  A key question in neuroscience is at which level functional meaning emerges
from biophysical phenomena. In most vertebrate systems, precise functions are
assigned at the level of neural populations, while single-neurons are deemed
unreliable and redundant. Here we challenge this view and show that many
single-neuron quantities, including voltages, firing thresholds, excitation,
inhibition, and spikes, acquire precise functional meaning whenever a network
learns to transmit information parsimoniously and precisely to the next layer.
Based on the hypothesis that neural circuits generate precise population codes
under severe constraints on metabolic costs, we derive synaptic plasticity
rules that allow a network to represent its time-varying inputs with maximal
accuracy. We provide exact solutions to the learnt optimal states, and we
predict the properties of an entire network from its input distribution and the
cost of activity. Single-neuron variability and tuning curves as typically
observed in cortex emerge over the course of learning, but paradoxically
coincide with a precise, non-redundant spike-based population code. Our work
suggests that neural circuits operate far more accurately than previously
thought, and that no spike is fired in vain.
