Designing optimal perturbation inputs for system identification in neuroscience

Abstract Investigating the dynamics of neural networks, which are governed by connectivity between neurons, is a fundamental challenge in neuroscience. Because passive (spontaneous) activity provides only limited information for estimating connectivity, perturbation-based approaches are widely applied in neuroscience, as they can evoke underlying hidden dynamics. However, the characteristics of such perturbations have typically been designed based on empirical or biological intuition. To enable more accurate estimation of connectivity, we propose a data-driven and theoretically grounded framework for optimally designing perturbation inputs, based on formulating the neural model as a control system. The core theoretical insight underlying our approach is that neural signals observed in the passive state lack sufficient latent information, which leads to failures in the system identification. Perturbations reveal these hidden dynamics and lead to improved estimation. Guided by these insights, we derive a theoretical basis for optimizing perturbation inputs that minimize estimation errors in neural system identification. Building upon this, we further explore the relationship of this theory with stimulation patterns commonly used in neuroscience, such as frequency, impulse, and step inputs. We demonstrate the effectiveness of this framework for neuroscience through simulations grounded in experimental paradigms such as neural state classification and optimal control of neural states. Our theoretical analysis, together with multiple simulations, consistently shows that perturbations designed according to our framework achieve substantially more accurate system identification compared to the conventional, intuition-based inputs. This study provides a theoretical foundation for designing perturbation inputs to achieve accurate estimation of neural dynamics. This, in turn, enables reliable discrimination of neural states such as levels of consciousness and pathological conditions, and facilitates precise control of their transitions toward recovery from abnormal states. Competing Interest Statement The authors have declared no competing interest. Footnotes ↵† c-oizumi{at}g.ecc.u-tokyo.ac.jp In this revision, we have comprehensively revised the theoretical framework. Accordingly, we have incorporated new simulation results based on this updated theory. Furthermore, we have added specific simulations to strengthen the connection with neuroscience and demonstrate the biological relevance of our model.