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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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Normal Amplitude + Normal Speed (NANS)

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Dr. Rishabh Pathak

In the context of transcranial magnetic stimulation (TMS) research, "Normal Amplitude + Normal Speed (NANS)" refers to a specific experimental condition or task protocol used to study motor function and cortical excitability. Here is an explanation of NANS in the context of TMS studies:


1.      Definition:

o NANS represents a condition in TMS experiments where participants are instructed to perform a motor task with a standard or typical level of movement (Normal Amplitude) at a regular speed (Normal Speed).

o This condition is designed to establish a baseline or reference point for motor performance and cortical excitability assessments during TMS procedures.

2.     Experimental Design:

oIn TMS studies focusing on motor tasks and MEP measurements, NANS is one of the task conditions used to evaluate the effects of TMS on motor cortex excitability and muscle responses.

oParticipants are asked to perform movements with a normal range of motion or muscle activation (Normal Amplitude) at a pace considered standard or comfortable for the individual (Normal Speed).

3.     Motor Task Parameters:

oNormal Amplitude: Participants are instructed to achieve a standard level of muscle contraction or movement range during the task, ensuring consistency in motor output across trials.

oNormal Speed: The task is performed at a regular speed that is typical for the individual or within a predefined range to maintain uniformity in task execution.

4.    Purpose:

oBaseline Comparison: NANS serves as a control condition for comparing changes in motor performance or cortical excitability under different task conditions or experimental manipulations.

oStandardization: By including NANS in the experimental design, researchers can establish a consistent reference point for assessing the impact of TMS interventions on motor function.

5.     Research Applications:

oCortical Excitability: NANS can help researchers evaluate the baseline level of cortical excitability and motor responses before applying TMS interventions.

oTreatment Effects: Comparing outcomes between NANS and other task conditions allows for the assessment of how TMS influences motor behavior and neural activity.

In summary, Normal Amplitude + Normal Speed (NANS) in TMS research represents a task condition where participants perform movements with a standard level of muscle activation and at a regular speed. By incorporating NANS as a baseline condition, researchers can assess motor function, cortical excitability, and the effects of TMS interventions in a standardized and controlled experimental setting.

 

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