PaperlayerView exact revision on arXiv

Source-linked AI summary

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

Alexander Johnson, Obadah Ghizawi, Ali A. Minai

arXiv:2608.18569v1cs.NEcs.AIcs.ROeess.SYq-bio.NC

TL;DR

Spatial aliasing can make distinct locations look alike in place-cell representations, especially when models rely on boundary cues alone. The paper adds analytically constructed grid-cell signals to BVC-driven place cells, reducing aliasing across environments by 94–99%.

  • Problem

    BVC-driven place representations can produce similar activity at distinct, visually similar locations, creating spatial aliasing.

  • Method

    The model combines BVC-driven place cells with analytically constructed grid-cell modules that provide an internal positional signal complementary to boundary representations.

  • Results

    Grid-cell input reduced aliasing across all three environments, including an approximately 99.3% reduction in averaged MSAI in the Cross environment.

  • Takeaways & Limitations

    Grid cells provide complementary spatial information that helps disambiguate place representations in environments with geometric ambiguity.

Abstract

from arXiv · show

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.

I. INTRODUCTION … C. Boundary Vector Cells

The paper situates spatial mapping in hippocampal place-cell activity and examines how complementary grid-cell signals can reduce aliasing in spatial representations. It also reviews place cells, head-direction cells, and boundary-vector cells as components of navigational circuitry.

  • I. INTRODUCTION: Hippocampal place cells support spatial mapping through localized activity regions called place fields.Their firing patterns depend on distal visual cues.
  • I. INTRODUCTION: Grid cells in the medial entorhinal cortex form triangular lattices through periodic firing fields at different orientations and spatial frequencies.These lattices cover environments visited by animals.
  • I. INTRODUCTION: Grid cells provide a context-dependent spatial metric for path integration and vector navigation, complementing place-cell signals in large-environment coding.The paper identifies reduced aliasing as one way grid cells improve spatial-representation accuracy.
  • A. Place Cells: Place cells are primarily located in hippocampal CA3 and CA1 regions and exhibit location-specific, boundary-aware firing within place fields.Their firing depends on the animal’s position and maintains a tunable distance and direction from boundaries.
  • B. Head Direction Cells: Head-direction cells fire rapidly when the animal’s head points within a restricted angular range, with each cell having a preferred direction.Together, activated cells provide a population-coded signal of facing direction.
  • B. Head Direction Cells: Head-direction cells are located in the postsubiculum and form an important component of the hippocampal navigational circuitry.Their population activity indicates the direction in which an animal is facing.
  • C. Boundary Vector Cells: Boundary-vector cells fire when an environmental boundary intersects a receptive field at a preferred distance and allocentric direction from the animal.The supplied passage states that BVC firing depends on the animal’s location rather than the animal’s…

D. Grid Cells … III. MODEL ARCHITECTURE

The paper uses analytically constructed grid-cell signals to provide periodic, metrically consistent spatial information that complements boundary-based inputs and reduces place-field aliasing. Its architecture combines head-direction, boundary-vector, grid-cell, and place-cell layers to form stable representations in geometrically ambiguous environments.

  • D. Grid Cells: Grid cells fire across space in periodic hexagonal lattices, with neighboring cells differing in field locations, or phases.Grid cells are key spatial units in the dorsocaudal medial entorhinal cortex.
  • 1) Grid Cell Modeling:: The model analytically constructs grid-like firing patterns through cosine interference, enabling precise control over grid scale and orientation.This approach prioritizes functional utility and computational control over reproducing grid-cell physiology.
  • 1) Grid Cell Modeling:: The approach leverages periodic, metrically consistent grid-cell information to reduce place-field aliasing in complex, symmetric environments.Its stated goal is functional use of grid-cell properties rather than biological replication.
  • E. Spatial Aliasing: Spatial aliasing occurs when visually similar locations produce similar place representations, especially when place-cell activity is driven mainly by BVC sensory inputs.This creates ambiguity because distinct locations can elicit similar responses.
  • E. Spatial Aliasing: The paper presents grid cells as a robust and universally applicable solution to spatial aliasing.A single place cell in the Cross environment illustrates the problem through four distinct activation maxima at separated locations.
  • III. MODEL ARCHITECTURE: The model contains four biological-counterpart layers: Head Direction Cell, Boundary Vector Cell, Grid Cell, and Place Cell.HDCs encode heading, BVCs encode obstacle and boundary information, and GCs provide an internal positional signal.
  • III. MODEL ARCHITECTURE: Positional input drives the grid-cell network, compass input drives head-direction cells, and lidar input drives BVCs.Grid-cell and BVC signals excite place cells, while afferent and recurrent inhibition regulate competition and sparsity.
  • III. MODEL ARCHITECTURE: The added grid-cell layer supplies a metric spatial coordinate system that complements boundary-based representations and supports stable place fields under geometric ambiguity.The HDC, BVC, and PC layers are adapted from previous models.

