# Multigrid Neural Memory

arXiv: https://arxiv.org/abs/1906.05948 · HTML: https://mlsanity.com/paper/1906.05948/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2019.

## Built on by (most cited first, 7 of 7)

- [Emergence of Maps in the Memories of Blind Navigation Agents](https://mlsanity.com/paper/2301.13261/) (2023)
- [Hierarchical Implicit Neural Emulators](https://mlsanity.com/paper/2506.04528/) (2025)
- [MANGO: A Benchmark for Evaluating Mapping and Navigation Abilities of Large Language Models](https://mlsanity.com/paper/2403.19913/) (2024)
- [State-Space Constraints Can Improve the Generalisation of the Differentiable Neural Computer to Input Sequences With Unseen Length](https://mlsanity.com/paper/2110.09138/) (2021)
- [Neural Multigrid Memory For Computational Fluid Dynamics](https://mlsanity.com/paper/2306.12545/) (2023)
- [Tensor Memory: Fixed-Size Recurrent State for Long-Horizon Transformers](https://mlsanity.com/paper/2605.27686/) (2026)
- [Embodied Spatial Intelligence: from Implicit Scene Modeling to Spatial Reasoning](https://mlsanity.com/paper/2509.00465/) (2025)

## Abstract (arXiv)

We introduce a novel approach to endowing neural networks with emergent, long-term, large-scale memory. Distinct from strategies that connect neural networks to external memory banks via intricately crafted controllers and hand-designed attentional mechanisms, our memory is internal, distributed, co-located alongside computation, and implicitly addressed, while being drastically simpler than prior efforts. Architecting networks with multigrid structure and connectivity, while distributing memory cells alongside computation throughout this topology, we observe the emergence of coherent memory subsystems. Our hierarchical spatial organization, parameterized convolutionally, permits efficient instantiation of large-capacity memories, while multigrid topology provides short internal routing pathways, allowing convolutional networks to efficiently approximate the behavior of fully connected networks. Such networks have an implicit capacity for internal attention; augmented with memory, they learn to read and write specific memory locations in a dynamic data-dependent manner. We demonstrate these capabilities on exploration and mapping tasks, where our network is able to self-organize and retain long-term memory for trajectories of thousands of time steps. On tasks decoupled from any notion of spatial geometry: sorting, associative recall, and question answering, our design functions as a truly generic memory and yields excellent results.