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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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Benign Epileptiform Transients of Sleep

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Dr. Rishabh Pathak

Benign Epileptiform Transients of Sleep (BETS) are transient EEG patterns that commonly occur during light sleep, particularly in stages 1 and 2 of non-rapid eye movement (NREM) sleep.

Characteristics:

o  BETS are sharply contoured, temporal region transients that are more apparent during the slow activity of sleep compared to wakefulness.

o  These transients typically have a monophasic or diphasic waveform with an abrupt rise and steeper fall, with the principal phase being electronegative on the scalp.

o While most BETS have a sharp contour, some may also exhibit an after-going slow wave, although less commonly.

2.     Occurrence:

o BETS are most commonly observed during stages 1 and 2 of NREM sleep, indicating a relationship between these EEG patterns and specific sleep stages.

o The occurrence of BETS during sleep suggests a physiological rather than pathological origin, as they are considered benign and not indicative of epilepsy.

3.     Localization:

o  Studies using low-resolution electromagnetic tomography (LORETA) have identified consistent localization patterns for BETS across different patients.

o The localization of BETS includes two components separated by a short interval, with one component in the ipsilateral posterior insular region and the other in the ipsilateral mesial temporal-occipital region.

4.    Differentiation from Epileptiform Activity:

o Depth electrode recordings of BETS have demonstrated differences from interictal epileptiform discharges (IEDs) occurring within the same recording, supporting the benign nature of BETS.

o The consistent localization of BETS and their distinct characteristics help differentiate them from epileptiform activity, emphasizing their benign nature.

Overall, BETS are transient EEG patterns that occur during sleep, particularly in NREM stages, and exhibit specific waveform characteristics and consistent localization patterns. Understanding the features of BETS is essential for accurate EEG interpretation and differentiation from epileptiform activity.

 

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