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Population coding and self-organized ring attractors in recurrent neural networks for continuous variable

Roman Kononov^1,2, Vasilii Tiselko^1,3,4, Oleg Maslennikov^1,2

¹Nonlinear Dynamics Department, Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia.

Frontiers in Network Physiology

|November 17, 2025

Summary

This study shows how recurrent neural networks can self-organize into specialized modules for path integration. These networks develop distinct ring attractors and control units essential for navigation and robust neuromorphic systems.

Keywords:

bump attractors continuous variable integration network physiology neural representation nonlinear dynamics population coding recurrent neural networks

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Area of Science:

Computational Neuroscience
Artificial Intelligence
Systems Neuroscience

Background:

The brain integrates continuous variables using ring attractor circuits.
Understanding self-organization in neural systems is crucial for neuroscience and AI.

Purpose of the Study:

To investigate the self-organization of neural structures for path integration.
To explore how recurrent neural networks (RNNs) can develop specialized modules.

Main Methods:

Training an RNN on a ring-based path integration task.
Utilizing population-coded velocity inputs.
Analyzing network architecture and module interactions through perturbations.

Main Results:

The RNN autonomously developed a modular architecture with a stable ring attractor and a dissipative control unit.
Functional specialization emerged for position maintenance and velocity translation.
Precise topological alignment between modules proved essential for reliable integration.

Conclusions:

Biologically plausible representations and functional specialization can arise from general learning objectives.
Findings offer insights into neural self-organization.
Provides a framework for developing interpretable and robust neuromorphic systems for navigation.