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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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Beta Activity compared to Muscles Artifacts

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Dr. Rishabh Pathak

Beta activity in EEG recordings can sometimes be confused with muscle artifacts due to their overlapping frequency components.

Frequency Components:

o Muscle artifacts often have frequency components of 25 Hz and greater, which can overlap with the frequency range of beta activity.

o Beta activity in EEG recordings typically falls within the beta frequency range of 13-30 Hz, with variations based on specific brain states and cognitive processes.

2.     Waveform Characteristics:

o Electromyographic (EMG) artifacts, which represent muscle activity, have distinct waveform characteristics that can help differentiate them from beta activity.

o EMG artifacts may exhibit a sharper contour with less rhythmicity, especially when the high-frequency filter is set at 70 Hz or higher, compared to the smoother contour and rhythmicity of beta activity.

3.     High-Frequency Filter Settings:

o Adjusting the high-frequency filter settings in EEG recordings can impact the appearance of muscle artifacts and beta activity.

o A high-frequency filter set to 40 Hz or lower can make EMG artifacts appear smoother and more rhythmic, potentially resembling beta activity if not properly distinguished.

4.    Duration and Intervals:

o EMG artifacts that occur within the beta frequency range may consist of individual EMG potentials with durations of less than 20 milliseconds, separated by repeating intervals that produce a rhythmic pattern.

o  Variations in the interval between repeating EMG potentials can serve as a distinguishing feature, especially when the intervals become so brief that the potentials appear continuous, indicating muscle artifact.

5.     Temporal Characteristics:

o  Normal beta activity typically begins and ends gradually, even if over a short duration, distinguishing it from the abrupt occurrence of muscle artifacts in EEG recordings.

o The temporal characteristics of beta activity and muscle artifacts play a crucial role in differentiating between these patterns and interpreting EEG findings accurately.

By considering these factors, EEG interpreters can effectively differentiate between beta activity and muscle artifacts, ensuring accurate analysis of brain wave patterns and minimizing misinterpretations in clinical and research settings.

 

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