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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 Photo paroxysmal Responses.

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Dr. Rishabh Pathak

Muscle artifacts and photoparoxysmal responses in EEG recordings can exhibit differences in waveform, localization, and response to stimulation. 

1.     Waveform:

o    Muscle Artifacts: Muscle artifacts typically have a spike-like or sharp waveform due to the individual motor unit potentials involved in muscle contractions. The waveform of muscle artifacts is often characterized by rapid and abrupt changes in amplitude.

o Photoparoxysmal Responses: Photoparoxysmal responses, on the other hand, may exhibit spike-and-wave complexes or other epileptiform patterns in response to visual stimulation. These responses often have a more stereotyped waveform compared to the variable nature of muscle artifacts.

2.   Localization:

o    Muscle Artifacts: Muscle artifacts are commonly localized near electrodes overlaying muscle groups generating the artifact, such as facial muscles or tongue muscles. The distribution of muscle artifacts reflects the locations of the muscles involved in the artifact.

oPhotoparoxysmal Responses: Photoparoxysmal responses often have fields with a frontal maximum, indicating a characteristic localization pattern in the frontal regions of the brain. This localization differs from the more diffuse distribution of muscle artifacts.

3.   Response to Stimulation:

oMuscle Artifacts: Muscle artifacts are typically not modulated by external stimuli and are primarily related to muscle contractions or movements. They do not exhibit specific responses to sensory or visual stimulation.

oPhotoparoxysmal Responses: Photoparoxysmal responses are triggered by visual stimulation, particularly flickering lights or specific visual patterns. These responses are time-locked to the stimulation and may show a consistent association with the visual trigger.

4.   Persistence:

o Muscle Artifacts: Muscle artifacts are transient and typically occur during muscle activity, with onset and offset corresponding to muscle contractions. They do not persist beyond the period of muscle activity.

oPhotoparoxysmal Responses: Photoparoxysmal responses may continue beyond the period of visual stimulation, indicating an ongoing epileptiform response in the brain. These responses can outlast the duration of the visual trigger.

5.    Frequency of Occurrence:

o    Muscle Artifacts: Muscle artifacts are commonly observed in EEG recordings due to muscle contractions or movements, especially in regions with underlying muscles. They may occur intermittently during muscle activity.

oPhotoparoxysmal Responses: Photoparoxysmal responses are specific EEG patterns triggered by visual stimuli and may occur at specific stimulation frequencies. These responses are more selective in their occurrence compared to the more widespread presence of muscle artifacts.

Understanding these distinctions between muscle artifacts and photoparoxysmal responses is essential for accurate EEG interpretation and the differentiation of physiological muscle activity from abnormal epileptiform responses triggered by external stimuli. Recognizing the waveform characteristics, localization patterns, response to stimulation, and persistence of these phenomena can aid in distinguishing between artifact-induced signals and pathological EEG patterns.

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