  Animals smelling in the real world use a small number of receptors to sense a
vast number of natural molecular mixtures, and proceed to learn arbitrary
associations between odors and valences. Here, we propose a new interpretation
of how the architecture of olfactory circuits is adapted to meet these immense
complementary challenges. First, the diffuse binding of receptors to many
molecules compresses a vast odor space into a tiny receptor space, while
preserving similarity. Next, lateral interactions "densify" and decorrelate the
response, enhancing robustness to noise. Finally, disordered projections from
the periphery to the central brain reconfigure the densely packed information
into a format suitable for flexible learning of associations and valences. We
test our theory empirically using data from Drosophila. Our theory suggests
that the neural processing of olfactory information differs from the other
senses in its fundamental use of disorder.
