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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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Neuronal Division and Migration

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Dr. Rishabh Pathak

Neuronal division and migration are critical processes in neurodevelopment that contribute to the formation of the complex structure of the human brain. Here is an explanation of neuronal division and migration:


1.     Neurogenesis: Neurogenesis is the process by which neurons are generated from neural stem cells. It involves a precisely orchestrated sequence of cellular events that begin with the formation of the neocortex at the rostral end of the neural tube during embryonic development. In humans, the neural tube closes around the fifth week of gestation, marking the initiation of rapid brain enlargement.


2.     Cellular Events: During neurogenesis, neural stem cells divide and differentiate into neurons through asymmetric and symmetric cell divisions. Asymmetric cell divisions produce one stem cell and one progenitor cell or neuron, while symmetric divisions generate two identical daughter cells. These divisions lead to a notable radial and tangential expansion of proliferative zones in the developing brain.


3.     Neuronal Migration: After being generated, neurons undergo migration to their final destinations within the brain. Radial migration is a process where neurons move from the ventricular zone to the outer layers of the cortex along radial glial fibers. This process is crucial for establishing the layered structure of the cerebral cortex. Tangential migration involves the movement of neurons parallel to the brain's surface and contributes to the diversification of neuronal types and the formation of neural circuits.


4.     Subventricular Zone: The subventricular zone plays a key role in coordinating the migration of pyramidal neurons and interneurons during brain development. Neurons pause in the subventricular zone before migrating radially, suggesting a synchronization mechanism for neuronal migration. Early-born cells in the preplate, a transient structure near the basal surface, will either migrate tangentially to become inhibitory interneurons or die during early neurogenesis.


5.     Intracranial Pressure: Intracranial pressure, regulated by the ventricular system and cerebrospinal fluid dynamics, is recognized as an important regulator of normal brain development. Changes in intracranial pressure can impact brain enlargement, tissue organization, and folding patterns during neurodevelopment.

In summary, neuronal division and migration are fundamental processes in neurodevelopment that shape the structure and connectivity of the human brain. Understanding the mechanisms underlying these processes is essential for unraveling the complexities of brain development and the pathogenesis of neurological disorders.
 

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