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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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Active Motor Threshold [AMT]

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Dr. Rishabh Pathak

The Active Motor Threshold (AMT) is a critical parameter in Transcranial Magnetic Stimulation (TMS) studies that plays a significant role in assessing cortical excitability and determining the appropriate stimulation intensity for inducing Motor Evoked Potentials (MEPs) in a target muscle. Here is a detailed explanation of the Active Motor Threshold:


1. Definition: The AMT is defined as the minimum intensity of magnetic stimulation required to elicit small MEPs (typically above 50 μV) in a specific muscle that is voluntarily contracted during the TMS procedure. This threshold is determined individually for each subject and is essential for adjusting the stimulation intensity to effectively activate the motor cortex.


2.  Measurement: The AMT is typically determined by gradually increasing the stimulation intensity until MEPs of the desired amplitude are consistently observed in at least half of the stimulation trials. This process helps researchers or clinicians identify the level of stimulation needed to evoke a motor response in the contracted muscle.


3.  Significance: The AMT reflects the excitability of the motor cortex and provides valuable information about the responsiveness of the corticospinal pathway to TMS. By establishing the AMT, researchers can ensure that the stimulation intensity is tailored to each individual's physiological characteristics, thereby optimizing the effectiveness and safety of the TMS procedure.


4.  Clinical Applications: In clinical settings, the AMT is used to guide TMS interventions for various neurological conditions, such as stroke rehabilitation, motor neuron diseases, and psychiatric disorders. By accurately determining the AMT, clinicians can deliver targeted stimulation to specific brain regions to modulate cortical activity and potentially improve motor function or alleviate symptoms.


5. Research Implications: In research studies utilizing TMS, the AMT serves as a crucial parameter for standardizing stimulation protocols and comparing cortical excitability across different populations or experimental conditions. Understanding and controlling the AMT allow researchers to investigate the neural mechanisms underlying motor function, plasticity, and disorders affecting the motor system.


In summary, the Active Motor Threshold is a fundamental aspect of TMS research and clinical practice, providing insights into cortical excitability and guiding the precise delivery of magnetic stimulation to modulate motor responses in the brain.

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