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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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Distinguishing Features Ictal Epileptiform Patterns

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Dr. Rishabh Pathak

The distinguishing features of ictal epileptiform patterns are critical for differentiating them from other EEG activities and for accurate seizure diagnosis. Here are the key distinguishing features outlined in the document:

1.    Stereotyped Nature: Ictal patterns are often stereotyped across seizures for the individual patient. This means that the same pattern tends to recur in different seizures, which aids in identification.

2.  Evolution of Activity: A hallmark of ictal patterns is their evolution, which can manifest as changes in frequency, amplitude, distribution, and waveform. This evolution is a key feature that helps differentiate ictal patterns from other types of EEG activity, such as normal rhythms or artifacts.

3. Behavioral Changes: Ictal patterns are typically associated with stereotyped behavioral changes. While some seizures may not exhibit obvious movements, the presence of behavioral changes is a significant indicator of seizure activity. In some cases, the lack of recognized behavioral change does not preclude the occurrence of a seizure.

4. Cognitive Impairment: Focal seizures may present without overt behavioral changes but can still lead to cognitive impairment, such as memory and concentration issues. Detailed cognitive testing during and after a seizure may be necessary to identify these dyscognitive focal seizures.

5.  Presence of Focal Interictal Discharges: The ictal patterns for focal-onset seizures do not resemble the patient's focal interictal epileptiform discharges (IEDs). This distinction is important for accurate diagnosis.

6. Visibility on EEG: Ictal patterns are visible on EEG only when a sufficient area of cortex (at least 10 cm² for temporal lobe seizures) is synchronized. This means that some focal seizures may not show an ictal pattern on scalp EEG if the seizure activity is too localized.

7.  Differentiation from Artifacts: Ictal patterns must be distinguished from artifacts, such as muscle activity (EMG). The evolution of the ictal pattern and the presence of postictal changes (like slowing or attenuation) can help differentiate true ictal patterns from artifacts.

8.    Frequency and Amplitude Changes: The electrographic evolution of a focal-onset seizure commonly includes changes in frequency and amplitude, which can be an increase or decrease within any of the normal EEG frequency bands.

These distinguishing features are essential for clinicians to accurately interpret EEG recordings and diagnose seizure types effectively.

 

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