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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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Photic Stimulation Responses in different Neurological Conditions

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Dr. Rishabh Pathak

Photic Stimulation Responses (PSR) can vary in their characteristics and significance across different neurological conditions. 

1.      Epilepsy:

§  In individuals with epilepsy, particularly those with photosensitive epilepsy, PSR may be abnormal. These patients can exhibit heightened responses to photic stimulation, which may lead to photoparoxysmal responses (PPR) characterized by spike and wave discharges. The presence of PSR in this context can indicate a predisposition to seizures triggered by light.

2.     Juvenile Myoclonic Epilepsy (JME):

§  JME is one of the generalized epilepsy syndromes most commonly associated with PSR. Approximately 17% of patients with JME demonstrate photoparoxysmal responses during photic stimulation. The PSR in these patients may be more pronounced, reflecting their sensitivity to light.

3.     Unverricht–Lundborg Disease:

§  This condition, a type of myoclonic epilepsy, is also associated with PSR. Patients may show abnormal photic responses, which can be indicative of their underlying neurological condition.

4.    Progressive Myoclonus Epilepsies:

§  In progressive myoclonus epilepsies, PSR may be altered, and patients can exhibit abnormal responses to photic stimulation. The presence of PSR in these patients can correlate with the severity of their condition and the likelihood of seizure activity.

5.     Degenerative Encephalopathies:

§  Conditions such as neuronal ceroid lipofuscinosis may show abnormal PSR, particularly at stimulation frequencies less than 3 Hz. This abnormality can be associated with significant clinical implications, including cognitive decline and seizures.

6.    Migraine:

§  Some studies have indicated that individuals with migraine may exhibit specific PSR patterns, particularly at higher frequencies (greater than 20 Hz). This association suggests a potential link between photic stimulation and migraine triggers.

7.     Normal Variants in the Elderly:

§  In the elderly population, the absence of PSR can be a common normal variant. This absence does not necessarily indicate pathology but may reflect age-related changes in brain function.

8.    Non-Epileptic Conditions:

§  In non-epileptic conditions, such as certain neurodegenerative diseases, PSR may still be present but can vary in amplitude and symmetry. The clinical significance of these responses in non-epileptic conditions is less clear and often requires further investigation.

Summary

Photic Stimulation Responses can provide valuable insights into various neurological conditions, particularly epilepsy and its syndromes. Abnormal PSR can indicate a predisposition to seizures, while normal PSR may reflect intact brain function. The interpretation of PSR must be contextualized within the broader clinical picture, including the patient's history and other EEG findings.

 

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