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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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Types of Ocular Artifacts

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Dr. Rishabh Pathak

Ocular artifacts in EEG recordings can manifest in various forms, each associated with specific eye movements or activities.

Blink Artifact:

o Description: Produced by rapid eye movements associated with blinking.

o    Characteristics: Appears as a bifrontal, diphasic, synchronous slow wave limited to the frontal region. The waveform is related to the rate and duration of eye movement.

o  Identification: The artifact decreases in amplitude with distance from the orbits and does not extend into the central region.

2.     Eye Flutter Artifact:

o    Description: Result of rapid eyelid flutter.

o  Characteristics: Typically seen in the alpha frequency range and limited to the anterior frontal region. May not always be time-locked to stimulation.

o    Differentiation: Waveform differences help distinguish it from 3 Hz epileptiform activity.

3.     Lateral Gaze Artifact:

o    Description: Occurs during lateral eye movements.

o  Characteristics: Includes positive and negative phase reversals at specific electrodes corresponding to the direction of gaze. Has a field that is maximum across the temples and frontal poles.

o Identification: Most apparent during drowsiness and produces rhythmic, slow artifact with a frequency less than 1 Hz.

4.    Rapid Eye Movements (REMs) of REM Sleep:

o    Description: Associated with lateral gaze movements during REM sleep.

o Characteristics: Waveform differs from lateral gaze during wakefulness, showing asymmetrically quicker rise than fall. Location is similar to other artifacts from lateral gaze.

o Differentiation: Specific movement features distinguish REM artifact from other ocular artifacts.

5.     Electroretinogram Artifact:

o  Description: Produced by photic stimulation and time-locked to the strobe.

o  Characteristics: Monomorphic waveform limited to specific frontal electrodes. Distinguished from photomyogenic artifact by waveform and field characteristics.

o  Identification: Covering an eye during stimulation can help diminish the artifact from the ipsilateral frontal polar electrode.

These types of ocular artifacts demonstrate the diverse ways in which eye movements and activities can influence EEG recordings. Understanding their characteristics and distinguishing features is crucial for accurate interpretation and differentiation from other EEG patterns.

 

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