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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 Paroxysmal Fast Activity

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Dr. Rishabh Pathak

Muscle artifacts and paroxysmal fast activity (PFA) in EEG recordings can share some similarities in terms of their abrupt onset and high amplitude fast activity. 

1.     Frequency Components:

o    Muscle Artifacts: Muscle artifacts typically contain a range of frequencies due to the diverse motor unit potentials involved in muscle contractions. This can result in a more disorganized appearance of the artifact.

o    Paroxysmal Fast Activity (PFA): PFA, on the other hand, may exhibit fast activity with high amplitudes but tends to have a more focused frequency range compared to muscle artifacts. PFA may show more coherence in its frequency components.

2.   Organization of Activity:

o Muscle Artifacts: Muscle artifacts, characterized by the superimposition of individual motor unit potentials, can appear disorganized on EEG recordings. The inconsistent contraction of muscle motor units contributes to the irregular appearance of muscle artifacts.

o  Paroxysmal Fast Activity (PFA): PFA, despite its fast and high-amplitude nature, may exhibit a more organized pattern of activity compared to muscle artifacts. The rapid and synchronized neuronal firing underlying PFA can give it a distinct appearance on EEG.

3.   Duration:

o Muscle Artifacts: Muscle artifacts can vary in duration based on the duration of the underlying muscle activity. They may range from brief bursts to persist throughout an EEG recording.

o  Paroxysmal Fast Activity (PFA): PFA typically presents as transient bursts of fast activity on EEG, often with a sudden onset and offset. The duration of PFA events is usually shorter compared to prolonged muscle artifacts.

4.   Amplitude:

o Muscle Artifacts: Muscle artifacts can have variable amplitudes depending on the intensity of muscle contractions and the proximity of the electrodes to the muscle source. Higher muscle activity may result in larger artifact amplitudes.

o Paroxysmal Fast Activity (PFA): PFA events often exhibit high amplitudes, similar to muscle artifacts. However, the amplitude characteristics of PFA may show more consistency and coherence compared to the variable amplitudes of muscle artifacts.

5.    Response to Stimulation:

o Muscle Artifacts: Muscle artifacts are typically associated with specific muscle movements or contractions and may not be modulated by external stimuli.

o Paroxysmal Fast Activity (PFA): PFA events may be triggered or influenced by various factors, including sensory stimuli, epileptic discharges, or other pathological processes. The responsiveness of PFA to stimulation can help differentiate it from muscle artifacts.

Recognizing these differences between muscle artifacts and PFA is crucial for accurate EEG interpretation and the identification of abnormal brain activity. Understanding the distinct characteristics of each type of activity can aid in distinguishing between artifact-induced signals and potentially pathological EEG patterns.

 

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