# State Space Models Naturally Produce Time Cell and Oscillatory Behaviors and Scale to Abstract Cognitive Functions

arXiv: https://arxiv.org/abs/2507.13638 · HTML: https://mlsanity.com/paper/2507.13638/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 25 references that are in the map.
- First posted on arXiv 18 Jul 2025.

## Builds on (most cited first, 5 of 5)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Gated Linear Attention Transformers with Hardware-Efficient Training](https://mlsanity.com/paper/2312.06635/) (2023)
- [Attractor and integrator networks in the brain](https://mlsanity.com/paper/2112.03978/) (2021)
- [Transformers and Cortical Waves: Encoders for Pulling In Context Across Time](https://mlsanity.com/paper/2401.14267/) (2024)

## Abstract (arXiv)

A grand challenge in modern neuroscience is bridging the gap between the microscale neural circuits and cognitive functions. While extensive knowledge exists about neuronal connectivity and biophysics, how low-level phenomena give rise to abstract behaviors remains largely unresolved. Here, we propose that a mathematical framework based on State Space Models offers mathematical sufficiency and computational plausibility to generate response profiles that resemble time cells, ramping activity, and oscillatory responses. Our results suggest that such behaviors can emerge from a structured multi-timescale complex rotational basis, which enables optimized history compression and naturally generates structured temporal dynamics even prior to training, mirroring recent findings in biological circuits. Learning exploits and adapts to the pre-existing temporal basis for specific tasks. We show that the model can readily scale to abstract cognitive functions such as event counting, supporting its use as a computationally tractable framework for understanding neural activities.