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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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Astrocytes guides the migration of developing axon and neurons

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Dr. Rishabh Pathak

Astrocytes, a type of glial cell in the central nervous system, play a crucial role in guiding the migration of developing axons and neurons during brain development. Here is an explanation of how astrocytes contribute to the intricate process of neuronal migration:


1. Structural Support: Astrocytes provide structural support and guidance for developing neurons and axons as they navigate through the developing brain. Astrocytes have specialized processes that extend and interact with neuronal growth cones, the dynamic structures at the tips of growing axons that lead the way during neuronal migration.


2.   Chemical Signaling: Astrocytes release signaling molecules and guidance cues that influence the direction and pathfinding of migrating neurons and axons. These chemical signals help steer developing neurons towards their target destinations and establish appropriate connections within the developing neural circuitry. Astrocyte-derived factors play a key role in regulating neuronal migration and axonal guidance.


3.     Physical Contact: Astrocytes establish physical contacts with developing axons and neurons, creating a supportive environment for neuronal migration. The interactions between astrocytes and migrating neurons facilitate the movement of neurons along specific pathways and help coordinate the intricate process of neuronal migration within the developing brain.


4.     Synaptic Transmission: In addition to guiding neuronal migration, astrocytes are involved in synaptic transmission and information processing within neural circuits. Astrocytes play a role in regulating synaptic activity, neurotransmitter release, and synaptic plasticity, contributing to the functional connectivity of the developing brain.


5.   Blood-Brain Barrier Formation: Astrocytes are also involved in the formation and maintenance of the blood-brain barrier, a protective barrier that regulates the passage of substances between the bloodstream and the brain. The interactions between astrocytes and blood vessels contribute to the structural integrity of the blood-brain barrier and help create a specialized microenvironment for neuronal migration and circuit formation.


In summary, astrocytes play a multifaceted role in guiding the migration of developing axons and neurons during brain development. Through their structural support, chemical signaling, physical interactions, and involvement in synaptic transmission, astrocytes contribute to the intricate process of neuronal migration and circuit formation in the developing brain. Understanding the mechanisms by which astrocytes guide neuronal migration is essential for unraveling the complexities of brain development and the establishment of functional neural circuits that underlie cognitive and behavioral functions.

 

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