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Not so griddy: Internal representations of RNNs path integrating more than one agent
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Trains RNNs (modified single-agent path-integration architecture) to path integrate two agents simultaneously and analyzes how their unit-level and population-level representations differ from single-agent RNNs.
Problem
How do neural representations for path integration change when a network must track the positions and trajectories of two agents at once, rather than one, and whether continuous attractor/grid codes can support multi-agent path integration.
Approach
Modify the grid-cell RNN framework (Sorscher et al./Cueva & Wei style) to take two agents' movement inputs, use summed difference-of-Gaussian place-cell targets for both agents, decode with k-means, and reduce weight decay; then compare functional classes (grid/border/band), relative-space tuning, and topology/dynamics (persistent homology, DSA) against single-agent RNNs.
Key results
- Dual agent RNNs reach decoding error below 0.10 m on nearly 50% of 5000 dual-agent trajectories, and single-agent RNNs tested on dual-agent path integration have about 1.0 m error (~10x higher).
- Dual agent RNNs develop lower grid scores and higher border and band scores than single agent RNNs (KS test, p<0.01), and are less sensitive to ablation of any one functional class.
- Persistence diagrams of dual agent RNN population activity lack clear 2D torus signatures, and DSA shows single and dual agent RNNs are dynamically distinct.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train an RNN on dual-agent rather than single-agent path integration | RNN path integration · Dual agent path integration | decoding error: nearly a 10× increase in error | Helped |
| Train on dual-agent rather than single-agent path integration | RNN path integration · Single agent path integration | decoding error: < 0.10 m | Mixed |
| Fine-tune all weights of the single-agent-trained RNN for 10 epochs on the dual agent task | Single agent RNN · Dual agent path integration | decoding error: 10 epochs | Helped |
| Freeze the recurrent weights while fine-tuning the single-agent-trained RNN (ablation) | Single agent RNN · Dual agent path integration | decoding error | Hurt |
| Freeze the recurrent weights while fine-tuning the dual-agent-trained RNN (ablation) | Dual agent RNN · Single agent path integration | decoding error | Helped |
| Reduce weight decay from λ = 10−4 to λ = 10−6 (ablation) | Dual agent RNN · Dual agent path integration | decoding error: λ = 10−4 to λ = 10−6 | Helped |
| Remove the highest-grid-score units (ablation) | Dual agent RNN · Dual agent path integration | decoding error | No clear effect |
| Remove the highest-border-score units (ablation) | Dual agent RNN · Dual agent path integration | decoding error | Mixed |
| Remove the highest-band-score units (ablation) | Dual agent RNN · Dual agent path integration | decoding error | Mixed |
| Remove units with the highest relative-space spatial information (ablation) | Dual agent RNN · Dual agent path integration | decoding error | Hurt |
| Use half as many recurrent and output units in the single-agent RNN (ablation) | Single agent RNN · Single agent path integration representations | functional representation similarity to dual agent RNN | No clear effect |
| Compute dual-agent rate maps while setting the second agent's inputs to 0 (ablation) | Dual agent RNN · Dual agent rate maps | representation change | No clear effect |
Surprising findings
- Dual agent RNNs can generalize to single agent path integration even with recurrent weights frozen.
- Units with the highest relative-space spatial information ablate to a larger deficit than grid, border, or band cells.
Limitations
- RNN biological plausibility is questionable and the summed place-cell target is only one possible choice of multi-agent target.
- No velocity noise modeled, which is likely important for human path integration.
- Only two agents tested; results for more agents are left to future work.
Experimental setup
Datasets: simulated two-agent trajectories generated on the fly
Benchmarks: simulated single-agent path integration simulated dual-agent path integration
Metrics: decoding error (m) grid score border score band score spatial information persistence diagram topology DSA Procrustes distance decoding error after ablation
Baselines: single agent RNN random unit ablation
Builds on: Sorscher et al. 2019 grid cell RNN Banino et al. grid cells in RNN continuous attractor networks dynamic similarity analysis
Closest papers by meaning
- Global Distortions from Local Rewards: Neural Coding Strategies in Path-Integrating Neural Systems (NeurIPS 2024 · similarity 0.88)
- A simple model of co-emergence of grid and place fields (NeurIPS 2026 · similarity 0.87)
- REMI: Reconstructing Episodic Memory During Internally Driven Path Planning (NeurIPS 2025 · similarity 0.87)
- Place Cells as Multi-Scale Position Embeddings: Random Walk Transition Kernels for Path Planning (NeurIPS 2025 · similarity 0.86)
- A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making (ICML 2025 · similarity 0.86)
- Flexible mapping of abstract domains by grid cells via self-supervised extraction and projection of generalized velocity signals (NeurIPS 2024 · similarity 0.85)
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