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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 Compared to Interictal Epileptiform Discharges

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Dr. Rishabh Pathak

Benign Epileptiform Transients of Sleep (BETS) and Interictal Epileptiform Discharges (IEDs) in EEG recordings have similarities in their epileptiform morphology and occurrence over the temporal lobes, but they also have key differences that aid in their differentiation.

Morphology and Occurrence:

o  BETS and IEDs share epileptiform morphology and can occur over the temporal lobes, making them more likely to be mistaken for each other.

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

o  IEDs, on the other hand, are interictal epileptiform discharges that represent abnormal electrical activity in the brain and are associated with epilepsy.

2.     Frequency of Occurrence:

o BETS are more likely to occur in adults between 30 and 60 years of age, with children younger than 10 years rarely exhibiting them.

o  IEDs can occur in individuals with epilepsy and may manifest during sleep, making the distinction between BETS and IEDs challenging in some cases.

3.     Waveform Characteristics:

o BETS typically have consistent waveform characteristics with shifting asymmetry, making their identification important.

o IEDs, in contrast, often vary in waveform with inconsistent amplitudes and durations, which can help differentiate them from BETS when the transients recur.

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  IEDs may have a more asymmetric field distribution across the frontal poles, helping to distinguish them from the more localized BETS.

Understanding these differences between BETS and IEDs is crucial for accurate EEG interpretation and the differentiation of benign transient patterns from pathological epileptiform activity associated with epilepsy.

 

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