  We present a generalized theoretical framework for olfactory representation
and plasticity, using the theory of smooth manifolds and sheaves to depict
categorical odor learning via distributed neural computation. Beginning with
the space of all possible inputs to the olfactory system, we develop a dynamic
model for odor learning that culminates in a perceptual space in which
categorical odor representations are hierarchically constructed through
experience, exhibiting statistically appropriate consequential regions and
clear relationships between the broader and narrower identities to which a
given odor might be assigned. The model reflects both the sampling-based
physical similarity relationships among odorants, as observed in physiological
receptor response profiles, and the acquired, learning-dependent perceptual
similarity relationships among odors that can be measured behaviorally, and
defines the relationship between them. Individual training and experience
generates correspondingly more sophisticated odor identification capabilities.
Because these odor representations are constructed from experience and depend
on local, distributed plasticity mechanisms, geometries that fix curvature are
insufficient to describe the capabilities of the system. This generative
framework also encompasses hypotheses explaining representational drift in
postbulbar circuits and the context-dependent remapping of perceptual
similarity relationships.
