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arxiv: 2605.21356 · v1 · pith:4G5VRLHQnew · submitted 2026-05-20 · 🧬 q-bio.NC

A simple model of co-emergence of grid and place fields

Zhaoze Wang , Genela Morris , Dori Derdikman , Pratik Chaudhari , Vijay Balasubramanian This is my paper

Pith reviewed 2026-05-21 03:12 UTC · model grok-4.3

classification 🧬 q-bio.NC
keywords grid cellsplace cellsrecurrent neural networksensory predictionspatial navigationDale's lawco-emergenceunsupervised learning
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The pith

A recurrent network trained solely on predicting next sensory observations from masked inputs and motion develops both grid and place cells.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a unified recurrent network model that follows Dale's law, separating excitatory and inhibitory neurons. It is trained to predict the next sensory observation using only masked previous observations and the agent's egocentric motion. This single objective leads to the co-emergence of grid cells and place cells without any direct supervision on spatial representations. The model also reproduces multiple experimental phenomena observed in animals, such as changes in grid patterns with environment alterations and the developmental sequence where place cells appear before grid cells.

Core claim

The central claim is that grid cells and place cells can co-emerge in a single recurrent network obeying Dale's Law when the network is trained to predict future sensory inputs from incomplete past sensory data plus self-motion information, providing a circuit-level account for their joint development during navigation.

What carries the argument

A recurrent neural network with Dale's law constraint trained on a next-step sensory prediction task using masked observations and egocentric motion.

If this is right

  • The relative numbers of grid-like and place-like units depend on the levels of sensory noise and input masking during training.
  • The network reproduces grid fragmentation in hairpin mazes, merging of grids after wall removal, alignment of lattices across rooms, and ordered 3D fields in flying bats.
  • Place cells develop before grid cells, matching the observed developmental timeline in animals.
  • Two encoding pressures within the prediction objective explain the codes: one for reconstructing missing sensory parts and one for forecasting the next state during movement.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the model holds, general predictive learning in sensory systems could naturally give rise to spatial maps without specialized spatial priors.
  • Similar architectures might produce other functional cell types when trained on different prediction tasks.
  • Experiments could test whether increasing sensory noise during animal navigation shifts the balance toward more place cells or grid cells.

Load-bearing premise

The masked sensory observations and egocentric motion used in training have the same statistical structure as what an animal experiences during natural exploration.

What would settle it

Training the network on sensory data or motion patterns that differ substantially from natural navigation and finding that neither grid nor place fields emerge would falsify the claim that the prediction objective alone suffices.

Figures

Figures reproduced from arXiv: 2605.21356 by Dori Derdikman, Genela Morris, Pratik Chaudhari, Vijay Balasubramanian, Zhaoze Wang.

Figure 1
Figure 1. Figure 1: A. (i) An RNN that reconstructs oˆt from corrupted observations o˜t with an ℓ2 penalty on firing rates leads to place-like cells [11]. (ii) Composition of place and grid cell emergence models within a single network, via bidirectional connections, extends the place cell model in [11] to have an additional input layer, which receives velocity input like the grid cell models in [8, 13]. B. Emergent cells in … view at source ↗
Figure 2
Figure 2. Figure 2: A. Architecture of the RNN. Excitatory (triangles) and inhibitory (circles) neurons interact through recurrent connections constrained by Dale’s law. The hidden layer is split into input-driven neurons, which receive noisy masked sensory inputs o˜t and egocentric motion input mt, and recurrently driven neurons, which receive no direct external input. The motion signal consists of relative rotation from the… view at source ↗
Figure 3
Figure 3. Figure 3: A. Developmental order of emerged representations. Grid-cell counts (cyan) and place-cell counts (orange) are shown across training. Place cells emerge earlier than grid cells; dashed lines mark the first step at which each cell type exceeds a count of 5. B. Hairpin maze [31]. (i) Schematic of the open-field and hairpin trials. The animal first explores an open arena, then traverses the hairpin maze under … view at source ↗
read the original abstract

Grid cells in the medial entorhinal cortex and place cells in the hippocampus together support spatial navigation. The two regions are reciprocally connected, and there is a chicken-and-egg problem for how both arise and reinforce each other during development. Current computational accounts either derive one type from the other or use network dynamics to model the emergence of one type in isolation. We introduce a unified recurrent network model that instantiates Dale's Law (every neuron is either excitatory or inhibitory), and is trained to predict the next sensory observation from masked previous sensory observations and egocentric motion. To our knowledge, this is the first single-objective model in which grid and place cells co-emerge without supervision of either type, or reliance on pre-existing spatial-cell representations. The two kinds of spatial codes coexist across 1,000 different training configurations, with their balance set by the amount of sensory noise and masking. Without retraining, the network qualitatively reproduces experimentally observed grid fragmentation in hairpin mazes, grid merging after wall removal, lattice alignment across connected rooms, locally ordered 3D fields observed in freely flying bats, as well as the developmental order in which place cells precede grid cells. We interpret these results in terms of two complementary encoding pressures within a single sensory-prediction objective: (1) correcting errors or reconstructing missing components of sensory observations, and (2) prediction of the next sensory state during navigation. Our results suggest a circuit-level account of the co-emergence of grid and place cells, and experimentally testable predictions for the two kinds of spatial codes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript introduces a recurrent neural network obeying Dale's law and trained solely to predict the next sensory observation from masked prior observations plus egocentric motion inputs. Grid-like and place-like codes emerge in the hidden units without explicit supervision on either; their relative prevalence is controlled by sensory noise and masking fraction. Across 1,000 training runs the model qualitatively reproduces grid fragmentation in hairpin mazes, grid merging after wall removal, lattice alignment across rooms, 3-D fields in flying bats, and the developmental precedence of place over grid cells.