A. Notation & Overview · B. Head Direction Cell Layer

The model uses consistent superscript notation for four cell types and their time-varying firing rates and synaptic weights. Its head-direction layer provides allocentric orientation through eight fixed preferred directions and cosine tuning to the agent’s heading.

  • A. Notation & Overview: Four cell types—head-direction, boundary-vector, grid, and place—use the superscripts h, b, g, and p, respectively.
  • A. Notation & Overview: The time-varying firing rate of the ith cell of type k is denoted by v^k_i(t), or v^k_i when time is omitted.
  • A. Notation & Overview: The synaptic weight from the jth cell of type l to the ith cell of type k is denoted W^kl_ij(t), or W^kl_ij without time indices.
  • A. Notation & Overview: These notation conventions apply throughout all network modules and environments unless otherwise specified.
  • B. Head Direction Cell Layer: The head-direction layer provides a global allocentric orientation signal, with each cell assigned a preferred direction.
  • B. Head Direction Cell Layer: N_h = 8 head-direction cells have fixed preferred directions spanning 0°, 45°, …, 315°.
  • B. Head Direction Cell Layer: Each head-direction cell responds through cosine tuning based on the agent’s current global heading θ(t).
  • B. Head Direction Cell Layer: Responses peak when the agent faces a cell’s preferred direction and decrease smoothly with angular deviation.The tuning is derived from the dot product of heading and preferred-direction unit vectors and is adapted from Erdem and Hasselmo.

C. Boundary Vector Cell Layer

The BVC layer encodes geometric spatial information from the agent’s relationship to environmental boundaries using LiDAR inputs and boundary-vector tuning. Its preferred displacements tile the boundary-coding space, while normalization keeps activations comparable across population sizes.

  • BVCs encode the agent’s relationship to environmental boundaries using the boundary vector formulation of Barry et al.
  • Each BVC is defined by a preferred radial distance d_i and allocentric bearing ϕ_i, and receives LiDAR ranges from 720 fixed-angle beams.
  • Each BVC combines radial and angular Gaussian tuning functions across all sensor beams, with widths σ_r and σ_θ.
  • Preferred distances span [0, r_max] and bearings span [0, 2π), uniformly tiling potential boundary configurations around the agent.Activations are normalized by N_BVC to remain in a consistent range across different BVC population sizes.

D. Grid Cell Layer · 1) Analytical Grid Cell Construction:

The model analytically constructs grid-cell activity to provide periodic spatial signatures that reduce aliasing, using controlled orientations, scales, phases, and biologically motivated post-processing. The construction combines three cosine gratings with normalization and thresholding to produce sharply tuned, sparse activations.

  • D. Grid Cell Layer: Grid cells address severe place-field aliasing caused by environmental symmetry or repeated geometry by providing internally generated spatial representations.Their hexagonal firing patterns combine into a unique spatial signature at every location.
  • D. Grid Cell Layer: The model analytically constructs hexagonal periodic grid patterns mathematically rather than simulating underlying neural mechanisms.This approach provides computational efficiency.
  • D. Grid Cell Layer: The construction maintains biological plausibility through post-processing and obstacle-aware masking while allowing precise control over spatial properties.These controls accompany the analytical grid-cell formulation.
  • D. Grid Cell Layer: The model uses M = 8 grid-cell modules aligned with head-direction cells at orientations α_m ∈ {0°, 45°, ..., 315°}.Each module contains N_m = 50 cells sharing scale λ but differing in phase offset ϕ_j.
  • 1) Analytical Grid Cell Construction:: For orientation α, scale λ, and phase offset ϕ = (ϕ_x, ϕ_y), the spatial frequency is defined as ω = 2π/λ.Position x = (x, y) is rotated into the grid cell’s reference frame and translated by its phase offset.
  • 1) Analytical Grid Cell Construction:: The canonical grid pattern is constructed as the mean of three cosine gratings oriented 60° apart.This produces the hexagonal periodic structure used by the analytical grid-cell model.
  • 1) Analytical Grid Cell Construction:: A power-law transformation adjusts the activation profile to achieve sharply tuned firing fields observed in biological recordings.The exponent β ∈ [1.2, 1.8] controls field sharpness.
  • 1) Analytical Grid Cell Construction:: Per-cell min-max normalization ensures consistent dynamic range, while soft thresholding creates sparse activations controlled by θ_gc.These post-processing steps follow the power-law transformation.

