grid-place-co-emergence

name

grid-place-co-emergence

description

First unified recurrent network model implementing Dale's Law (every neuron is either excitatory or inhibitory) that trains via masked next-observation prediction to co-emerge both grid and place cells from a single architecture. Use when researching: grid cell emergence, place cell models, entorhinal-hippocampal circuits, spatial navigation neural networks, Dale's Law in computational models, co-emergence of spatial representations, MEC-HPC reciprocal connectivity, developmental spatial cognition.

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

Overview

Grid cells in the medial entorhinal cortex (MEC) and place cells in the hippocampus (HPC) together support spatial navigation. The two regions are reciprocally connected, creating a chicken-and-egg problem: how do both arise and reinforce each other during development? Current computational accounts either derive one type from the other or model emergence in isolation.

This paper introduces the first unified recurrent network model that:

1. Instantiates Dale's Law (each neuron is either exclusively excitatory or exclusively inhibitory)
2. Is trained to predict the next sensory observation from masked observations
3. Co-emerges both grid-like and place-like spatial representations within a single network

Key Findings

1. Co-emergence: Grid and place fields emerge simultaneously, not sequentially — one does not cause the other
2. Dale's Law compatibility: The model respects biological Dale's Law while still producing both cell types
3. Self-supervised learning: Trained via masked next-observation prediction (no explicit spatial labels)
4. Grid-like patterns: Regular hexagonal firing patterns emerge in model units resembling MEC grid cells
5. Place-like patterns: Localized spatial firing fields emerge resembling hippocampal place cells
6. Mutual reinforcement: The two cell types mutually reinforce each other through the reciprocal architecture

Core Mechanisms

Unified Recurrent Architecture

• Single recurrent neural network with Dale's Law constraints
• Excitatory and inhibitory populations with biologically realistic connectivity
• Trained end-to-end via self-supervised prediction objective

Training Objective

• Masked next-observation prediction: Given partial sensory observations, predict the next observation
• No explicit spatial supervision (no coordinates, no place labels)
• Forces the network to develop internal spatial representations to solve the task

Emergent Properties

• Grid cells: Neurons with periodic, hexagonal spatial firing fields
• Place cells: Neurons with localized, single-peak spatial firing fields
• Both emerge from the same training objective without architectural specialization

Methodology

Model Architecture

• Recurrent neural network with Dale's Law constraints
• Excitatory/inhibitory balanced network dynamics
• Sensory input → recurrent processing → prediction output

Training

• Self-supervised on spatial navigation trajectories
• Masked prediction objective
• No spatial label supervision

Evaluation Metrics

• Spatial information content
• Gridness score (hexagonal regularity measure)
• Place field size and number of fields
• Spatial correlation between model units and biological recordings

Significance

For Neuroscience

• Resolves the chicken-and-egg problem: grid and place cells co-emerge through reciprocal connectivity
• Shows Dale's Law is compatible with complex spatial representations
• Provides a unified learning framework for entorhinal-hippocampal development
• Predicts that grid cells can arise without path integration (contra some theories)

For AI / Machine Learning

• Demonstrates self-supervised spatial representation learning without explicit spatial labels
• Shows that biological constraints (Dale's Law) are compatible with complex emergent representations
• Provides a blueprint for biologically inspired spatial navigation in artificial agents
• Suggests masked prediction as a general principle for representation learning

Activation Keywords

• grid cell co-emergence
• place cell model
• Dale's Law neural networks
• entorhinal-hippocampal circuit
• spatial navigation self-supervised learning
• grid cell emergence from prediction
• MEC-HPC unified model
• spatial representation learning

References

• Wang, Z., Morris, G., Derdikman, D., Chaudhari, P., & Balasubramanian, V. (2026). A Simple Model of Co-emergence of Grid and Place Fields. arXiv:2605.21356
• Hafting et al. (2005). Microstructure of a spatial map in the entorhinal cortex
• O'Keefe & Dostrovsky (1971). The hippocampus as a spatial map
• Moser, Moser & Roudi (2014). Neural representations of space
• Cueva & Wei (2018). Emergence of grid-like representations by training recurrent networks
• Banino et al. (2018). Vector-based navigation using grid-like representations in artificial agents