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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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Dr. Rishabh Pathak


 

Fourteen and Six Per Second Positive Bursts (Ctenoids) can be distinguished from Sleep Spindles based on the following characteristics:


1.     Distribution:

o  Ctenoids have a broad and uniformly distributed field, often extending across different regions of the scalp, including the occipital and parietal areas.

o    Sleep Spindles, on the other hand, are typically confined to the central regions of the brain and do not extend as widely across the scalp as Ctenoids.

2.   Frequency:

o Ctenoids exhibit rhythmic activity at frequencies ranging from 6 to 14 Hz, with bursts lasting for about 1 second.

o Sleep Spindles are characterized by rhythmic activity in the sigma frequency range (11-16 Hz) and have a distinctive waxing and waning pattern.

3.   Duration:

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

o Sleep Spindles may have longer durations, typically lasting for a few seconds up to 2 seconds or more.

4.   Spatial Characteristics:

o Ctenoids have a more widespread distribution across the scalp, involving multiple regions such as the occipital and parietal areas.

o    Sleep Spindles are more localized to the central regions of the brain, such as the frontal and central areas, and may show shifting asymmetry but remain confined to these regions.

5.    Appearance:

o Ctenoids present as arciform repetitions with an arc-like shape in EEG channels, often showing sharply contoured components pointing downward, termed "positive".

o Sleep Spindles have a characteristic spindle-shaped appearance on EEG, with a waxing and waning morphology that distinguishes them from the arciform pattern of Ctenoids.

6.   Clinical Significance:

o  Ctenoids are considered benign epileptiform variants and are typically not associated with pathological conditions or epileptic seizures.

o Sleep Spindles are a normal EEG feature seen during non-REM sleep and are associated with sleep architecture rather than pathological conditions.

Understanding these differences between Fourteen and Six Per Second Positive Bursts (Ctenoids) and Sleep Spindles is essential for accurate EEG interpretation and differentiation between normal sleep patterns and benign epileptiform variants in EEG recordings.

 

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