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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 Burst Suppression Activity

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Dr. Rishabh Pathak



The Burst-Suppression Pattern in EEG recordings exhibit several distinguishing features that differentiate it from other EEG patterns. These features include:


1. Bursts and Suppressions: The presence of alternating bursts of high-voltage, high-frequency activity followed by periods of low-voltage, low-frequency electrical silence or suppression is a hallmark feature of burst suppression.


2.Amplitude Contrast: Contrasting amplitudes between the bursts and suppressions, with bursts typically showing high amplitudes and suppressions showing low amplitudes, creating a distinct pattern on the EEG.


3.Duration: Bursts of activity typically last for a few seconds, followed by suppressions of electrical silence lasting a similar or different duration, contributing to the characteristic cyclic nature of burst suppression.


4.Waveform Components: Bursts may contain sharp waves, spikes, or a mixture of frequencies, while suppressions often lack these features, contributing to the dynamic nature of the patterns.


5. Background Activity: The background activity between bursts and suppressions may vary, with some recordings showing symmetric background rhythms with a mixture of frequencies and absence of abnormal discharges.


6.Clinical Context: Burst suppression is often associated with specific clinical conditions such as severe encephalopathy, coma, anesthesia, or hypoxic-ischemic insults, providing important diagnostic and prognostic information.


By recognizing these distinguishing features of burst suppression activity in EEG recordings, clinicians can better interpret the EEG patterns, understand the underlying brain activity, and make informed decisions regarding patient management and treatment strategies.

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