Neuronal common input strength is unidentifiable from average firing rates and synchrony

Observing firing rates of neurons and the level of synchrony between them is a common technique to draw conclusions on the micro-circuitry of the neuronal network they are embedded in, and on the input they receive from other stages of the nervous system. These questions are obviously of great importance for understanding the nature of neural coding. Using a very simple model network of leaky integrate and fire neurons that receive a mixture of common and independent inputs, we show that separating a synchrony code from a firing rate code from measurements of average spike counts and spike-spike synchrony is mathematically impossible.