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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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Rapid Eye Movements (REMs) of REM Sleep

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Dr. Rishabh Pathak

Rapid Eye Movements (REMs) of REM sleep can produce specific artifacts in EEG recordings.

1.               Nature of REM Artifacts:

o   REM artifacts are associated with the rapid eye movements that occur during REM sleep.

o   These artifacts have a waveform that differs from lateral gaze artifacts during wakefulness due to the specific movement features of REMs.

2.     Characteristics:

o REM artifacts appear as waves with an asymmetrically quicker rise than fall, similar to the REM eye movement pattern.

o  The location of REM artifacts is typically the same as other artifacts produced by lateral gaze, with specific electrode involvement.

3.     Differentiation:

o Specific movement features of REMs, such as the waveform characteristics, help differentiate REM artifacts from other ocular artifacts and EEG patterns.

o Understanding the unique features of REM artifacts is crucial for accurate interpretation and differentiation from pathological brain activity or other types of artifacts in EEG recordings.

Recognizing the distinct characteristics of REM artifacts and their association with REM sleep can aid in accurate EEG interpretation and the identification of normal physiological patterns during sleep stages.

 

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