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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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Early development is characterized through early proliferation

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Dr. Rishabh Pathak

Early development is characterized by early proliferation, a crucial phase in neurodevelopment that lays the foundation for the formation of the complex structure of the human brain. Here is an explanation of how early proliferation contributes to brain development:


1. Interkinetic Nuclear Migration: Early proliferation is marked by interkinetic nuclear migration, an oscillatory process observed in neuroepithelial cells. During this process, neuroepithelial cells divide symmetrically at the margin of the ventricle and undergo four phases. The cell nuclei position themselves at basal locations, move towards the apical ventricular surface, divide symmetrically into two new progenitor cells at the apical surface, and then return to their basal position. This dynamic process exponentially increases the number of progenitor cells, leading to the expansion of the ventricular zone.


2. Increased Surface Area and Thickness: The early proliferation of neuroepithelial cells results in both an increased surface area and thickness of the ventricular zone. The rapid division and expansion of progenitor cells contribute to the growth and development of the neural tube, which eventually gives rise to the brain structures. This phase sets the stage for subsequent neurogenesis and neuronal migration processes that shape the intricate architecture of the developing brain.


3.     Transition to Asymmetric Cell Division: Around gestational week 5, progenitor cells in the ventricular zone, particularly radial glial cells, begin to switch from symmetric to asymmetric cell division. Asymmetric cell divisions produce differentiating neurons and progenitor cells, leading to the generation of a diverse array of neuronal types in the developing brain. This transition marks the onset of neurogenesis, a critical phase in brain development where neurons are generated from neural stem cells.


4. Regulation of Proliferative Zones: Early proliferation plays a key role in regulating the proliferative zones of the developing brain. The balance between symmetric and asymmetric cell divisions, as well as the proliferation and differentiation of neural stem cells, influences the generation and organization of neurons in specific brain regions. Disruptions in early proliferation can lead to abnormalities in brain structure and function, contributing to neurodevelopmental disorders.


In summary, early proliferation is a fundamental process in early brain development characterized by the rapid division and expansion of neuroepithelial cells. This phase sets the stage for subsequent neurogenesis, neuronal migration, and the establishment of the intricate neuronal circuitry that underlies brain function. Understanding the mechanisms and regulation of early proliferation is essential for unraveling the complexities of brain development and addressing developmental disorders that arise from disruptions in this critical phase.

 

 

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