Research map / Learning theory and algorithms / Matrix and tensor methods
On Path Integration of Grid Cells: Group Representation and Isotropic Scaling
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace LSTM baseline with proposed group-representation model | grid cell models · grid cell learning | gridness score: 0.18 -> 0.90 | Helped |
| replace RNN baseline with proposed model | grid cell models · grid cell learning | gridness score: 0.48 -> 0.90 | Helped |
| replace RNN baseline with proposed model | grid cell models · grid cell learning | % of grid cells: 56.10 -> 73.10 | Helped |
| remove loss term L2 enforcing isotropic scaling (ablation) | proposed model · hexagon pattern emergence | hexagon patterns | Hurt |
| remove non-negativity constraint u(x') >= 0 (ablation) | proposed model · hexagon pattern emergence | hexagon patterns | No clear effect |
| remove skew-symmetric assumption on B(theta) (ablation) | proposed model · hexagon pattern emergence | hexagon patterns | No clear effect |
| vary block size and number of blocks (ablation) | proposed model · hexagon pattern emergence | hexagon patterns | No clear effect |
| use a single block instead of multiple blocks (ablation) | proposed model · grid scales | multi-scale patterns | Hurt |
| re-encode position after decoding at each step | path integration · 500 time steps | path integration error (cm): < 0.01 vs 0.0 to 4.2 (mean 1.9) | Helped |
Closest papers by meaning
- On Conformal Isometry of Grid Cells: Learning Distance-Preserving Position Embedding (ICLR 2025 · similarity 0.90)
- Flexible mapping of abstract domains by grid cells via self-supervised extraction and projection of generalized velocity signals (NeurIPS 2024 · similarity 0.85)
- Global Distortions from Local Rewards: Neural Coding Strategies in Path-Integrating Neural Systems (NeurIPS 2024 · similarity 0.85)
- Place Cells as Multi-Scale Position Embeddings: Random Walk Transition Kernels for Path Planning (NeurIPS 2025 · similarity 0.85)
- A simple model of co-emergence of grid and place fields (NeurIPS 2026 · similarity 0.84)
- Not so griddy: Internal representations of RNNs path integrating more than one agent (NeurIPS 2024 · similarity 0.83)
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