Identifying the impact of local connectivity patterns on dynamics in excitatory-inhibitory networks

Networks of excitatory and inhibitory (EI) neurons form a canonical circuit in the brain. Seminal theoretical results on dynamics of such networks are based on the assumption that synaptic strengths depend on the type of neurons they connect, but are otherwise statistically independent. Recent synaptic physiology datasets however highlight the prominence of specific connectivity patterns that go well beyond what is expected from independent connections. While decades of influential research have demonstrated the strong role of the basic EI cell type structure, to which extent additional connectivity features influence dynamics remains to be fully determined. Here we examine the effects of pairwise connectivity motifs on the linear dynamics in EI networks using an analytical framework that approximates the connectivity in terms of low-rank structures. This low-rank approximation is based on a mathematical derivation of the dominant eigenvalues of the connectivity matrix and predicts the impact on responses to external inputs of connectivity motifs and their interactions with cell-type structure. Our results reveal that a particular pattern of connectivity, chain motifs, have a much stronger impact on dominant eigenmodes than other pairwise motifs. An overrepresentation of chain motifs induces a strong positive eigenvalue in inhibition-dominated networks and generates a potential instability that requires revisiting the classical excitation-inhibition balance criteria. Examining effects of external inputs, we show that chain motifs can on their own induce paradoxical responses where an increased input to inhibitory neurons leads to a decrease in their activity due to the recurrent feedback. These findings have direct implications for the interpretation of experiments in which responses to optogenetic perturbations are measured and used to infer the dynamical regime of cortical circuits.

Brief technical note on linearizing recurrent neural networks (RNNs) before vs after the pointwise nonlinearity

Linearization of the dynamics of recurrent neural networks (RNNs) is often used to study their properties. The same RNN dynamics can be written in terms of the ``activations" (the net inputs to each unit, before its pointwise nonlinearity) or in terms of the ``activities" (the output of each unit, after its pointwise nonlinearity); the two corresponding linearizations are different from each other. This brief and informal technical note describes the relationship between the two linearizations, between the left and right eigenvectors of their dynamics matrices, and shows that some context-dependent effects are readily apparent under linearization of activity dynamics but not linearization of activation dynamics.