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Global Distortions from Local Rewards: Neural Coding Strategies in Path-Integrating Neural Systems
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Trains path-integrating RNNs with a spatial saliency loss near rewards and analyzes how grid-cell firing fields and neural manifolds become globally distorted while keeping toroidal topology when place-cell readouts are frozen.
Problem
How reward-relevant landmarks distort grid cell firing fields and their neural manifolds during path integration, and whether such distortions are local magnifications or global changes.
Approach
Adds a saliency kernel (1 + s(x)) to the piRNN path-integration loss to upweight position decoding near rewards, and freezes place-cell readouts so the toroidal grid manifold is preserved; finds global (diffused, band, ring) distortions rather than local attraction.
Key results
- Saliency training with frozen place-cell readout preserves toroidal topology (Betti numbers 1,2,1), while unfrozen readout destroys it.
- Saliency-tuned piRNNs develop diffused, band, and ring units; attracted units predicted by prior experiments were not observed.
- Modules with many diffused units show preserved topology but reduced manifold size, as predicted by the reduction conjecture.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add frozen place-cell readout weights during saliency training | piRNN · Spatial navigation with saliency | topology | Helped |
| Allow place-cell readout weights to change during saliency training (ablation) | piRNN · Spatial navigation with saliency | topology | Hurt |
| Add local reward saliency to training | piRNN · Spatial navigation with saliency | firing-field distortion | Mixed |
| Add local reward saliency to training | piRNN with frozen readout · Spatial navigation with saliency | topology | No clear effect |
| Smooth firing fields with a Gaussian filter | Synthetic grid cell modules · Synthetic grid cell modules | manifold size | Hurt |
| Smooth firing fields with a Gaussian filter | Synthetic grid cell modules · Synthetic grid cell modules | topology | No clear effect |
| Displace firing-field centers toward a reward region | Synthetic grid cell modules · Synthetic grid cell modules | topology | No clear effect |
| Replace some grid units with band units | Synthetic grid cell modules · Synthetic grid cell modules | topology | No clear effect |
| Replace some grid units with band units | Synthetic grid cell modules · Synthetic grid cell modules | geometry | No clear effect |
| Add diffused units through saliency training | piRNN grid cell modules · Modules with diffused units | manifold size | Hurt |
| Add diffused units through saliency training | piRNN grid cell modules · Modules with diffused units | topology | No clear effect |
Surprising findings
- No attracted firing-field units emerged despite predictions and prior rodent reports of attraction to rewards.
- Local reward changes produced global distortions of grid-cell firing fields.
Limitations
- Attracted-unit distortions seen in experiments were not reproduced in the piRNN.
- Theoretical deformation model Phi is not given in closed form and is only estimated empirically.
- Continual learning link is conjectural and not tested across multiple saliency phases.
Experimental setup
Datasets: simulated 2D path-integration trajectories
Metrics: gridness score Betti numbers via persistent homology PCA/MDS manifold size
Baselines: pretrained piRNN without saliency training unfrozen readout piRNN
Builds on: piRNN (Xu et al.) Sorscher et al. grid cell RNN gridness score
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