  Cortical populations of neurons develop sparse representations adapted to the
statistics of the environment. While existing synaptic plasticity models
reproduce some of the observed receptive-field properties, a major obstacle is
the sensitivity of Hebbian learning to omnipresent spurious correlations in
cortical networks which can overshadow relevant latent input features. Here we
develop a theory for synaptic plasticity that is invariant to second-order
correlations in the input. Going beyond classical Hebbian learning, we show how
Hebbian long-term depression (LTD) cancels the sensitivity to second-order
correlations, so that receptive fields become aligned with features hidden in
higher-order statistics. Our simulations demonstrate how correlation-invariance
enables biologically realistic models to develop sparse population codes,
despite diverse levels of variability and heterogeneity. The theory advances
our understanding of local unsupervised learning in cortical circuits and
assigns a specific functional role to synaptic LTD mechanisms in pyramidal
neurons.