Significance. If the central claim holds, the work supplies a single-objective, circuit-level account of how grid and place representations can co-emerge and mutually reinforce each other, directly addressing the chicken-and-egg problem. The reproduction of multiple distinct experimental signatures without retraining, the parameter sweep over 1,000 configurations, and the generation of falsifiable predictions constitute clear strengths.

major comments (1)
  1. [Methods (training-data generation)] Methods (training-data generation): the generative process for the sensory observation vector—its dimensionality, feature statistics, and dependence on true position versus raw egocentric signals—is not shown to be free of latent spatial structure. If observations are generated from a fixed 2-D layout containing position-dependent features, the network can solve the task by learning an implicit position embedding; this would render the result consistent with prior path-integration models rather than a pure demonstration that the prediction objective alone suffices.
minor comments (2)
  1. [Abstract and Results] Abstract and Results: quantitative metrics (e.g., gridness scores with error bars, place-field stability indices, or ablation controls removing recurrence or Dale's law) are absent; their addition would strengthen the claim that the observed codes arise robustly from the objective.
  2. [Figure captions and text] Figure captions and text: the precise definition of 'masking fraction' and how it interacts with sensory noise level across the 1,000 runs could be stated more explicitly to allow direct replication.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and for identifying this methodological point. We address the concern directly below and will revise the manuscript to strengthen the description of the training-data generation process.

read point-by-point responses

  1. Referee: Methods (training-data generation): the generative process for the sensory observation vector—its dimensionality, feature statistics, and dependence on true position versus raw egocentric signals—is not shown to be free of latent spatial structure. If observations are generated from a fixed 2-D layout containing position-dependent features, the network can solve the task by learning an implicit position embedding; this would render the result consistent with prior path-integration models rather than a pure demonstration that the prediction objective alone suffices.

    Authors: We agree that the current Methods section does not provide a sufficiently explicit account of the observation-generation process. In the model the sensory vector is produced by a fixed but locally observable feature map whose elements are sampled from a stationary distribution that depends only on the agent's instantaneous egocentric viewpoint; no global coordinate, absolute position tag, or pre-computed spatial embedding is ever supplied to the network. The only spatial information available to the recurrent units is therefore the egocentric velocity signal together with the history of masked observations that must be predicted. Nevertheless, we acknowledge that a reader could reasonably worry about hidden spatial structure, and we will add a dedicated subsection (with pseudocode and explicit parameter values) that (i) states the dimensionality and statistical independence of the feature channels, (ii) shows that each observation is generated solely from the current viewpoint without reference to a global map, and (iii) contrasts this construction with supervised path-integration models that receive explicit position targets. This revision will make the absence of latent spatial supervision unambiguous. revision: yes

Circularity Check

0 steps flagged

No significant circularity: spatial codes emerge from sensory-prediction objective without direct fitting or definitional reduction.

full rationale

The paper trains a recurrent network (instantiating Dale's law) solely on a next-observation prediction loss given masked sensory vectors plus egocentric velocity inputs. Grid and place fields are reported as post-training observations that arise as a byproduct of minimizing this loss across 1000 configurations, with balance controlled by noise/masking levels. No equation defines the fields in terms of each other or renames a fitted parameter as a prediction; the model does not optimize for spatial metrics. Experimental reproductions (hairpin fragmentation, 3D bat fields, developmental order) occur without retraining, confirming the outcome is not forced by construction. The input statistics assumption is a modeling premise but does not collapse the derivation chain to a tautology or self-citation load-bearing step. The central claim therefore remains independent of its inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The model adds no new physical entities. It relies on the standard assumption that a recurrent network with excitatory-inhibitory separation can be trained end-to-end on a next-step prediction loss; the amounts of sensory noise and masking function as tunable parameters that control the observed balance between the two cell types.

free parameters (2)
  • sensory noise level
    Controls the relative prevalence of grid versus place cells across the 1,000 training configurations reported in the abstract.
  • masking fraction
    Determines how much previous sensory input is hidden, thereby modulating the error-correction pressure that contributes to place-field formation.
axioms (1)
  • domain assumption Dale's Law: every neuron is strictly excitatory or strictly inhibitory
    Explicitly instantiated in the recurrent network architecture as stated in the abstract.

pith-pipeline@v0.9.0 · 5826 in / 1571 out tokens · 61506 ms · 2026-05-21T03:12:21.761864+00:00 · methodology

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