Research map / Probabilistic and scientific modeling / Dynamical systems
A unified theory for the origin of grid cells through the lens of pattern formation
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add nonnegativity constraint on hidden unit activations | 1-layer NN, RNN, LSTM trained on place cell encoding · grid pattern structure | lattice type | Helped |
| use broad Gaussian place cell tuning | 1-layer NN, RNN, LSTM · grid pattern structure | lattice type | Mixed |
| use difference-of-Gaussians or one-hot place cell tuning instead of Gaussian | 1-layer NN, RNN, LSTM · grid pattern structure | lattice regularity | Hurt |
| add cubic term (symmetry-breaking nonlinearity) to objective (ablation) | position encoding objective · grid pattern structure | hexagonality: L_int 3/2 (stripe+overtone) vs 1.63 (equilateral) | Helped |
| use nonlinearity preserving g -> -g symmetry | continuous attractor model · grid pattern structure | lattice type | Hurt |
| add nonnegativity with many grid maps | multi-cell pattern forming dynamics · multi-scale grid maps | hexagonality | Helped |
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