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Place Cells as Multi-Scale Position Embeddings: Random Walk Transition Kernels for Path Planning
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Models place cell populations as non-negative spectral embeddings of multi-step random walk transition kernels, whose inner products reproduce normalized transition probabilities, and uses them for gradient-based path planning across scales.
Problem
Explaining hippocampal place cell population coding (localized fields, multi-scale organization, cognitive maps) and using it for trap-free spatial navigation and path planning in 2D environments with obstacles.
Approach
Learn non-negative position embeddings h(x,tau) whose inner products match normalized multi-step random walk transition kernels q(y|x,tau), with time scale tau setting spatial scale; non-negativity plus orthogonality yields sparse localized fields, and navigation is gradient ascent on q with adaptive scale selection.
Key results
- Learned embeddings reproduce normalized transition kernels with correlation above 0.9 at all scales in the open field.
- Gradient-based planner achieves 100% success in open field, U-shape, S-shape and four-room mazes over 50 trials per environment.
- In the four-room maze, the method reaches 100% success and SPL 1.00 versus 0.66 for Bug with oracle and 1.08 for A* search.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use adaptive-scale transition-kernel gradient path planning instead of Bug (without oracle) | Path planning · Four-room | Success: 14% -> 100% | Helped |
| Use adaptive-scale transition-kernel gradient path planning instead of Bug (without oracle) | Path planning · Four-room | SPL: 0.15\pm 0.00 -> 1.00 | Helped |
| Use adaptive-scale transition-kernel gradient path planning instead of Bug (with oracle) | Path planning · Four-room | SPL: 0.66\pm 0.51 -> 1.00 | Helped |
| Use adaptive-scale transition-kernel gradient path planning instead of A* Search | Path planning · Four-room | SPL: 1.08\pm 0.50 -> 1.00 | Hurt |
| Use adaptive-scale transition-kernel gradient path planning instead of Random Walk | Path planning · Four-room | Success: 2% -> 100% | Helped |
| Use adaptive-scale transition-kernel gradient path planning instead of Random Walk | Path planning · Four-room | SPL: 0.01\pm 0.00 -> 1.00 | Helped |
Surprising findings
- Reported SPL for S-shape (1.392) and four-room (1.519) exceed 1.0, which is inconsistent with the usual SPL bound and not explained in the main text.
- The method's four-room SPL (1.00) is below A* search (1.08), contrary to the claim of finding shortcuts.
Limitations
- No sensory integration; embeddings are learned from pre-defined transition kernels.
- Limited to 2D static environments on small discrete lattices.
- Batch learning rather than online sequential learning.
Experimental setup
Datasets: simulated 40x40 lattice open field U-shaped, S-shaped, and four-room mazes
Benchmarks: open field U-shape maze S-shape maze four-room maze
Metrics: success rate SPL correlation of inner products with transition kernel
Baselines: Bug algorithm Bug algorithm with oracle A* search Random walk
Builds on: successor representation Horn's theorem AdamW
Closest papers by meaning
- Time Makes Space: Emergence of Place Fields in Networks Encoding Temporally Continuous Sensory Experiences (NeurIPS 2024 · similarity 0.90)
- Learning Place Cell Representations and Context-Dependent Remapping (NeurIPS 2024 · similarity 0.90)
- REMI: Reconstructing Episodic Memory During Internally Driven Path Planning (NeurIPS 2025 · similarity 0.89)
- A simple model of co-emergence of grid and place fields (NeurIPS 2026 · similarity 0.89)
- Binding in hippocampal-entorhinal circuits enables compositionality in cognitive maps (NeurIPS 2024 · similarity 0.89)
- Trading Place for Space: Increasing Location Resolution Reduces Contextual Capacity in Hippocampal Codes (NeurIPS 2024 · similarity 0.89)
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