# Learning infinite context windows in recurrent architectures via spatial neural computing

arXiv: https://arxiv.org/abs/2610.10690 · HTML: https://mlsanity.com/paper/2610.10690/

## Key facts

- No citing papers in the map yet (data through 7 Oct 2026).
- Builds on 6 of its 53 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## Builds on (most cited first, 6 of 6)

- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [A Simple Way to Initialize Recurrent Networks of Rectified Linear Units](https://mlsanity.com/paper/1504.00941/) (2015)
- [Higher Order Recurrent Neural Networks](https://mlsanity.com/paper/1605.00064/) (2016)
- [Advancing Intelligent Sequence Modeling: Evolution, Trade-offs, and Applications of State-Space Architectures from S4 to Mamba](https://mlsanity.com/paper/2503.18970/) (2025)
- [A Spatiotemporal Perspective on Dynamical Computation in Neural Information Processing Systems](https://mlsanity.com/paper/2409.13669/) (2024)
- [Energy-Based Dynamical Models for Neurocomputation, Learning, and Optimization](https://mlsanity.com/paper/2604.05042/) (2026)

## Abstract (arXiv)

Recurrent neural networks (RNNs) offer linear-time scaling with sequence length while requiring only constant memory, yet they struggle to capture long-range dependencies due to vanishing gradients and limited receptive fields. To address these limitations, we introduce a second-order recurrent model in which the standard neuron-to-neuron communication is replaced by a spatially evolving field governed by (discretized) partial differential equations. Drawing inspiration from the role of cortical waves in brain computation, this mechanism allows structured spatiotemporal patterns to serve as an implicit, high-capacity memory. We show that the resulting model is equivalent to a structured infinite-order RNN in which the current state depends explicitly on its entire history of past states, yielding an effectively unbounded receptive field with a fixed number of parameters. We further derive constructive conditions to ensure marginal stability, constraining the gradient spectrum on the unit circle and thereby eliminating vanishing and exploding gradients. Empirically, the proposed architecture outperforms other recurrent models on long-horizon benchmarks while using substantially fewer parameters, demonstrating that spatial dynamics can effectively bridge the gap between efficient inference and long-term memory.