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Energy Manifold Natural Gradient Descent: From Riemannian Optimization to Modern Neuroscience, NeuroAI and Quantum Physics

Dr. Rishabh Pathak
When Geometry, Energy, Artificial Intelligence and Neuroscience Converge Modern Artificial Intelligence is rapidly moving beyond the idea that learning simply means minimizing an error function. Increasingly, researchers are asking a deeper question: what is the structure of the space in which learning takes place? This question becomes particularly important when the system being modelled is constrained, nonlinear, dynamic, or governed by physical principles. A recent work titled “Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers” , by Zhangyong Liang and Huanhuan Gao, introduces Energy Manifold Natural Gradient Descent (EMNGD) , a mathematical framework that extends energy-based natural-gradient optimization from unconstrained Euclidean parameter spaces to constrained Riemannian parameter manifolds . At its core, the framework proposes a simple but powerful principle: An optimization algorithm should not only determine how to reduce error; it sh...
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How does sensorimotor mu rhythm activity impact corticospinal output during TMS delivery?

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Dr. Rishabh Pathak


Sensorimotor mu rhythm activity plays a significant role in influencing corticospinal output during transcranial magnetic stimulation (TMS) delivery. The sensorimotor mu rhythm is an oscillatory brain activity that occurs in the frequency range of 8-13 Hz and is predominantly observed over sensorimotor cortical regions. Here is how sensorimotor mu rhythm activity impacts corticospinal output during TMS delivery:


1.     Phase-Dependent Effects: Studies have shown that the phase of the sensorimotor mu rhythm can influence corticospinal excitability. Specifically, corticospinal output is modulated by the phase of the mu rhythm, with increased excitability observed during specific phases of the mu rhythm cycle. For example, corticospinal output tends to be higher during the trough (negative peak) phases of the mu rhythm compared to the peak (positive peak) phases.

2.     Enhancement vs. Suppression: When TMS is delivered to the primary motor cortex (M1) during the trough phases of the mu rhythm, it can lead to enhanced corticospinal transmission and improved motor learning. In contrast, TMS delivered during the peak phases of the mu rhythm may result in weaker corticospinal transmission and have less impact on motor learning. This phase-dependent effect highlights the importance of timing TMS interventions based on the ongoing sensorimotor mu rhythm activity.

3.     Interhemispheric Communication: In addition to influencing corticospinal output, sensorimotor mu rhythm activity also affects interhemispheric communication between homologous motor cortex regions. Studies have demonstrated that the phase synchronicity of the mu rhythm can determine the efficacy of communication between motor cortices, further emphasizing the role of mu rhythm activity in shaping neural interactions.

4.     Complex Interplay: The interplay between sensorimotor mu rhythm phase and power is complex and interdependent in shaping corticospinal tract activity. Both the phase and power of the mu rhythm contribute to modulating corticospinal output, highlighting the need to consider both aspects when utilizing TMS for measurement or interventional purposes.


In conclusion, sensorimotor mu rhythm activity exerts a significant influence on corticospinal output during TMS delivery, with phase-dependent effects playing a crucial role in modulating neural excitability and motor learning processes. Understanding and leveraging the impact of mu rhythm activity can enhance the efficacy of TMS interventions and provide insights into the mechanisms underlying motor control and plasticity in the human brain.

 

 

Hussain, S. J., Claudino, L., Bönstrup, M., Norato, G., Cruciani, G., Thompson, R., ... Cohen, L. G. (2019). Sensorimotor oscillatory phase–power interaction gates resting human corticospinal output. Cerebral Cortex, 29(9), 3766–3777. https://doi.org/10.1093/cercor/bhy255.

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