Grid-cell firing fields lack local sixfold symmetry
Abstract
The firing fields of a grid cell form a hexagonal lattice, yet each field's intrinsic geometric structure remains unclear: Are individual grid fields radially symmetric or do they exhibit (weak) sixfold modulation inherited from the global lattice? To address this question, we quantified the within-field angular structure using harmonic analysis and per-cell matched simulations that preserved sampling statistics, field scale, and lattice geometry after correction for global elliptic deformation. We found that, across the investigated cells, the sixfold harmonic power fraction was consistent with values from matched locally circular reference fields. Experimental fields further showed substantially less sixfold modulation than matched simulations with an imposed local sixfold component, demonstrating sensitivity to sixfold structure at that level. This conclusion was supported by a complementary sixfold regression metric, harmonic leave-one-out sensitivity analyses, and robustness checks across radial-window choices, smoothing, and simulated background-noise levels. An observation-matched Burak--Fiete continuous-attractor network likewise showed no selective local sixfold enhancement despite its globally periodic grid structure, and this conclusion persisted when grid scale and relative field width were matched more closely to the experimental regime. These results suggest that the global hexagonal lattice organization need not be accompanied by detectable local sixfold angular modulation of individual firing fields, placing quantitative constraints on grid-field microstructure and mechanistic models of grid formation.
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BibTeX
@misc{kerscher2026gridcell,
title = {{Grid-cell firing fields lack local sixfold symmetry}},
author = {Anian Kerscher},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31145},
eprint = {2609.31145},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31145},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Grid-cell firing fields lack local sixfold symmetry
AU - Anian Kerscher
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31145
UR - https://arxiv.org/abs/2609.31145
AB - The firing fields of a grid cell form a hexagonal lattice, yet each field's intrinsic geometric structure remains unclear: Are individual grid fields radially symmetric or do they exhibit (weak) sixfold modulation inherited from the global lattice? To address this question, we quantified the within-field angular structure using harmonic analysis and per-cell matched simulations that preserved sampling statistics, field scale, and lattice geometry after correction for global elliptic deformation. We found that, across the investigated cells, the sixfold harmonic power fraction was consistent with values from matched locally circular reference fields. Experimental fields further showed substantially less sixfold modulation than matched simulations with an imposed local sixfold component, demonstrating sensitivity to sixfold structure at that level. This conclusion was supported by a complementary sixfold regression metric, harmonic leave-one-out sensitivity analyses, and robustness checks across radial-window choices, smoothing, and simulated background-noise levels. An observation-matched Burak--Fiete continuous-attractor network likewise showed no selective local sixfold enhancement despite its globally periodic grid structure, and this conclusion persisted when grid scale and relative field width were matched more closely to the experimental regime. These results suggest that the global hexagonal lattice organization need not be accompanied by detectable local sixfold angular modulation of individual firing fields, placing quantitative constraints on grid-field microstructure and mechanistic models of grid formation.
ER -