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Résumé |
Modular structures in the brain are hypothesized to play a central role in
intelligence by permitting compositional representations, but the general
mechanisms driving discrete structure emergence from more-continuous genetically
specified morphogens have remained elusive. Grid cells represent self-location
during navigation in 2D spaces with spatially periodic codes of a small number of
discrete periodicities. They present a paradigmatic example of the computational
advantages of modular representations– permitting exponential representational
capacity and strong intrinsic error-correction by representing a continuous
euclidean variable (location), with a modular set of position-encoding phases.
Underlying this discrete modular coding, which emerges rapidly postnatally, are
biophysical gradients that vary smoothly. I will consider how smooth gradients can
give rise to globally discrete function through self-organization in the context
of this system. We show that two purely local lateral interactions, one with a
smoothly graded parameter in the brain and another without a spatial gradient can
simultaneously give rise to local pattern formation and global modularity. We show
that this mechanism of modularity emergence is highly generic, robust, and almost
completely insensitive to parameters because it is a topological process. The
model makes predictions for the relationships between modules that furnish the
most accurate match to data to date. Abstractly, the mechanism involves dynamics
on the sum of two energy landscapes, one of which is a shallow global minimum that
smoothly moves with the spatial parametric variation, and the other of which is a
static landscape with multiple narrow minima. We believe this is a novel self-
organization mechanism by which simple local interactions and smooth gradients may
interact to induce macroscopic modular organization. |
