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New on the VVTNS YouTube Channel https://www.wwtns.online/past-seminars-2025-2026 *Flexible analog computation in low-rank balanced spiking networks* Lecture delivered on November 26, 2025 by Alfonso Renart Champalimaud Centre for the Unknown, Lisbon *Abstract:* 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. *About VVTNS : Launched as the World Wide Theoretical Neuroscience Seminar (WWTNS) in November 2020 and renamed in homage to Carl van Vreeswijk in Memoriam (April 20, 2022), Speakers have the occasion to talk about theoretical aspects of their work which cannot be discussed in a setting where the majority of the audience consists of experimentalists. The seminars, **held on Wednesdays at 11 am ET,** are 45-50 min long followed by a discussion. The talks are recorded with authorization of the speaker and are available to everybody on our YouTube channel.* ᐧ