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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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Can the triphasic pattern occur in individuals with normal cognitive function?

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Dr. Rishabh Pathak

The triphasic pattern is generally associated with significant cognitive impairment, such as that seen in encephalopathy, dementia, stupor, or coma. However, it is quite rare for this pattern to occur in individuals with normal cognitive function. 

1.    Clinical Context: The triphasic pattern is most commonly observed in patients with altered mental status due to various metabolic disturbances, particularly hepatic encephalopathy. Its presence typically indicates a significant impairment in cognitive function, making it unusual for it to appear in individuals who are cognitively intact.

2.     Exceptions: While the triphasic pattern is primarily linked to cognitive impairment, there are rare instances where it may be observed in patients who are otherwise alert and functioning normally. These cases are atypical and not well understood, suggesting that the triphasic pattern may not always correlate directly with cognitive status.

3.     Underlying Mechanisms: The triphasic pattern is thought to arise from specific neurophysiological changes associated with metabolic disturbances. In the absence of such disturbances, the likelihood of observing this pattern in a cognitively normal individual is low.

In summary, while the triphasic pattern is predominantly associated with significant cognitive impairment, there may be rare exceptions where it could appear in individuals with normal cognitive function. However, these instances are not common and typically warrant further investigation to understand the underlying causes.

 

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