The Role of Grid Cells in Reducing Spatial Aliasing in Hippocampal Place Representations

Abstract: Spatial aliasing occurs when two or more distinct locations produce highly similar place-cell representations, primarily due to environmental symmetry or repetitive structures. This issue is most pronounced when place representations are constructed solely from boundary vector cell (BVC) inputs, because symmetric or repetitive structures can yield indistinguishable sensory patterns across multiple locations in an environment. This work introduces grid cell signals to mitigate spatial aliasing in such settings. Because grid cells contribute periodic, internally generated spatial signals that vary independently of environmental geometry, they play a key role in disambiguating perceptually identical locations. We integrate multiple modules of analytically constructed grid cells with BVC-driven place cells and show that this leads to a 94--99% reduction in spatial aliasing relative to a BVC-only baseline across three environments: an open environment without obstacles; an environment with a cross-shaped central obstacle creating high visual symmetry; and a maze environment. The greatest improvement occurs in the environment with the highest visual symmetry. These results indicate that grid cells provide information complementary to boundary-based inputs, yielding more reliable place representations in geometrically ambiguous environments.

• The paper demonstrates that combining analytically constructed grid-cell signals with boundary-vector-cell inputs reduces mean spatial aliasing by 94.73–99.29% across open, cross-shaped, and maze environments.
• The model uses 400 grid cells across eight modules, Oja-rule learning, and obstacle-aware masking to provide periodic positional information that distinguishes locations with similar boundary cues.
• The results suggest grid cells complement boundary sensing, but single-scale analytical grids, hand-set masking parameters, and residual maze aliasing limit conclusions about biological and real-world performance.

Overview

This paper by Johnson, Ghizawi, and Minai addresses a well-defined failure mode of boundary-driven hippocampal models: spatial aliasing, in which distinct locations produce nearly identical place-cell activation vectors. The authors' central claim is that grid cell input—periodic, internally generated, and largely independent of environmental geometry—supplies the complementary information needed to break this degeneracy. They integrate analytically constructed grid cells into a previously established BVC-based place-cell model [alabi2020oneshot, alabi2023] and quantify aliasing with a Spatial Aliasing Index (SAI) / Mean Spatial Aliasing Index (MSAI) metric across three 20 m × 20 m simulated environments. The headline result is a 94–99% reduction in MSAI relative to a BVC-only baseline, with the largest gain in the environment with the highest rotational symmetry.

Motivation: aliasing in BVC-only place codes

Place cells fire in localized fields determined substantially by distance-and-direction relationships to environmental boundaries [hartley2000modeling, o1996geometric]. When a model's place representations are driven exclusively by BVC inputs, any two locations sharing equivalent boundary configurations—e.g., rotationally symmetric quadrants of a cross-shaped arena—yield indistinguishable sensory patterns, so a single place cell may exhibit multiple firing-field peaks. The paper illustrates this directly: an example neuron in the Cross environment shows four distinct activation maxima corresponding to the four symmetric quadrants. Prior work from the same group showed that 3-D LiDAR structure can partially mitigate the problem [GerstenslagerDukenbaevMinai2025]; this paper proposes grid cells as a more general remedy.

The biological rationale follows Bush et al. [bush2014what]: grid cells provide a context-dependent spatial metric via path integration that interacts with place cells to support reliable coding. Because the population phase of a grid-cell module varies continuously with position regardless of wall geometry, it disambiguates perceptually identical locations—a property also implicated empirically in Skaggs and McNaughton's recordings in visually identical compartments [skaggs1998spatial].

Model architecture

The architecture comprises four layers adapted from prior hippocampal models:

• Head direction cells: 8 cosine-tuned units at 45° increments following Erdem and Hasselmo [erdemHasselmo2012].
• Boundary vector cells: 400 units (50 per heading direction) integrating LiDAR returns over radial Gaussian ($\sigma_r = 1.0$ m) and angular Gaussian ($\sigma_\theta = 3°$) tuning functions, per Barry et al. [barry2006boundary].
• Grid cells: 400 cells in 8 modules aligned with head directions, each module containing 50 cells sharing scale $\lambda = 5.5$ but differing in spatial phase.
• Place cells: 1000 leaky-integrator units receiving weighted excitatory input from both BVCs and GCs, with afferent and recurrent inhibition producing winner-take-all dynamics.

The grid cell layer is the principal contribution. Rather than simulating oscillatory interference or continuous attractor dynamics, the authors construct hexagonal firing patterns analytically as the mean of three cosine gratings oriented 60° apart, followed by three post-processing steps: a power-law sharpening transform ($\beta \in [1.2, 1.8]$), min-max normalization, and soft thresholding for sparsity. This choice is explicitly functional rather than mechanistic—it buys precise control over scale and orientation at low computational cost, at the expense of biological realism in how grids emerge.

