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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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Wicket Rhythms

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Dr. Rishabh Pathak

Wicket rhythms are a specific EEG pattern that can be observed in EEG recordings. 


1.     Description:

o The wicket rhythm is characterized by a 6 to 11 Hz repetition of monophasic waves with alternating sharply contoured and rounded phases, giving it an arciform appearance similar to the Mu rhythm.

o    The polarity of the wicket rhythm consists of negative sharp components followed by positive rounded components.

o    The frequency of the wicket rhythm typically falls within the alpha frequency range, and its amplitude is in the medium range of other alpha frequency activities.

2.   Location and Distribution:

o Wicket rhythms are maximal over the anterior or mid-temporal regions of the brain.

o They occur unilaterally with a shifting asymmetry, often making them bilaterally symmetric overall.

o  In some cases, a minor asymmetry favoring the left temporal lobe may be observed.

3.   Phase Reversals:

o Phase reversals of the negative sharp component may be present within the wicket rhythm or its fragments.

o These phase reversals can occur at specific electrode locations such as F7, F8, T3, and T4.

4.   Appearance in EEG Recordings:

o Wicket rhythms can be visually identified in EEG recordings by their distinct waveform and frequency characteristics.

o They may appear as regular, phase-reversing rhythms within the background EEG activity.

5.    Co-occurrence:

o Wicket rhythms may co-occur with Mu rhythms and other EEG patterns in certain states of wakefulness.

o They are one of the EEG patterns that can be observed alongside Mu rhythms and other activities in EEG recordings.

Understanding the characteristics and features of wicket rhythms is essential for accurate interpretation of EEG recordings. Recognizing wicket rhythms, along with their distinct waveform and distribution, can provide valuable insights into the neural activity patterns present in the brain and aid in the differential diagnosis of EEG findings in clinical practice.

 

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