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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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Seizures

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Dr. Rishabh Pathak

Seizures are episodes of abnormal electrical activity in the brain that can lead to a wide range of symptoms, from subtle changes in awareness to convulsions and loss of consciousness. Understanding seizures and their manifestations is crucial for accurate diagnosis and management. Here is a detailed overview of seizures:

1.      Definition:

oA seizure is a transient occurrence of signs and/or symptoms due to abnormal, excessive, or synchronous neuronal activity in the brain.

oSeizures can present in various forms, including focal (partial) seizures that originate in a specific area of the brain and generalized seizures that involve both hemispheres of the brain simultaneously.

2.     Classification:

oSeizures are classified into different types based on their clinical presentation and EEG findings. Common seizure types include focal seizures, generalized seizures, and seizures of unknown onset.

oThe classification of seizures is essential for determining the underlying cause, selecting appropriate treatment, and predicting prognosis.

3.     EEG Correlates:

oEEG plays a crucial role in the diagnosis and management of seizures. It can provide valuable information about the type of seizure, localization of epileptic foci, and response to treatment.

oInterictal epileptiform discharges (IEDs) on EEG may indicate a predisposition to seizures, while ictal discharges recorded during a seizure can help confirm the diagnosis of epilepsy.

4.    Localization and Localization:

oFocal seizures originate in a specific area of the brain and may present with localized symptoms, such as motor movements or sensory disturbances. EEG findings can help localize the seizure onset zone.

oGeneralized seizures involve both hemispheres of the brain and typically present with bilateral motor manifestations. EEG patterns associated with generalized seizures are more stereotyped compared to focal seizures.

5.     Monitoring and Diagnosis:

oEEG monitoring is essential for capturing seizure activity, especially in cases of non-convulsive seizures or states of altered awareness. Continuous EEG monitoring in the intensive care unit or emergency department can provide valuable information for diagnosis and treatment.

oThe transition from interictal to ictal activity on EEG represents a continuum, and recognizing this transition is important for identifying seizure onset and evolution.

In summary, seizures are episodic manifestations of abnormal brain activity that can vary in presentation and severity. EEG plays a critical role in diagnosing seizures, localizing epileptic foci, and monitoring seizure activity to guide treatment decisions. Understanding the different types of seizures and their EEG correlates is essential for providing optimal care to patients with epilepsy and seizure disorders.

 

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