Intrinsic time scale growth in a linear stochastic neural chain

A model of stochastic neurons on a chain is solved analytically. Each neuron is defined by its own leak rate $\gamma_i$, noise strength $\sigma_i$ and synaptic strength $W_i$, that is the strength of the connection between neuron $i$ and $i-1$ on the chain. A recursive solution for the steady state covariance $C(t,t')$ is derived. Our main finding is that, in a linear stochastic feedforward chain, the intrinsic timescale of neural dynamics increases along the chain, when synaptic connections are sufficiently strong. This result supports the idea that feedforward computation can slow down neural dynamics within higher cortical hierarchies. This effect has been proposed to contribute to the emergence of invariant representations in higher-level visual areas.