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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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The formation of Neural tube: The first brain Structure

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Dr. Rishabh Pathak

The formation of the neural tube represents a significant milestone in early brain development, serving as the foundation for the central nervous system. Here are key points regarding the formation of the neural tube:


1.     Neural Tube Development:

o    The neural tube is the precursor to the brain and spinal cord, forming during the third week of gestation in humans.

o    Neural progenitor cells, located along the rostral-caudal midline of the embryo within the neural plate, play a crucial role in the formation of the neural tube.

o    Initially, two ridges form along the sides of the neural plate, with neural progenitor cells positioned between them.

o    Over several days, these ridges rise, fold inward, and fuse to create a hollow tube structure that will give rise to the central nervous system.

2.     Structural Significance:

o    The neural tube represents the first well-defined brain structure in embryonic development, laying the groundwork for the organization of the central nervous system.

o    As the neural tube forms, it establishes the basic structural framework for the brain and spinal cord, setting the stage for further differentiation and maturation of neural cell types.

o    The closure of the neural tube is a critical event in early brain development, ensuring the proper formation of the central nervous system and the subsequent development of neural circuits.

3.     Role in Brain Maturation:

o    The formation of the neural tube marks a crucial step in early brain development, initiating the process of central nervous system formation and organization.

o    Neural progenitor cells within the neural tube give rise to the diverse cell types that populate the brain and spinal cord, contributing to the complexity and functionality of the developing nervous system.

o    Genetic patterning and molecular signaling pathways regulate the development and closure of the neural tube, highlighting the intricate interplay of genetic and environmental factors in brain maturation.

In summary, the formation of the neural tube serves as the initial brain structure in embryonic development, playing a pivotal role in establishing the central nervous system's structural foundation and paving the way for subsequent stages of brain maturation and neural circuit formation.

 

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