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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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Distinguishing features of Wickets Rhythms

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Dr. Rishabh Pathak

The wicket rhythm pattern in EEG recordings has several distinguishing features that differentiate it from other EEG patterns. 


1.     Waveform:

o The wicket rhythm is characterized by a unique waveform consisting of monophasic waves with alternating sharply contoured and rounded phases, giving it an arciform appearance.

o  This waveform includes negative sharp components followed by positive rounded components, similar to the mu rhythm but with distinct features.

2.   Frequency:

oThe wicket rhythm typically occurs within the alpha frequency range, although it may occasionally manifest in the theta frequency range.

oUnlike some focal seizures and subclinical rhythmic electrographic discharges of adults, the wicket rhythm lacks evolution in frequency, waveform, or distribution during its occurrence.

3.   Location:

o Wicket rhythms are often maximal over the anterior or mid-temporal regions and may exhibit unilateral occurrence with shifting asymmetry that maintains bilateral symmetry overall.

o The field of the wicket rhythm is typically centered in the temporal region, distinguishing it from other EEG patterns like subclinical rhythmic electrographic discharges of adults.

4.   Duration:

oWicket rhythms typically have a shorter duration compared to patterns like rhythmic mid-temporal theta activity, with durations not lasting as long as the typical minimum duration of 5 or 10 seconds for the latter.

oWhile wicket rhythms may occur in wakefulness and light sleep, they are most commonly associated with drowsiness and light sleep states.

5.    Association with Pathology:

o The wicket rhythm is considered a normal variant in EEG recordings and is not inherently associated with epilepsy.

oAlthough suspicion exists regarding a potential association with cerebral vascular disease, further validation with control populations is required to confirm this link.

Understanding these distinguishing features of wicket rhythms is essential for accurate interpretation of EEG recordings and differentiating normal variants from pathological findings. Healthcare professionals can utilize these characteristics to identify and interpret wicket rhythms correctly in clinical practice.
 

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