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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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What role do physical forces play in translating cellular mechanisms into the intricate structure of the human brain?

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Dr. Rishabh Pathak

Physical forces play a crucial role in translating cellular mechanisms into the intricate structure of the human brain. Here is an explanation of how physical forces influence brain development:


1.     Regulation of Pattern Selection: Physical forces, such as mechanical stress and tension, regulate pattern selection during brain development. These forces influence the growth and organization of neuronal structures, guiding the formation of neural circuits and brain regions. By exerting mechanical forces on developing neurons, the brain can achieve specific patterns of connectivity and organization.


2.     Surface Morphogenesis: Physical forces contribute to surface morphogenesis, including the folding of the cerebral cortex. The mechanical interactions between neurons, glial cells, and the extracellular matrix play a role in shaping the convolutions and gyri of the brain. Differential growth and tension within the brain tissue lead to the characteristic folds and wrinkles observed in the human cortex.


3.     Cellular Migration and Connectivity: Physical forces generated during cellular migration and connectivity impact the wiring of the brain. Neuronal migration is guided by mechanical cues, such as substrate stiffness and topographical features, which influence the positioning of neurons within the developing brain. Additionally, forces generated during synaptogenesis and synaptic pruning shape the formation and elimination of neuronal connections, sculpting the neural network.


4.     Pathological Conditions: Disruptions in physical forces can lead to abnormal brain development and neurological disorders. Conditions such as lissencephaly, polymicrogyria, microcephaly, and megalencephaly are associated with alterations in mechanical forces during neurodevelopment. Computational models of differential growth can simulate these pathologies, highlighting the impact of physical forces on brain structure.


In summary, physical forces act as regulators in translating cellular mechanisms into the complex structure of the human brain. By understanding the role of mechanical forces in brain development, researchers can gain insights into normal brain function, pathological conditions, and potential therapeutic interventions.

 

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