  Representing and reasoning about physical space is fundamental to animal
survival, and the mammalian lineage expresses a wealth of specialized neural
representations that encode space. Grid cells, whose discovery earned a Nobel
prize, are a striking example: a grid cell is a neuron that fires if and only
if the animal is spatially located at the vertices of a regular triangular
lattice that tiles all explored two-dimensional environments. Significant
theoretical work has gone into understanding why mammals have learned these
particular representations, and recent work has proposed a ``unified theory for
the computational and mechanistic origin of grid cells," claiming to answer why
the mammalian lineage has learned grid cells. However, the Unified Theory makes
a series of highly specific assumptions about the target readouts of grid cells
- putatively place cells. In this work, we explicitly identify what these
mathematical assumptions are, then test two of the critical assumptions using
biological place cell data. At both the population and single-cell levels, we
find evidence suggesting that neither of the assumptions are likely true in
biological neural representations. These results call the Unified Theory into
question, suggesting that biological grid cells likely have a different origin
than those obtained in trained artificial neural networks.
