Fast rate coding in heterogeneous spiking networks

A network of spiking neurons is said to operate in the rate coding regime if its dynamics can be accurately described by a continuous rate network. But how can discrete spike-based communication between neurons give rise to continuous rate-based dynamics? Computational studies showing that heterogeneous spiking networks can approximate the dynamics of recurrent neural networks (RNNs), a special case of rate network, assume that spikes are approximately Poisson or that network dynamics are slow. Here, we show that neither assumption is necessary: heterogeneous networks of non-Poisson neurons can produce fast rate-based dynamics. To demonstrate this, we show that signal transmission in feedforward networks of integrate-and-fire-type neurons can be described by a history-dependent rate network that is asymptotically exact as network size grows, even if heterogeneity persists, while linear-nonlinear rate networks fail. By providing a constructive model of fast rate coding in heterogeneous networks, this work lays the foundation for extending rate-based analyses of neural recordings beyond the assumption of slow dynamics or Poisson rate codes.