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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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Mitotic Activity Level

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Dr. Rishabh Pathak

At the mitotic activity level, plasticity in the brain involves processes related to cell division, neurogenesis, and the generation of new neurons from neural stem cells. Here is an overview of mitotic activity in the context of brain plasticity:


1.     Neurogenesis:

§  Neurogenesis refers to the process of generating new neurons from neural stem cells or progenitor cells in specific regions of the adult brain, such as the hippocampus and olfactory bulb.

§  Mitotic activity plays a crucial role in neurogenesis by supporting the proliferation, differentiation, and migration of neural precursor cells to integrate into existing neural circuits and contribute to brain plasticity.

2.     Stem Cell Dynamics:

§  Neural stem cells located in specialized niches within the brain, such as the subventricular zone and the dentate gyrus of the hippocampus, exhibit mitotic activity to self-renew and generate neural progenitor cells that can differentiate into neurons or glial cells.

§  The regulation of stem cell proliferation, quiescence, and activation influences neurogenesis, synaptic integration, and functional recovery following brain injury or environmental stimuli.

3.     Cellular Turnover:

§  Mitotic activity at the cellular level contributes to the turnover of neural cells, including the generation of new neurons, the replacement of damaged or dying cells, and the maintenance of neural circuitry in response to physiological demands or pathological conditions.

§  The balance between cell proliferation, differentiation, and cell death influences the structural and functional plasticity of the brain, shaping neural connectivity and information processing.

4.     Adult Neurogenesis:

§  In the adult brain, mitotic activity supports ongoing neurogenesis in specific regions, such as the hippocampal dentate gyrus, where new neurons are continuously generated and integrated into existing circuits to support learning, memory, and cognitive functions.

§  Adult neurogenesis is modulated by various factors, including environmental enrichment, physical exercise, stress, and neurotrophic factors, highlighting the dynamic nature of mitotic activity in response to external stimuli.

5.     Functional Implications:

§  Mitotic activity and neurogenesis contribute to brain plasticity by adding new neurons, diversifying neural populations, and enhancing neural circuit complexity, which may underlie cognitive flexibility, memory formation, and adaptive behaviors.

§  Understanding the regulation of mitotic activity and neurogenesis provides insights into the mechanisms of neural repair, regeneration, and functional recovery in the context of brain development, aging, and neurological disorders.

By studying mitotic activity in the brain, researchers can elucidate the cellular mechanisms underlying neurogenesis, neural regeneration, and the dynamic changes in neural populations that support brain plasticity, cognitive functions, and adaptive responses to environmental stimuli.

 

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