Tatiana Engel: Unifying neural population dynamics, manifold geometry, and single-cell selectivity

Single neurons show complex, heterogeneous responses during cognitive tasks, which often form low-dimensional manifolds in the population state space. Accordingly, it is often assumed that neural computations arise from low-dimensional population dynamics, while functional properties of individual neurons are not interpretable. I will present our recent work bridging single-neuron selectivity with manifold geometry and population dynamics. First, we developed a flexible approach for simultaneously inferring single-trial population dynamics and tuning functions of individual neurons to the latent population state. Applied to spike data recorded during decision-making, our model revealed that all neurons encode the same dynamic decision variable, and heterogeneous firing rates result from diverse tuning of single neurons to this decision variable. Second, using a firing-rate recurrent network model, we mathematically prove that responses of single neurons cluster into functional types when population dynamics are confined to a low-dimensional linear subspace, with the number of distinct response types equal to the linear dimension of the neural manifold. We confirm these predictions in recurrent neural networks trained on cognitive tasks and brain-wide neural recordings from mice during decision-making. Our results show that low-dimensional population dynamics must arise from a few interacting subpopulations, revealing a fundamental constraint on how recurrent circuits represent information.