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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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What is Neuron Migration?

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Dr. Rishabh Pathak

Neuron migration is a fundamental process in brain development where neurons move from their site of origin to their final destination within the developing brain. This process is essential for establishing the intricate neural circuits and structures that underlie brain function. Neuron migration ensures that neurons reach their appropriate locations and establish connections with other neurons to form functional networks.


There are several mechanisms involved in neuron migration, including somal translocation, radial glial guidance, and tangential migration. In somal translocation, a neuron extends a process that attaches to the outer surface of the brain, allowing the nucleus to move into the brain area. Radial glial cells provide a scaffold for neuron migration along their processes, guiding neurons to their correct positions. Tangential migration involves neurons moving in specific directions from proliferative zones to reach their destinations within the brain.


Proper neuron migration is crucial for the formation of the six-layered neocortical mantle and the establishment of functional neural circuits. Disruptions in neuron migration can lead to structural abnormalities in the brain and contribute to neurodevelopmental disorders. Understanding the mechanisms and regulation of neuron migration is essential for unraveling the complexities of brain development and addressing related neurological conditions.

 

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