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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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Co-occurring waves of Paroxysmal Fast Activity

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Dr. Rishabh Pathak

Co-occurring waves with Paroxysmal Fast Activity (PFA) are important for understanding the context in which PFA occurs and its clinical significance. 

1. Background Activity

    • PFA typically occurs in EEGs that exhibit at least mildly abnormal background activity. More commonly, the background may show moderately abnormal slowing, which can be indicative of underlying neurological conditions.

2. Other Epileptiform Abnormalities

    • PFA often co-occurs with other types of interictal epileptiform discharges (IEDs), such as spikes, sharps, or complexes of either a spike or a sharp followed by an after-going slow wave. These additional abnormalities may appear immediately following PFA.

3. Multifocal Independent Spike Discharges (MISD)

    • The presence of PFA is frequently associated with multifocal independent spike discharges (MISD). This means that the EEG may show multiple localizations of spikes that are independent of each other, which can complicate the interpretation of the EEG and provide insights into the patient's seizure activity.

4. Ictal Context

    • In some cases, PFA may be observed in the context of seizures, particularly generalized-onset seizures. When PFA is associated with seizures, it may be accompanied by very fast activity related to seizure-related muscle artifact, which can further complicate the EEG interpretation.

Summary

In summary, Paroxysmal Fast Activity (PFA) is often seen alongside abnormal background activity and other interictal epileptiform discharges, such as spikes and sharps. The presence of multifocal independent spike discharges (MISD) and the potential for PFA to occur in ictal contexts are also significant. Recognizing these co-occurring waves is essential for accurate EEG interpretation and understanding the clinical implications of PFA in patients with epilepsy or other neurological disorders.

 

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