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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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Types of Ictal Epileptiform Patterns

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Dr. Rishabh Pathak

Several types of ictal epileptiform patterns, particularly focusing on focal-onset and generalized-onset seizures.

1.      Focal-Onset Seizures:

o  Characteristics: The ictal pattern for focal-onset seizures is defined by the EEG findings present during the seizure. These patterns are often stereotyped for the individual patient and typically include evolving rhythms or repetitive sharp waves.

o Evolution: The ictal activity usually demonstrates clear evolution, which can include changes in frequency, amplitude, distribution, and waveform. This evolution is crucial for identifying the seizure onset.

o  Duration: Focal-onset seizure patterns generally last several seconds, distinguishing them from other patterns like the fourteen and six positive spikes (14&6), which last less than 2 seconds.

2.     Generalized-Onset Seizures:

o  Characteristics: Ictal patterns for generalized-onset seizures differ from those of focal-onset seizures. They tend to show greater similarity between their ictal and interictal EEG patterns.

o  Variability: The ictal patterns for generalized seizures can vary based on the type of seizure, which is not the case for focal-onset seizures.

3.     Non-Evolving Patterns:

o Description: Infrequently, the ictal pattern may not include evolution and can manifest as desynchronization, regular repetitive spikes, or regular rhythmic slowing. These patterns are more commonly associated with focal motor seizures without cognitive impairment.

4.    Secondary Bilateral Synchrony:

o    Occurrence: While focal-onset seizures typically do not present with bilateral fields at their onset, secondary bilateral synchrony can occur. This is an exception and does not represent the typical pattern for focal-onset seizures.

5.     Behavioral Correlation:

o Stereotyped Behavioral Change: Ictal patterns are usually accompanied by a stereotyped behavioral change, which is a critical feature for identifying seizures. However, some focal seizures may occur without noticeable behavioral changes, making it essential to consider cognitive testing to determine if a seizure has occurred.

These types of ictal patterns are essential for clinicians to recognize and differentiate during EEG interpretation, as they provide vital information for diagnosing and managing epilepsy.

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