# Place Cells

In large environments at naturalistic scale, rat and bat hippocampal CA1 place cells often carry multiple irregularly spaced firing fields, whereas the classical single-scale successor representation holds only in small enclosures. The factorised hierarchical successor representation (fHSR) folds one-step actions together with subgoal-directed subroutines into a predictive map, then decomposes the maps of several tasks into a non-negative overcomplete basis that gives each model cell its tuning. On a 48 m rat track and a 200 m bat track the model reproduced the gamma-Poisson overdispersion of field counts, and it predicted a spatial periodicity of population activity whose wavelength is independent of track length, a prediction tested in rat data.

In large environments at naturalistic scale, rat and bat hippocampal CA1 place cells often carry multiple irregularly spaced firing fields, whereas the classical single-scale successor representation holds only in small enclosures. The factorised hierarchical successor representation (fHSR) folds one-step actions together with subgoal-directed subroutines into a predictive map, then decomposes the maps of several tasks into a non-negative overcomplete basis that gives each model cell its tuning. On a 48 m rat track and a 200 m bat track the model reproduced the gamma-Poisson overdispersion of field counts, and it predicted a spatial periodicity of population activity whose wavelength is independent of track length, a prediction tested in rat data.

A theory treats spatial memory as a universal computer: a learner that reads only coincidences, whether two quantities are equal, rather than coordinates such as position or count that keep taking new values, has its rule fixed by finite experience at every length. The resulting machine pairs coprime-period rings, called clocks, with a controller that never reads them; trained on strings of up to 40 symbols, it holds its rule to length 500 on nine of fifteen benchmark tasks, five of which no LSTM or Transformer solves, and after training with new periods it reverses strings of 15,015 symbols without error before failing on the predicted curve.

A theory treats spatial memory as a universal computer: a learner that reads only coincidences, whether two quantities are equal, rather than coordinates such as position or count that keep taking new values, has its rule fixed by finite experience at every length. The resulting machine pairs coprime-period rings, called clocks, with a controller that never reads them; trained on strings of up to 40 symbols, it holds its rule to length 500 on nine of fifteen benchmark tasks, five of which no LSTM or Transformer solves, and after training with new periods it reverses strings of 15,015 symbols without error before failing on the predicted curve.