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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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How do genetic patterning and neurogenesis play a role in brain maturation?

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Dr. Rishabh Pathak

Genetic patterning and neurogenesis are fundamental processes that play crucial roles in brain maturation, as outlined in the PDF file on brain development.


1.     Genetic Patterning: Genetic patterning refers to the intricate process by which genes regulate the development of the brain. Genes play a significant role in orchestrating the formation of various brain structures and functions. During the embryonic period, genetic signaling is essential for initiating and guiding the development of the brain. Specific genes are expressed in different populations of cells, generating molecular signals that influence the developmental trajectory of other cell populations. This genetic interplay is vital for establishing the initial framework of the brain's structure and function.


2.     Neurogenesis: Neurogenesis is the process by which new neurons are generated from neural stem cells and progenitor cells. This process is particularly active during prenatal and early postnatal periods, contributing to the expansion of the brain's neuronal population. The document highlights that structural changes in both gray and white matter compartments continue through childhood and adolescence, paralleling changes in functional organization and behavior.


During early brain development, neurogenesis is essential for the formation of neural circuits and the establishment of neuronal connections. The exuberant connectivity observed in the developing brain is a result of neurogenesis, creating a foundation for subsequent pruning and refinement of neural networks based on experience. Additionally, genetic interplay between transcription factors, such as Sp8 and Emx2, influences the patterning of the forebrain, further shaping the developing brain.


In conclusion, genetic patterning and neurogenesis are integral processes in brain maturation. Genetic factors guide the initial development of the brain, while neurogenesis contributes to the generation of neurons and the establishment of neural circuits critical for brain function. These processes work in concert to shape the complex and dynamic maturation of the brain throughout development.

 

Stiles, J. (2008). The fundamentals of brain development: Integrating nature and nurture. Cambridge, MA: Harvard University Press.

 

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