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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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Mechanisms of Brain Development

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Dr. Rishabh Pathak

Brain development is a complex and highly orchestrated process involving a series of intricate mechanisms that shape the structure and function of the brain. Here are some key mechanisms of brain development:


1.     Neurogenesis: Neurogenesis is the process by which neurons are generated from neural stem cells. It occurs predominantly during embryonic development but continues in certain brain regions throughout life. Neurogenesis is essential for the formation of the brain's neuronal circuitry.


2. Cell Migration: Once neurons are generated, they must migrate to their appropriate locations within the brain to form functional circuits. Cell migration is crucial for establishing the correct connectivity and organization of the brain.


3.  Axon Guidance: Axon guidance is the process by which developing axons navigate to their target regions and establish connections with other neurons. Guidance cues, such as growth factors and cell adhesion molecules, play a critical role in directing axon growth and pathfinding.


4.  Synaptogenesis: Synaptogenesis is the formation of synapses, the connections between neurons that allow for communication in the brain. Synaptic connections are essential for neural signaling and the establishment of functional circuits.


5. Apoptosis: Apoptosis, or programmed cell death, is a natural process that eliminates excess neurons and synapses during brain development. Apoptosis helps sculpt the developing brain by removing unnecessary or improperly connected cells.


6.  Myelination: Myelination is the process by which axons are insulated with myelin, a fatty substance that enhances the speed and efficiency of neural signaling. Myelination occurs throughout development and is essential for proper brain function.


7.     Experience-Dependent Plasticity: Experience-dependent plasticity refers to the brain's ability to reorganize and adapt in response to sensory experiences and environmental stimuli. This mechanism plays a crucial role in shaping neural circuits and optimizing brain function.


8. Critical Periods: Critical periods are specific windows of time during development when the brain is particularly sensitive to certain types of stimuli. During these periods, neural circuits are more malleable and can be shaped by sensory experiences.


9.  Hormonal Influence: Hormones play a significant role in brain development, influencing processes such as cell proliferation, differentiation, and synaptic connectivity. Hormonal signals help coordinate various aspects of brain development.


10. Genetic Regulation: Genetic factors play a fundamental role in brain development, influencing the formation of neural structures, cell types, and connectivity patterns. Genetic regulation guides the intricate processes of brain development from the molecular level up to the macroscopic organization of the brain.


Understanding these mechanisms of brain development is essential for unraveling the complexities of how the brain forms and functions. Researchers continue to investigate these processes to gain insights into neurodevelopmental disorders, brain plasticity, and the fundamental principles underlying brain structure and function.

 

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