2) Obstacle-Aware Masking:

Obstacle-aware masking modifies analytically constructed grid-cell activations so they fragment at barriers while preserving local phase coherence, addressing activations that otherwise extend across walls.

  • Obstacle-Aware Masking:: Analytical position-only construction produces activations extending across walls, motivating spatial masking applied independently to each grid cell.This contradicts biological observations that grid cells fragment at barriers while maintaining phase coherence.
  • Obstacle-Aware Masking:: Blobs intersecting obstacles covering ≥20% of their diameter are split or suppressed, with only the largest component retained after splitting.Connected activation components are identified before obstacle masks are applied.
  • Obstacle-Aware Masking:: Dilated obstacle boundaries fragment blobs that remain connected after initial masking, followed by Gaussian smoothing with σ ≈0.5.Smoothing restores biologically plausible curved edges.
  • Obstacle-Aware Masking:: Masked activations fragment at boundaries while preserving local phase coherence within each compartment, unlike raw activations that extend across walls.Figure 3 illustrates the contrast between unmasked and masked activations in an obstacle-filled environment.

E. Place Cell Layer · 1) Membrane Dynamics and Activation:

The place-cell layer forms the model’s core spatial representation by integrating boundary and grid-cell inputs. Its leaky-integrator dynamics, inhibition, and rectifying saturation produce sparse, localized place fields.

  • E. Place Cell Layer: Place cells encode specific environmental locations through spatially localized receptive fields developed by competitive learning.These receptive fields are the model’s place fields.
  • E. Place Cell Layer: The layer combines BVC-derived geometric constraints with GC-derived metric phase information to disambiguate perceptually similar locations.BVCs represent environmental boundaries, whereas GCs provide internally generated spatial information.
  • 1) Membrane Dynamics and Activation:: Each place-cell membrane potential evolves as a leaky integrator combining excitatory BVC and GC inputs with global inhibition.The dynamics combine afferent excitation with inhibitory control.
  • 1) Membrane Dynamics and Activation:: Excitatory drive is constructed from synaptic weights linking BVCs and GCs to each place cell.The supplied passage introduces the excitatory-drive formulation but does not display its full equation.
  • 1) Membrane Dynamics and Activation:: Inhibitory drive includes afferent boundary and grid inhibition and recurrent place-to-place inhibition, regulated by inhibitory gain parameters.Γpb, Γpg, and Γpp control these inhibitory contributions.
  • 1) Membrane Dynamics and Activation:: Place-cell firing rates are obtained through rectification and saturation, using a gain factor and [·]+ = max(0, ·).The nonlinearity operates on the membrane-potential output.
  • 1) Membrane Dynamics and Activation:: Global inhibition and thresholding together generate sparse, localized place fields.This mechanism shapes the spatial selectivity of the place-cell layer.
  • 1) Membrane Dynamics and Activation:: The evaluation uses Open, Cross, and Maze environments, each measuring 20m x 20m.These are the three environments shown in Fig. 4.

2) Self-Organization via Competitive Learning:

Place fields emerge through competitive learning during exploration, with sparse BVC and grid-cell inputs shaped by Oja’s rule. Hebbian strengthening, synaptic normalization, and global inhibition produce winner-take-all dynamics that specialize place cells to distinct input combinations.

  • Place fields emerge through competitive learning during exploration.
  • Approximately 0.25 and 0.30 connection probabilities initialize sparse, distinct BVC and grid-cell input subsets for each place cell.
  • Oja’s rule strengthens synapses between co-active pre- and postsynaptic cells while normalizing total synaptic input and enforcing competition.Learning time constants and normalization factors control weight decay and synaptic normalization.
  • Global inhibition produces winner-take-all dynamics, causing each place cell to specialize to a unique combination of BVC and grid-cell inputs.

IV. EXPERIMENTAL SETUP · A. Data Collection · B. Model Parameters

Experiments used a Roomba agent in Webots across three environments, comparing grid-cell and no-grid-cell conditions. The model included 400 BVCs and, when enabled, 400 grid cells distributed across eight modules.

