Rings, Lines and Rotations: A Comparative Geometry of Neural Activity in Mouse, Crow and Macaque From Open Recordings

When many neurons fire together, their joint activity traces a shape. I asked what shapes appear in three very different brains, using only public recordings and one analysis pipeline. In a mouse, 31 head-direction cells formed a closed ring whose loop was about four times stronger than in shuffled data, and the ring returned during REM sleep. In crows, 486 neurons of the nidopallium caudolaterale coded the numbers 1 to 5 along an open, bent line that fitted a logarithmic scale best (Spearman 0.94 for tuned cells). In a macaque, 182 motor cortex units held reach directions on a loop and then rotated through time, with 62% of the fitted dynamics rotational. The shape follows what is being coded: circles for directions, ordered lines for quantities, rotations for movement. Bird and mammal brains, built very differently, reach similar geometric solutions. The proposal sets out tests, limits and next steps.