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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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Fourteen and Six Per Second Positive Bursts (Ctenoids) compared to subclinical rhythmic electrographic discharge in adults

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Dr. Rishabh Pathak


 

Fourteen and Six Per Second Positive Bursts (Ctenoids) can be distinguished from Subclinical Rhythmic Electrographic Discharge (SREDA) in adults based on the following characteristics:


1.     Frequency and Morphology:

o Ctenoids exhibit rhythmic activity at frequencies ranging from 6 to 14 Hz, with bursts lasting for about 1 second and typically showing an arciform appearance.

o SREDA is characterized by rhythmic discharges at frequencies typically below 2.5 Hz, often with a monomorphic appearance and slower frequency compared to Ctenoids.

2.   Distribution:

o Ctenoids have a broad and uniformly distributed field across the scalp, often involving regions like the occipital and parietal areas.

o  SREDA may have a more focal or regional distribution in the brain, with a tendency to involve specific areas rather than the widespread distribution seen in Ctenoids.

3.   Duration:

o Ctenoids bursts usually last for about 1 second, rarely exceeding 2 seconds in duration.

o SREDA discharges may have variable durations but often persist for longer periods compared to the brief bursts of Ctenoids.

4.   Clinical Significance:

o  Ctenoids are considered benign epileptiform variants and are typically not associated with pathological conditions or epileptic seizures, commonly observed in children during drowsiness.

o SREDA, on the other hand, may raise concerns for underlying pathology or epileptiform activity, especially when observed in adults, and may warrant further investigation for potential seizure activity.

5.    Electrode Configuration:

o Ctenoids are best recorded with long interelectrode distances to capture their broad field distribution accurately, while short interelectrode distances may result in lower amplitude recordings.

o SREDA may exhibit specific regional patterns that can be captured using appropriate electrode montages to localize the origin of the rhythmic discharges.

Understanding these differences between Fourteen and Six Per Second Positive Bursts (Ctenoids) and Subclinical Rhythmic Electrographic Discharge (SREDA) is essential for accurate EEG interpretation and differentiation between benign variants and potentially pathological findings in adult EEG recordings.

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