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

TL;DR

A recurrent network trained on a single task, predicting the next sensory observation, develops both grid-like and place-like spatial representations. Neither code is supplied as a target or assumed to exist beforehand.

Recurrent network architecture, Dale-constrained connectivity, spatial autocorrelation, grid spacing and orientation, and examples of emergent grid and place fields — One predictive network, two complementary spatial codes.

How Can Two Spatial Codes Emerge Together?

Many models explain grid cells by assuming place cells already exist, or vice versa. We ask whether both can emerge together from predicting sensory experience during navigation.

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.

One Recurrent Network, One Predictive Objective

Of 2,048 recurrent units, half receive sensory and motion input; the rest receive only recurrent input. All learn through the same next-observation prediction objective.

Structured recurrence: Dale-constrained connections and homeostatic synaptic scaling.
Incomplete observations: sensory masking and firing-rate-dependent noise.
Continuous experience: recurrent state carried across training segments.

Co-Emergent Grid and Place Fields

Repeated grid-like fields and localized place-like fields emerge in the same network, supporting complementary demands: recovering sensory state and updating it during movement.

Spatial Representations Across Environments

Development: place-like fields emerge before grid-like fields.
Changing environments: grid patterns fragment in hairpin mazes and reorganize across connected rooms.
3D traversal: localized place-like fields and locally ordered volumetric grid-like fields.

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

@misc{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},
  year={2026},
  eprint={2605.21356},
  archivePrefix={arXiv},
  primaryClass={q-bio.NC},
  url={https://arxiv.org/abs/2605.21356}
}