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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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Distinguishing Features of Beta Activity

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Dr. Rishabh Pathak

The distinguishing features of beta activity in EEG recordings help differentiate it from other brain wave patterns and provide valuable insights into the individual's cognitive state and brain function.

Frequency Range:

o Beta activity is typically defined as brain waves in the beta frequency range, which commonly ranges from 13 to 30 Hz in EEG recordings.

o While beta activity can extend beyond this range, it often exhibits frequencies within the narrower range of 20 to 30 Hz, particularly in the frontal and central regions of the brain.

2.     State Dependency:

oBeta activity is state-dependent and is commonly associated with specific states of consciousness, such as drowsiness and sleep onset.

o It may continue through stage 2 of non-rapid eye movement (NREM) sleep and is observed as bursts with distinct characteristics during these states.

3.     Amplitude and Symmetry:

o Normal beta activity is characterized by symmetric amplitude, with an amplitude asymmetry greater than 35% considered abnormal.

o The amplitude of beta activity may vary but is typically within a certain range, reaching a maximum of about 60 μV in specific contexts.

4.    Distribution and Localization:

o Beta activity is often distributed across the frontal and central regions of the brain, with a more prominent presence in these areas compared to other regions.

o Studies have depicted an anatomic correlate for frontal-central beta activity, suggesting a greater role in motor processing and cognitive functions in these regions.

5.     Temporal Characteristics:

oBeta activity may exhibit specific temporal characteristics, such as shorter duration and less regular patterns compared to other brain wave activities.

o The temporal features of beta activity, along with its relationship to background EEG frequencies, contribute to its distinct identification in EEG recordings.

Understanding these distinguishing features of beta activity in EEG recordings is essential for accurate interpretation, clinical assessment, and monitoring of brain wave patterns in various states of consciousness and cognitive processing.

 

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