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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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Sensitive of surface morphology with respect to Growth Ratio

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Dr. Rishabh Pathak

The sensitivity of surface morphology with respect to the growth ratio between the cortex and subcortex is a critical aspect in understanding the mechanisms of cortical folding and brain development. Here are some key points regarding the sensitivity of surface morphology to the growth ratio:


1.     Secondary Folds Formation: The growth ratio between the cortex and subcortex is a key parameter controlling the formation of secondary folds in the cerebral cortex. Variations in the growth ratio can lead to changes in the complexity and distribution of cortical folds, influencing the overall surface morphology of the brain.


2.     Impact on Folding Patterns: The growth ratio influences the rate and extent of cortical growth, which in turn affects the folding patterns of the cortex. Variations in the growth ratio can result in alterations in the depth, frequency, and orientation of cortical folds, shaping the overall morphology of the brain surface.


3. Mechanotransduction Pathways: The growth ratio between the cortex and subcortex is linked to Mechanotransduction pathways that regulate cellular responses to mechanical stimuli. Changes in the growth ratio can modulate these pathways, leading to alterations in cell growth, proliferation, and tissue remodeling, which impact cortical folding patterns.


4.     Computational Modeling: Computational models can simulate the sensitivity of surface morphology to variations in the growth ratio by adjusting this parameter and observing the resulting changes in cortical folding patterns. These models provide insights into how the growth ratio influences the morphological features and structural organization of the cerebral cortex.


5.   Cellular Mechanisms: The growth ratio is closely tied to cellular mechanisms such as axon elongation, cell proliferation, and tissue growth, which collectively contribute to cortical development and folding. Understanding the interplay between the growth ratio and cellular processes is essential for unraveling the complexities of brain morphogenesis.


6.     Clinical Implications: Abnormalities in the growth ratio between cortical layers have been implicated in various neurodevelopmental disorders and brain pathologies. Investigating the sensitivity of surface morphology to the growth ratio can provide valuable insights into the underlying mechanisms of these conditions and potential therapeutic targets.


7.  Biological Significance: The growth ratio is a fundamental parameter that governs the dynamic changes in brain structure during development. It reflects the intricate balance between cortical and subcortical growth processes and their impact on cortical folding, highlighting the biological significance of the growth ratio in shaping brain morphology.


By exploring the sensitivity of surface morphology to the growth ratio, researchers can enhance their understanding of the mechanical and biological factors that drive cortical folding and brain development. This knowledge is essential for deciphering the complex interplay between growth processes, cellular mechanisms, and structural changes in the developing brain.

 

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