A Simple Model of Co-Emergence of Grid and Place Fields

¹ Dept. of Electrical and Systems Engineering, University of Pennsylvania
² Tel Aviv Sourasky Medical Center ³ Gray Faculty of Medical and Health Sciences, Tel Aviv University
⁴ Rappaport Faculty of Medicine, Technion - Israel Institute of Technology
⁵ Dept. of Physics, University of Pennsylvania ⁶ Santa Fe Institute

About

The brain uses place cells to link sensory experience to locations, and grid cells to track position through movement. Most models explain one by assuming the other already exists.

Our model develops both representations through a single objective: predicting the next sensory observation, without predefined spatial codes. It also reproduces grid fragmentation in hairpin mazes and develops locally ordered grid-like fields alongside localized place-like fields in 3D.

We systematically swept over 1,000 training configurations, varying sensory masking, recurrent noise, activity timescales, and random seeds. We also tested how the learned representations change across open arenas, hairpin mazes, separate and connected rooms, and 3D environments.

Recurrent network architecture, Dale-constrained connectivity, spatial autocorrelation, grid spacing and orientation, and examples of emergent grid and place fields — Network architecture, emergent grid and place fields, and the parameter sweep.

Model

The network receives noisy, partially masked sensory observations and body-centered motion signals, then predicts the next observation. Each recurrent neuron has either excitatory or inhibitory outgoing connections, following Dale's law. Neither position labels nor predefined grid or place fields are used as training targets.

Simply connecting models that develop each cell type separately does not produce both codes together. In our model, they emerge within a shared recurrent network trained on the same prediction task.

Single-cell-type models and their direct composition, with the resulting spatial response maps — Simply combining single-cell-type models does not yield robust co-emergence.

Interpretation

Our interpretation is that sensory experiences within a room form a low-dimensional manifold. The network learns to recover a consistent location from noisy or incomplete sensory cues, producing place-like representations. It also learns how movement changes the expected sensory input, producing grid-like representations. These two processes connect associating sensory cues with a place and tracking position as the agent moves.

Experiments

Place-like fields emerge before grid-like fields. The network develops these representations in the same order reported in developing rodents.

Hexagonal grid patterns fragment in hairpin mazes. Constrained movement breaks the grid into corridor-specific patterns. Regular grids recover with further training in the open arena, while place-field locations stay stable.

Separate grids merge after wall removal. When two rooms become one, their grid patterns reorganize into a shared lattice. Place fields remain anchored to the same locations.

Grid patterns align across connected rooms. With further exploration and training, some cells develop patterns that extend across both rooms and the connecting corridor.

Grid-like and place-like representations extend to 3D. Place fields remain localized, while grid-like fields show local spatial order without forming a perfect global lattice.

Developmental order, hairpin mazes, wall removal, connected rooms, and original three-dimensional place-like and grid-like firing fields — Spatial codes develop and reorganize across navigation conditions, including volumetric 3D traversal.

Code and Released Results

GitHub includes the model, simulator, training configurations, and saved rate maps. Explore the results in the notebook.

Cite this Paper

@inproceedings{wang2026coemergence,
  title={A simple model of co-emergence of grid and place fields},
  author={Zhaoze Wang and Genela Morris and Dori Derdikman and Pratik Chaudhari and Vijay Balasubramanian},
  booktitle={Advances in Neural Information Processing Systems (NeurIPS)},
  year={2026},
  url={https://arxiv.org/abs/2605.21356}
}