  • IV. EXPERIMENTAL SETUP: Experiments ran in Webots R2025a on an RTX 3090 GPU and Ryzen 9 9900X CPU using a Roomba equipped with a compass and 720-beam rangefinder.The rangefinder covered 360 degrees and had a maximum distance of 25m.
  • A. Data Collection: The agent explored an obstacle-free environment, a cross-wall environment dividing the space into four regions, and a maze.These environments represented increasing structural complexity for testing spatial aliasing.
  • A. Data Collection: 30 trials were conducted across the environments: 5 with grid cells and 5 without grid cells per environment, with results averaged for each condition.Each trial included training and evaluation phases, and training continued until at least 95 percent of the environment was covered.
  • B. Model Parameters: The model used 50 BVCs along each of 8 head directions, yielding 400 BVCs in total.Table I summarizes the neural cell populations, while Table II summarizes BVC parameters.
  • B. Model Parameters: Grid cells were organized into 8 modules with 50 cells per module, yielding 400 grid cells, and λ = 5.5 produced an activation diameter of roughly 2.7m.For no-grid-cell experiments, η was set to 0 to remove grid-cell effects.
  • B. Model Parameters: Place-cell learning and inhibition parameters were summarized in Table IV; both normalization factors were set to 0.4.Afferent inhibitory gains for BVC and GC inputs were each set to half the recurrent inhibition gain.

C. Metrics for Spatial Aliasing

Spatial aliasing is evaluated with the Spatial Aliasing Index (SAI) for individual bins and the Mean Spatial Aliasing Index (MSAI) averaged across the environment. Higher SAI and MSAI values indicate greater aliasing, whereas lower values indicate stronger localization and spatial discrimination.

  • Metrics: SAI measures how similarly place-cell activation vectors respond across spatially separated bins.The metric uses cosine similarity between activation vectors while excluding nearby bins with a distance threshold dth.
  • Metrics: MSAI summarizes overall environmental aliasing by averaging SAI across all bins.It provides an aggregate measure of place-cell representation quality across the environment.
  • Interpretation: Higher SAI(i) and MSAI values indicate that spatially distant bins have similar place-cell activation patterns.The SAI excludes nearby bins using an indicator function based on whether inter-bin distance exceeds dth.
  • Interpretation: Lower SAI(i) and MSAI values indicate stronger place-cell localization and improved spatial discrimination.Thus, reduced metric values correspond to less spatial aliasing.

V. RESULTS & DISCUSSION · VI. CONCLUSION & FUTURE WORK

Across Open, Cross, and Maze environments, grid-cell input reduced spatial aliasing relative to BVC-only representations, with the strongest improvement in the symmetric Cross environment. The authors conclude that path-integration signals improve place-cell disambiguation and propose testing attractor-based grid-cell models in future work.

  • V. RESULTS & DISCUSSION: Five independent trials per configuration and environment were averaged to compute the Mean Spatial Aliasing Index (MSAI).Results were reported for models with and without grid cells in Open, Cross, and Maze environments.
  • V. RESULTS & DISCUSSION: Heatmaps showed lower Spatial Aliasing Index (SAI) across most spatial bins when grid-cell input was included, especially in Cross.The heatmaps localized where aliasing was mitigated and complemented the averaged MSAI results.
  • V. RESULTS & DISCUSSION: Rotational symmetry divides Cross into four similar quadrants, making BVC-based place representations especially prone to place-field aliasing.Repeated sensory configurations increase similarity between distinct locations.
  • V. RESULTS & DISCUSSION: Approximately 99.3% reduction in averaged Mean Spatial Aliasing Index (MSAI) was observed after adding grid cells in Cross across five trials.Grid cells provide path-integration signals that improve disambiguation of perceptually similar regions.
  • V. RESULTS & DISCUSSION: Open showed more moderate baseline aliasing because it contained fewer repeated boundary configurations.Its lower repetition reduced the potential for BVC-induced ambiguity relative to more structurally repetitive settings.
  • V. RESULTS & DISCUSSION: Maze showed substantial but more variable improvement, because repeated corridors allowed some distant locations to retain moderate place-cell similarity.These repeated spatial patterns contributed to higher and more variable MSAI values despite grid-cell mitigation.
  • VI. CONCLUSION & FUTURE WORK: The findings show that grid-cell path-integration signals mitigate place-cell aliasing across environments with varying structural symmetry.Future work will test attractor-based grid-cell models and examine biological-plausibility trade-offs in aliasing mitigation and stability.
Loading 2608.18569v1…