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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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Cooccurring patterns of Ictal Epileptiform Patterns

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Dr. Rishabh Pathak


Co-occurring patterns of ictal epileptiform patterns can provide important insights into the nature of seizures and their electrographic characteristics.

1.      Generalized-Onset Motor Seizures:

o  Ictal patterns during generalized-onset motor seizures often include various artifacts, particularly muscle and movement artifacts. These artifacts can complicate the interpretation of the EEG.

2.     Interictal Epileptiform Discharges (IEDs):

o  Generalized interictal epileptiform discharges (IEDs) are commonly present at other times in the EEG. Their presence can help differentiate between ictal and non-ictal activity, as they may appear alongside ictal patterns.

3.     Postictal Changes:

o    After an ictal event, postictal slowing or attenuation may occur. These features can sometimes help differentiate an ictal pattern from artifacts, although they are not entirely reliable as distinguishing features.

4.    Absence Seizures:

o  In the context of absence seizures, there are typically no changes to the background activity following the seizure. This lack of postictal change is a distinguishing feature when considering co-occurring patterns.

5.     Focal and Generalized Patterns:

o Co-occurring patterns may include both focal and generalized features. For instance, focal-onset seizures may have distinct patterns that do not resemble generalized patterns, while generalized-onset seizures may show greater similarity between their ictal and interictal EEG patterns.

6.    Behavioral Changes:

o  Ictal patterns are almost always accompanied by behavioral changes when they last more than a few seconds. This behavioral change is a critical aspect of identifying seizures and understanding their clinical significance.

7.     Artifacts:

o  The presence of artifacts, such as those from muscle activity, can complicate the interpretation of ictal patterns. Differentiating between true ictal activity and artifacts is essential for accurate diagnosis.

In summary, co-occurring patterns with ictal epileptiform patterns can include various artifacts, interictal discharges, postictal changes, and different seizure types. Understanding these co-occurring patterns is crucial for accurate EEG interpretation and for distinguishing between ictal and non-ictal activity.

 

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