units, like neurons, can generate such slow dynamics is still an open question. One possible mechanism is based on positive feedback: in randomly connected networks, the collective timescale can be set arbitrarily long by balancing the intrinsic decay rate of individual neurons with recurrent input. This type of mechanism relies however on a precise fine-tuning of the synaptic coupling.

Another possibility is that slow dynamics are induced by structured connectivity between neurons. Indeed the connectivity of cortical networks is not fully random. The simplest and most prominent deviation from randomness found in experimental data is the overrepresentation of bidirectional connections among pyramidal cells. Here we argue that symmetry in the connectivity can act as a robust mechanism for the generation of slow dynamics in networks of fast units.

Using numerical and analytical methods, we investigate the dynamics of networks with partially symmetric structure. We consider the two dynamical regimes exhibited by random neural networks: the weak-coupling regime, where the firing activity decays to a single fixed point unless the network is stimulated, and the strong-coupling or chaotic regime, characterized by internally generated fluctuating firing rates. We determine how symmetry modulates the timescale of the noise filtered by the network in the weak-coupling regime, as well as the timescale of the intrinsic rate fluctuations in the chaotic regime. In both cases symmetry increases the characteristic asymptotic decay time of the autocorrelation function. Furthermore, for sufficiently symmetric connections the network operating in the chaotic regime exhibits aging effects, by which the timescale of the rate fluctuations slowly grows as time evolves. Such history-dependent dynamics might constitute a new mechanism for short-term memory storage in random networks.