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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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Co-occurring Patterns of Wicket Rhythms

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Dr. Rishabh Pathak

The co-occurring patterns of Wicket Rhythms in EEG recordings include various EEG activities and waveforms that may accompany or be observed alongside the presence of Wicket Rhythms. 


1.     Wakefulness and Light Sleep:

o    In wakefulness and light sleep, all normal waveforms of these states may accompany Wicket Rhythms.

o  The alpha rhythm is commonly observed alongside Wicket Rhythms in wakefulness.

2.   Other Co-occurring Patterns:

o  Mu Rhythm: The Mu Rhythm, also known as Rolandic Mu Rhythm or Central Mu Rhythm, may accompany Wicket Rhythms.

o Subclinical Rhythmic Electrographic Discharge of Adults (SREDA): While SREDA and Wicket Rhythms have differences, they both involve rhythmic activity and may co-occur in EEG recordings.

o Rhythmic Mid-temporal Theta Activity: Wicket Rhythms and Rhythmic Mid-temporal Theta Activity may share similarities in location and occurrence during drowsiness.

Understanding the co-occurring patterns of Wicket Rhythms is important for comprehensive EEG interpretation and recognizing the context in which these patterns manifest. The presence of these co-occurring patterns can provide additional insights into the EEG findings and aid in the accurate interpretation of brain activity.

 

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