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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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From jean cruveilhier and robert Carswell To jean martin charcot: the initial description Of multiple sclerosis

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Dr. Rishabh Pathak

The initial description of multiple sclerosis (MS) can be traced back to several key figures in the history of medicine, including Jean Cruveilhier, Robert Carswell, and Jean Martin Charcot. Here is a brief overview of their contributions to the understanding of MS:


1.Jean Cruveilhier (1791-1874): A French anatomist and pathologist, Cruveilhier is known for his detailed anatomical studies of the nervous system. In 1835, he provided one of the earliest pathological descriptions of what is now recognized as multiple sclerosis. Cruveilhier observed and documented the characteristic plaques and lesions in the brains and spinal cords of individuals with MS, laying the foundation for future research on the disease.


2.Robert Carswell (1793-1857): A Scottish pathologist, Carswell independently described the pathological features of multiple sclerosis around the same time as Cruveilhier. In his work, Carswell identified the presence of demyelination and inflammation in the brains and spinal cords of MS patients, further contributing to the early understanding of the disease.


3. Jean Martin Charcot (1825-1893): A prominent French neurologist, Charcot is often referred to as the "father of neurology." Charcot made significant contributions to the clinical characterization and diagnosis of multiple sclerosis. He distinguished MS as a distinct neurological disorder and described its clinical manifestations, including the triad of symptoms known as Charcot's triad (nystagmus, intention tremor, and scanning speech). Charcot's work helped establish MS as a recognized disease entity and laid the groundwork for future research and treatment developments.


The collective efforts of Cruveilhier, Carswell, and Charcot in the 19th century were instrumental in shaping our early understanding of multiple sclerosis. Their observations and descriptions of the pathological and clinical features of MS paved the way for further research into the etiology, pathogenesis, and management of this complex neurological condition.

 

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