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Updated: Jun 8, 2025
11:18
Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks
Published on: March 2, 2015
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On the control of recurrent neural networks using constant inputs
Cyprien Tamekue1, Ruiqi Chen2, ShiNung Ching1
1Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, 63130, MO, USA.
Arxiv
|November 6, 2024
Summary
This study explores controlling recurrent neural networks for brain modeling using non-invasive stimulation. We developed a new method to synthesize control inputs for these complex systems, enabling targeted brain activity modulation.
Area of Science:
- Theoretical Neuroscience
- Computational Neuroscience
- Control Theory
Background:
- Recurrent neural networks (RNNs) are crucial for modeling large-scale human brain dynamics and hypothesis generation.
- Non-invasive neurostimulation techniques, like transcranial direct current stimulation (tDCS), offer potential for modulating brain activity.
- Controllability analysis is essential for designing effective brain stimulation protocols.
Purpose of the Study:
- To investigate the controllability of a general class of continuous Hopfield-type recurrent neural networks.
- To develop a control synthesis method for these nonlinear systems using constant or piecewise constant inputs.
- To enable the design of brain stimulation protocols for therapeutic and cognitive enhancement applications.
Main Methods:
- Formulation and solution of a control synthesis problem for nonlinear RNNs.
- Generalization of the variation of the constants formula for novel state trajectory representation.
- Verification of conditions for constant control input existence via a two-point boundary value problem.
- Application of algorithmic optimization tools for input synthesis.
- Analysis reduction to algebraic conditions for linear activation functions.
Main Results:
- A novel representation of the system's state trajectory was derived.
- A verifiable condition for the existence of constant control inputs was established.
- The proposed control synthesis method was demonstrated to be effective through simulations.
- The approach is applicable to nonlinear RNNs with arbitrary input matrices.
Conclusions:
- The study presents a novel control synthesis for a significant class of neural network models used in neuroscience.
- The findings facilitate the design of brain stimulation protocols to modulate whole-brain activity.
- This work bridges theoretical neuroscience, control theory, and neurostimulation applications.
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