# High-resolution spatial memory requires grid-cell-like neural codes

arXiv: https://arxiv.org/abs/2507.00598 · HTML: https://mlsanity.com/paper/2507.00598/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 105 references that are in the map.
- First posted on arXiv 1 Jul 2025.

## Builds on (most cited first, 14 of 14)

- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part I: Models and Data Transformations](https://mlsanity.com/paper/2111.06077/) (2021)
- [Attractor and integrator networks in the brain](https://mlsanity.com/paper/2112.03978/) (2021)
- [Linking connectivity, dynamics and computations in low-rank recurrent neural networks](https://mlsanity.com/paper/1711.09672/) (2017)
- [A Theoretical Perspective on Hyperdimensional Computing](https://mlsanity.com/paper/2010.07426/) (2020)
- [Computing on Functions Using Randomized Vector Representations](https://mlsanity.com/paper/2109.03429/) (2021)
- [Variable Binding for Sparse Distributed Representations: Theory and Applications](https://mlsanity.com/paper/2009.06734/) (2020)
- [Replay and compositional computation](https://mlsanity.com/paper/2209.07453/) (2022)
- [Binding in hippocampal-entorhinal circuits enables compositionality in cognitive maps](https://mlsanity.com/paper/2406.18808/) (2024)
- [Vector Symbolic Finite State Machines in Attractor Neural Networks](https://mlsanity.com/paper/2212.01196/) (2022)
- [Distributed Representations Enable Robust Multi-Timescale Symbolic Computation in Neuromorphic Hardware](https://mlsanity.com/paper/2405.01305/) (2024)
- [Optimizing working memory with heterogeneity of recurrent cortical excitation](https://mlsanity.com/paper/1310.3754/) (2013)
- [Crosstalk and transitions between multiple spatial maps in an attractor neural network model of the hippocampus: Collective motion of the activity (II)](https://mlsanity.com/paper/1310.3044/) (2013)

## Abstract (arXiv)

Continuous attractor networks (CANs) are widely used to model how the brain temporarily retains continuous behavioural variables via persistent recurrent activity, such as an animal's position in an environment. However, this memory mechanism is very sensitive to even small imperfections, such as noise or heterogeneity, which are both common in biological systems. Previous work has shown that discretising the continuum into a finite set of discrete attractor states provides robustness to these imperfections, but necessarily reduces the resolution of the represented variable, creating a dilemma between stability and resolution. We show that this stability-resolution dilemma is most severe for CANs using unimodal bump-like codes, as in traditional models. To overcome this, we investigate sparse binary distributed codes based on random feature embeddings, in which neurons have spatially-periodic receptive fields. We demonstrate theoretically and with simulations that such grid-cell-like codes enable CANs to achieve both high stability and high resolution simultaneously. The model extends to embedding arbitrary nonlinear manifolds into a CAN, such as spheres or tori, and generalises linear path integration to integration along freely-programmable on-manifold vector fields. Together, this work provides a theory of how the brain could robustly represent continuous variables with high resolution and perform flexible computations over task-relevant manifolds.