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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 Vertex Sharp Transients

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Dr. Rishabh Pathak

Vertex Sharp Transients (VSTs) can be categorized based on their morphology, frequency, and clinical context. Here are the main types and characteristics of VSTs:

1.      Monophasic VSTs: These are characterized by a single sharp wave without the typical triphasic or diphasic morphology. They may appear as isolated sharp waves and are less common than other forms.

2.     Diphasic VSTs: This type features two distinct phases, typically consisting of a sharp negative wave followed by a positive wave. Diphasic VSTs can be seen in various contexts, including normal sleep.

3.     Triphasic VSTs: The most recognized form of VSTs, triphasic VSTs consist of three phases: two small positive waves that precede and follow a larger negative sharp wave. This morphology is often associated with normal sleep patterns and is the most commonly referenced type in clinical settings.

4.    VST Bursts: These occur as a train of successive VSTs that can last several seconds. They may be distinguished from isolated VSTs by their repetitive nature and can be indicative of specific sleep stages or responses to stimuli.

5.     VSTs with Background Activity: Sometimes, VSTs may occur against a background of other EEG activities, such as alpha or beta waves. This can complicate their interpretation and may indicate underlying neurological conditions if observed in awake individuals.

6.    VSTs in Pathological Contexts: While VSTs are typically benign, their presence in certain pathological contexts (e.g., during wakefulness or in conjunction with other abnormal EEG patterns) may suggest underlying neurological issues, such as seizures or encephalopathy.

In summary, Vertex Sharp Transients can be classified into various types based on their morphology and clinical context. The most common and clinically significant type is the triphasic VST, which is typically associated with normal sleep patterns. However, variations exist, and their interpretation should consider the overall clinical picture.

 

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