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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 Benign Epileptiform Transients of Sleep

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Dr. Rishabh Pathak

Benign Epileptiform Transients of Sleep (BETS) have distinguishing features that differentiate them from other EEG patterns.

Waveform Characteristics:

o BETS are sharply contoured, temporal region transients that commonly occur during light sleep, particularly in stages 1 and 2 of NREM sleep.

o  The waveform of BETS is characteristically monophasic or diphasic, with one principal phase showing an abrupt rise and an even steeper fall. This phase is typically electronegative on the scalp.

o Some BETS may exhibit an after-going slow wave, although this feature is less common.

2.     Amplitude and Duration:

o BETS are typically less than 90 μV in amplitude and 90 milliseconds in duration, with the average amplitude and duration being around 60 μV and 60 milliseconds, respectively.

o  The term "small sharp spikes" is sometimes used to describe BETS due to their typical size, but larger and longer BETS can also occur, highlighting variability in their characteristics.

3.     Occurrence and Distribution:

o BETS often occur in multiple occurrences within a recording, with several similarly formed temporal spikes observed during drowsiness or light sleep.

o The shifting lateralization of BETS should be symmetric, with an equivalent number of BETS on each side. Recurrence on one side is typically separated by more than 1 second and often more than 10 seconds.

4.    Localization and Field Distribution:

o BETS are almost always centered in the mid-temporal region, extending over the entire temporal lobe and sometimes involving the adjacent frontal lobe.

o The best montages for observing BETS are those utilizing a contralateral reference electrode, which can show a transverse dipole with a negative phase reversal over one temporal lobe and a positive one over the other.

Understanding these distinguishing features of BETS is essential for accurate EEG interpretation and differentiation from other transient EEG patterns or epileptiform discharges.

 

 

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