Slow, low-dimensional dynamics in balanced networks with partially symmetric connectivity

Cortical dynamics are slow and low dimensional. Relaxation, as measured for instance by the auto-correlation of the spike counts, can be slow (~seconds) compared to single neurons and synapses’ time constants (~hundreds of milliseconds). Moreover, spiking activity is coordinated across neural circuits despite weak, zero-lag cross-correlations between pairs of neurons. Thus, neural circuit dynamics can be described by a small number of collective variables compared to the number of neurons. By which mechanism(s) do slow and low-dimensional dynamics arise in cortical networks, and how are they related? Existing theories explain them as a result of precise adjustments of the synaptic connectivity. Slow relaxation is obtained, for instance, when the network operates close to the edge of stability, which depends on the variance of the synaptic efficacies. Low-dimensional dynamics is obtained, for instance, if the connectivity matrix is rank-deficient, which seems to require some form of synaptic plasticity. We note that the rank of a matrix and the variance of its elements can be independently adjusted. Here, we show that slow and low-dimensional dynamics naturally arise in balanced networks in the presence of partially symmetric synaptic connectivity that is consistent with experimental observations. The partial symmetry leads to an effective retarded self-interaction that slows down the dynamics and it tends to induce strong cross-correlations between pairs of neurons. These, however, are actively suppressed in the balanced regime, leading to strongly correlated network states with weak pair-wise correlations. We illustrate the computational relevance of this regime by showing that the network can dynamically (and robustly) retain the memory of a random stimulation over long time intervals. Taken together, our results suggest that slow and low-dimensional dynamics are a generic feature of balanced cortical networks, and can lead to robust, long-lived memory traces even in the absence of learning-related synaptic plasticity.