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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 Photic Stimulation Responses

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Dr. Rishabh Pathak

Photic Stimulation Responses (PSR) can be categorized into several types based on their characteristics and clinical significance. 

1.      Photic Driving Response:

§  This is a normal response characterized by a series of sharply contoured, positive, monophasic transients that occur at the frequency of the light stimulation. For example, a 10 Hz stimulation may elicit a 10 Hz driving response in the EEG. The response typically reflects the brain's ability to synchronize with the external visual stimulus.

2.     Photoparoxysmal Response:

§  This response is associated with epilepsy and is characterized by the occurrence of epileptiform discharges during photic stimulation. Photoparoxysmal responses often manifest as spikes or spike-and-wave complexes that do not occur at the same frequency as the stimulation. They may continue after the cessation of stimulation and are more likely to occur in individuals with a predisposition to seizures.

3.     Photic Myogenic Response:

§  This type of response is related to muscle activity and can occur during photic stimulation. It may present as movement artifacts in the EEG, particularly if the patient exhibits myoclonus or other involuntary movements in response to the light.

4.    Abnormal Photic Driving Response:

§  An abnormal photic driving response may occur when the response is diminished or absent, particularly in patients with certain neurological conditions. For instance, a photic driving response at a stimulation frequency less than 3 Hz may indicate underlying pathology, such as degenerative encephalopathies.

5.     Asymmetric Photic Response:

§  Asymmetry in the photic driving response can occur and may not necessarily indicate pathology. However, if the asymmetry is significant and not consistent with other EEG features, it may suggest an underlying abnormality, such as a structural lesion in the brain.

6.    Photic Responses in Different Frequencies:

§  The frequency of photic stimulation can influence the type of response observed. For example, stimulation at frequencies greater than 20 Hz has been associated with migraine, while lower frequencies may be linked to other neurological conditions.

Summary

Photic Stimulation Responses encompass a range of patterns that can provide valuable diagnostic information in clinical settings. The main types include the normal photic driving response, the photoparoxysmal response associated with epilepsy, and various abnormal responses that may indicate underlying neurological issues. Understanding these types is crucial for interpreting EEG results accurately and guiding further clinical management.

 

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