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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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Posterior Basic Rhythm

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Dr. Rishabh Pathak

The Posterior Basic Rhythm is a term used in the field of electroencephalography (EEG) to describe a specific type of brainwave activity. 

1.     Definition:

§ The Posterior Basic Rhythm refers to the dominant rhythmic activity typically observed over the posterior head regions in EEG recordings.

§ It is characterized by rhythmic oscillations in the alpha frequency range (8 to 13 Hz) and is associated with a state of relaxed wakefulness with the eyes closed.

2.   Location:

§ The Posterior Basic Rhythm is primarily localized over the occipital and posterior regions of the brain, including the visual cortex.

§It is often most prominent in electrodes placed over the occipital lobes in EEG recordings.

3.   Behavior:

§ The Posterior Basic Rhythm tends to attenuate or disappear in response to various stimuli such as drowsiness, concentration, visual fixation, or cognitive tasks.

§Abrupt changes or blocking of the alpha rhythm due to external stimuli or cognitive activity are common features associated with the Posterior Basic Rhythm.

4.   Variants:

§The Posterior Basic Rhythm may exhibit variations in amplitude, frequency, and reactivity among individuals.

§ Slow alpha and fast alpha variants of the rhythm may also be observed, each with specific characteristics related to the alpha frequency band.

5.    Clinical Significance:

§Monitoring the Posterior Basic Rhythm in EEG recordings can provide valuable information about the individual's state of wakefulness, attention, and cognitive processing.

§Changes in the Posterior Basic Rhythm may indicate shifts in mental states, alertness levels, or responses to external stimuli.

6.   Age-Related Changes:

§The characteristics of the Posterior Basic Rhythm, including its amplitude, frequency, and reactivity, may vary with age.

§ In general, the amplitude and persistence of the alpha rhythm tend to decrease with aging, reflecting changes in brain function and neural activity.

7.    Abnormalities:

§Complete absence of blocking or unilateral blocking of the alpha rhythm is considered abnormal and may indicate underlying neurological conditions.

§Aberrant patterns in the Posterior Basic Rhythm, such as deviations in frequency or reactivity, can be indicative of cerebral dysfunction or pathological processes.

Understanding the Posterior Basic Rhythm in EEG recordings is essential for interpreting brainwave activity, assessing cognitive states, and monitoring changes in neural oscillations. Studying the characteristics and behavior of the Posterior Basic Rhythm contributes to the broader understanding of brain function, neural dynamics, and the relationship between EEG patterns and cognitive processes.

 

 

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