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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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Muscles Artifacts compared to Beta Activity

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Dr. Rishabh Pathak

Muscle artifacts and beta activity in EEG recordings can sometimes exhibit similar characteristics, particularly in terms of frequency and location. 

1.     Frequency:

o    Muscle Artifacts: Muscle artifacts often manifest as high-frequency, fast activity on EEG recordings, resembling beta activity in terms of frequency (>25 Hz). However, muscle artifacts typically have a sharper contour and less rhythmicity compared to beta activity.

o Beta Activity: Beta activity in EEG is characterized by rhythmic oscillations in the beta frequency range (typically 13-30 Hz). Beta activity tends to have a more regular and rhythmic pattern compared to muscle artifacts.

2.   Waveform:

o    Muscle Artifacts: Muscle artifacts may have a spike-like or sharp waveform due to the rapid muscle contractions generating the artifact. The individual motor unit potentials involved in muscle contractions contribute to the waveform characteristics of muscle artifacts.

o Beta Activity: Beta activity typically exhibits a smoother and more sinusoidal waveform compared to the sharp spikes often seen in muscle artifacts.

3.   Duration:

o Muscle Artifacts: Muscle artifacts, particularly those induced by muscle contractions, may have shorter durations due to the transient nature of muscle activity. The onset and offset of muscle artifacts are often abrupt.

o Beta Activity: Beta activity can be sustained over longer periods, reflecting ongoing cortical processes associated with motor planning, movement, or cognitive tasks.

4.   Location:

o  Muscle Artifacts: Muscle artifacts are commonly observed near electrodes overlaying muscle groups generating the artifact, such as facial muscles or tongue muscles. The location of muscle artifacts can provide clues to their origin.

o  Beta Activity: Beta activity is often distributed over central and frontal regions of the brain, reflecting motor and cognitive processing areas. Co-localization of muscle artifacts with regions of maximum beta activity can occur, complicating differentiation.

5.    Inter-Interval Variation:

o Muscle Artifacts: In muscle artifacts, there may be significant variation in the interval between individual potentials, especially when these intervals become very brief, leading to the merging of potentials. This rapid activity beyond the beta frequency range is indicative of muscle artifact.

o Beta Activity: Beta activity typically exhibits more consistent inter-interval durations, contributing to its rhythmic and periodic nature within the beta frequency range.

Understanding these distinctions between muscle artifacts and beta activity is essential for accurate EEG interpretation and artifact identification. Recognizing the subtle differences in frequency, waveform, duration, and spatial distribution can help differentiate between genuine brain activity and artifact-induced signals in EEG recordings.

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