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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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Brain Development in the embryonic and early fetal periods

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Dr. Rishabh Pathak

During the embryonic and early fetal periods, significant developmental processes shape the formation of the human brain. Here are some key points regarding brain development during these stages:


1.     Embryonic Period:

o    The embryonic period extends through the eighth week post-conception (gestational week eight, or GW8) in humans.

o    By the end of the embryonic period, rudimentary structures of the brain and central nervous system are established, defining major compartments of the central and peripheral nervous systems.

o    Interactions between genetic signaling and environmental factors are crucial during this period, influencing the development of the embryonic brain.

o    Genetic patterning and neurogenesis play essential roles in guiding the initial stages of brain development, setting the foundation for subsequent growth and maturation.

2.     Early Fetal Period:

o    The early fetal period, extending to approximately midgestation, is critical for neocortical development.

o    Most cortical neurons are generated during this period, migrating to their positions in the neocortex and forming essential brain networks for information processing.

o    Rapid growth and elaboration of both cortical and subcortical structures occur during the fetal period, including the development of major fiber pathways.

o    Experience-dependent processes during the early postnatal period shape connectivity and neural competition, influencing the organization and function of the developing brain.

In summary, the embryonic and early fetal periods are foundational stages in brain development, marked by the establishment of basic brain structures, genetic influences, neurogenesis, and the beginning of essential brain networks. These early stages set the stage for further maturation and refinement of the intricate neural architecture that underlies human brain function.

 

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