Before revision:  This algebraic viewpoint provides intuition about how the network ingredients shape the input-output mapping for moments, as well as cumulants  .
After revision:  This algebraic viewpoint provides intuition about how the network ingredients shape the input-output mapping for moments, as well as cumulants . We also show using numerical simulation that our results hold for neurons with refractoriness implemented by self-inhibition, provided the corresponding negative feedback for each neuron only mildly alters its mean firing probability .