Flexible analog computation in low-rank balanced spiking networks
Recurrent networks with balanced excitation-inhibition explain a wide range of neurophysiological observations, but can only implement a limited set of transformations on their input. On the other hand networks of firing-rate units with low-rank connectivity have universal computational capabilities, but do not work with spikes or generate noise self-consistently. Although empirical approaches to merge these two computational frameworks have been constructed, there is no established theory describing their unification. Here we develop such a theory. We study analytically and numerically networks with connectivity comprising random “strong”, and low-rank “weak” components. When the low-rank connectivity is slow, a well-defined notion of instantaneous firing rate emerges which implies universal computation as previously shown. However, the fact that such time-varying rates are the result of E-I balance has important implications. We show that internally or externally generated fluctuations along particular latent modes tend to break the E-I balance. Its maintenance is obtained through the emergence of a spontaneous coupling between the mean and the variance of the membrane potential and the norm of the latent state driving these modes. This leads to several predictions, the most counterintuitive of which is that coherent global fluctuations in subthreshold membrane potential (Vm) should coexist with desynchronized activity at constant firing rates when the dynamics of these modes is excited. To test our theory, we show that the coupling between the average Vm and the latent state adds new non-linear dimensions to the low-dimensional manifold of the network, which lead to a frequency doubling when the input to the network is periodic, a prediction that is borne out in population recordings from mouse V1. Our results unify two prevalent frameworks for cortical computation and clarify the relationship between computation, dynamics and geometry in circuits of spiking neurons. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2025-11-26. Recording duration: 00:39:26.
Self-organisation in interneuron circuits
Inhibitory interneurons come in different classes and form intricate circuits. While our knowledge of these circuits has advanced substantially over the last decades, it is not fully understood how the structure of these circuits relates to their function. I will present some of our recent attempts to “understand” the structure of interneuron circuits by means of computational modeling. Surprisingly (at least for us), we found that prominent features of inhibitory circuitry can be accounted for by an optimisation for excitation-inhibition (E/I) balance. In particular, we find that such an optimisation generates networks that resemble mouse V1 in terms of the structure of synaptic efficacies between principal cells and parvalbumin-positive interneurons. Moreover, an optimisation for E/I balance across neuronal compartments promotes a functional diversification of interneurons into two classes that resemble parvalbumin and somatostatin-positive interneurons. Time permitting, I may briefly touch on recent work in which we link E/I balance to prediction error coding in V1.