A notable modeling detail is obstacle-aware masking. Position-only analytical construction produces activations that extend through walls, contradicting the fragmentation of grid maps at barriers observed biologically [derdikman2009fragmentation]. The masking procedure detects connected activation blobs intersecting obstacles (thresholded at ≥20% diameter coverage), splits or suppresses them while retaining only the largest component, applies dilated obstacle boundaries to force fragmentation, and applies Gaussian smoothing ($\sigma \approx 0.5$) to restore curved, tapering field edges. The result preserves local phase coherence within compartments, consistent with empirical observations.

Place cell learning

Place fields self-organize during exploration via Oja-rule competitive learning [oja1982simplified], with sparse initial connectivity (~0.25 BVC→PC, ~0.30 GC→PC probability). A weighting parameter $\eta = 0.35$ governs the relative contribution of the two input streams; setting $\eta = 0$ recovers the BVC-only baseline. Membrane dynamics follow a leaky integrator with global inhibition scaled separately for BVC afferent, GC afferent, and recurrent pathways (gains 0.35/0.35/0.70), and firing rates pass through rectification and tanh saturation.

Evaluation methodology

Experiments ran in Webots R2025a with a differential-drive agent carrying a compass and a 720-beam, 360° rangefinder (25 m maximum range). Five training/evaluation trial pairs were run per condition per environment (30 trials total). Training proceeded until ≥95% coverage on a 0.5 m bin grid; evaluation used 0.2 m bins matching the SAI metric's resolution.

The SAI quantifies aliasing at each bin as the mean cosine similarity between its place-cell activation vector $\mathbf{a}^{(i)}$ and those of all sufficiently distant bins (distance threshold $d_{\mathrm{th}}$), so higher values indicate worse discrimination. MSAI averages SAI over all bins.

Results

Environment	MSAI with GC	MSAI without GC	Improvement
Open	$0.3 \pm 0.1$	$\sigma_\theta = 3°$0	94.73%
Cross	$\sigma_\theta = 3°$1	$\sigma_\theta = 3°$2	99.29%
Maze	$\sigma_\theta = 3°$3	$\sigma_\theta = 3°$4	96.65%

(Values are MSAI ×10⁻⁴, mean ± SD over five trials.)

Three patterns stand out. First, the improvement scales with baseline aliasing severity: the Cross environment, whose four quadrants are rotationally symmetric and therefore maximally aliased under BVC-only coding, shows the largest gain (~99.3%). Second, the Open environment has moderate baseline aliasing because repeated boundary configurations are rarer, yet grid cells still reduce MSAI nearly 95%. Third, the Maze result is qualified by the authors themselves: corridors introduce repeated spatial motifs that retain moderate similarity even with grid input, yielding both a lower improvement percentage and markedly higher variance ($\sigma_\theta = 3°$5 vs. $\sigma_\theta = 3°$6 elsewhere). SAI heatmaps localize these effects spatially, confirming reductions across most bins rather than in isolated regions.

Limitations and open questions

Several caveats bound the interpretation of these results. The grid cells are analytically constructed rather than emergent from path-integration dynamics, so the study isolates the functional contribution of periodic positional signals but says nothing about whether dynamically generated grids—which accumulate integration error over time—would sustain comparable disambiguation. The obstacle-aware masking procedure involves several hand-set thresholds (the 20% blob-coverage cutoff, smoothing kernel width), and the paper does not report sensitivity analyses for them. The evaluation uses a single grid scale and orientation set ($\sigma_\theta = 3°$7, eight modules); whether multi-scale grids, which are characteristic of the dorsal-to-ventral MEC gradient [hafting2005microstructure], further improve robustness in large environments remains untested. Finally, the Maze results indicate that corridor-heavy environments retain residual aliasing even with grid input, and the simulator platform itself is not yet publicly released, limiting independent verification.

Conclusion

The paper demonstrates quantitatively that supplementing BVC-driven place-cell learning with periodic grid-cell input reduces spatial aliasing by 94–99% across environments of increasing geometric complexity, with gains concentrated precisely where symmetry-induced aliasing is worst. The work positions grid cells as a general-purpose disambiguation signal complementary to boundary sensing, though its reliance on analytically constructed grids and single-scale modules leaves open whether attractor-based, multi-scale implementations would preserve these gains—and how the approach extends to real-world, non-idealized environments.