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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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Small Amplitude + Fast Speed (SAFS)

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Dr. Rishabh Pathak

Small Amplitude + Fast Speed (SAFS) is a specific experimental condition commonly used in transcranial magnetic stimulation (TMS) studies, particularly in the context of motor evoked potentials (MEPs) and motor function assessments. Here is an overview of Small Amplitude + Fast Speed (SAFS) in the context of TMS research:


1.      Definition:

oSmall Amplitude + Fast Speed (SAFS) refers to a combination of parameters employed during TMS experiments to elicit motor responses, typically MEPs, with a specific level of neural excitation (small amplitude) while participants perform movements at an increased speed (fast speed).

2.     Experimental Design:

oIn TMS studies, the SAFS condition involves delivering TMS pulses to the motor cortex at an intensity that results in small-amplitude MEPs in the target muscle. Participants are instructed to execute motor tasks or movements at an accelerated speed while MEPs are recorded to assess cortical excitability and motor system function.

3.     Purpose:

oThe SAFS condition allows researchers to investigate the impact of TMS-induced cortical stimulation on motor output when neural excitation is relatively low (small amplitude) but movement speed is increased. This condition can help assess how changes in cortical excitability influence motor performance under fast speed conditions.

4.    Motor Control Assessment:

oBy combining small MEP amplitudes with fast movement speed, the SAFS condition provides a controlled setting to examine the relationship between cortical excitability, motor output, and task execution speed. Researchers can explore how variations in neural excitability affect motor function under conditions of increased movement speed.

5.     Comparison with Other Conditions:

o SAFS is often used in conjunction with other TMS conditions, such as Small Amplitude + Normal Speed (SANS) or Normal Amplitude conditions, to compare the effects of different levels of neural excitation and movement speed on motor responses. Contrasting SAFS with other conditions can yield insights into the neural mechanisms underlying motor control.

6.    Clinical Relevance:

oUnderstanding the responses elicited under the SAFS condition can have implications for clinical assessments of motor function in neurological disorders or rehabilitation settings. Assessing small-amplitude MEPs at fast movement speeds can provide valuable information about cortical excitability and motor system integrity in dynamic motor tasks.

In summary, Small Amplitude + Fast Speed (SAFS) is a specific experimental condition used in TMS research to study motor responses and cortical excitability. By combining small MEP amplitudes with increased movement speed, researchers can investigate the interplay between neural excitability, motor control, and task performance in controlled experimental settings.

 

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