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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 + Fast Speed (NAFS)

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Dr. Rishabh Pathak

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


1.      Definition:

o NAFS 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 an increased or faster speed than usual (Fast Speed).

o This condition is designed to assess how changes in movement speed impact motor performance, cortical excitability, and the response to TMS stimulation.

2.     Experimental Design:

o In TMS studies focusing on motor tasks and MEP measurements, NAFS is used to investigate the modulation of motor cortex excitability and muscle responses when movements are executed at an accelerated pace.

o Participants are asked to maintain the standard range of motion or muscle activation (Normal Amplitude) while increasing the speed of movement beyond the usual rate.

3.     Motor Task Parameters:

o Normal Amplitude: Participants are required to achieve a standard level of muscle contraction or movement range during the task, ensuring consistency in motor output across conditions.

oFast Speed: The task is performed at a higher speed than the standard or comfortable pace, challenging the participants to execute movements more rapidly while maintaining the prescribed range of motion.

4.    Purpose:

o Speed-Dependent Effects: NAFS allows researchers to investigate how changes in movement speed influence motor performance, cortical excitability, and the response to TMS, providing insights into speed-dependent neural mechanisms.

o Motor Control Assessment: By comparing NAFS with other task conditions, researchers can evaluate the adaptability of motor control systems to varying movement speeds under TMS modulation.

5.     Research Applications:

oCortical Excitability Modulation: NAFS can help researchers explore the impact of fast-paced movements on cortical excitability and the recruitment of motor neurons in response to TMS.

oMotor Learning and Plasticity: Studying NAFS conditions may provide insights into motor learning processes, adaptation to speed changes, and the plasticity of motor circuits following TMS interventions.

In summary, Normal Amplitude + Fast Speed (NAFS) in TMS research represents a task condition where participants perform movements with a standard level of muscle activation at an increased speed. By incorporating NAFS into experimental protocols, researchers can investigate the effects of movement speed on motor function, cortical excitability, and the response to TMS stimulation, offering valuable insights into speed-dependent motor control mechanisms and neural plasticity.

 

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