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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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Gestational Week 5 Marks the onset of Neurogenesis

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Dr. Rishabh Pathak

Gestational week 5 marks a crucial milestone in brain development as it signifies the onset of neurogenesis, the process by which neurons are generated from neural stem cells. Here is an explanation of the significance of gestational week 5 in the context of neurogenesis:


1. Neurogenesis Initiation: Around gestational week 5, progenitor cells in the ventricular zone of the developing brain, particularly radial glial cells, begin to transition from symmetric to asymmetric cell division. This transition marks the initiation of neurogenesis, a fundamental process in brain development where neural stem cells give rise to neurons that will populate the various regions of the brain.


2. Formation of Neocortex: The neocortex, the outer layer of the cerebral hemispheres responsible for higher cognitive functions, begins to form during this period. Neurogenesis in the neocortex is a highly regulated process that involves the generation of different neuronal subtypes and the establishment of the layered structure of the cortex. The neocortex plays a critical role in sensory processing, motor control, and cognitive functions in the mature brain.


3. Proliferation and Differentiation: During neurogenesis, neural stem cells undergo divisions that give rise to both neurons and progenitor cells. Asymmetric cell divisions produce neurons that will populate the cortical layers, while symmetric divisions generate more progenitor cells to sustain the pool of neural stem cells. This balance between proliferation and differentiation is essential for generating the diverse array of neuronal types required for proper brain function.


4.     Establishment of Neural Circuitry: The neurons generated during neurogenesis will migrate to their appropriate locations within the developing brain and establish connections with other neurons to form neural circuits. This process of neuronal migration and circuit formation is crucial for the functional organization of the brain and the development of complex behaviors and cognitive abilities.


5.     Critical Period for Brain Development: Gestational week 5 represents a critical period in brain development when the foundation for the intricate structure and connectivity of the brain is laid down. Disruptions or abnormalities during this period can have long-lasting effects on brain function and may contribute to neurodevelopmental disorders. Understanding the molecular and cellular mechanisms underlying neurogenesis is essential for elucidating brain development and addressing developmental disorders that arise from perturbations in this process.


In summary, gestational week 5 marks the onset of neurogenesis, a pivotal stage in brain development where neural stem cells begin to generate neurons that will populate the developing brain. This period sets the stage for the formation of the complex neuronal circuitry that underlies brain function and behavior. Understanding the events that unfold during neurogenesis is essential for unraveling the mysteries of brain development and addressing the challenges associated with neurodevelopmental disorders.

 

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