Transient amplification in balanced neural networks

Transient amplification has been proposed as an important mechanism not only in neuroscience but in many areas modeled by dynamical systems. Despite that, there is no clear biologically plausible mechanism which fine-tunes the coupling matrix or selects signals to be amplified. In this work we quantitatively study transient dynamics in the Rajan-Abbott model of a recurrent neural network [K. Rajan and L.F. Abbot PRL 97, 188104 (2006)]. We find a second order transition between a phase of weakly or no amplified transients and a phase of strong amplification, where the average trajectory is amplified. In the latter phase the combination of Dale's principle and excitatory/inhibitory balance allows for strong weights, while maintaining the system at the edge of chaos. Moreover, we show that the amplification goes hand in hand with greater variability of the dynamics. By numerically studying the full probability density of the squared norm, we observe as the strength of weights grows, the right tail of the distribution becomes heavier, moving from the Gaussian to the exponential tail.