State space models naturally produce time cell and oscillatory behaviors and scale to abstract cognitive functions

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.

L acknowledges support from the James R. This work was supported in part by the National Science Foundation under Grant CCF-2413293 and by the Michigan Semiconductor Talent and Technologies for Automotive Research program. These authors contributed equally: Sen Lu, Xiaoyu Zhang.

Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA Sen Lu, Xiaoyu Zhang, Mingtao Hu, Eric Yeu-Jer Lee, Soohyeon Kim & Wei D. Lu The authors declare no competing interests. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Lu, S., Zhang, X., Hu, M. et al. State space models naturally produce time cell and oscillatory behaviors and scale to abstract cognitive functions. Nat Commun (2026). https://doi.org/10.1038/s41467-026-79286-y DOI: https://doi.org/10.1038/s41467-026-79286-y