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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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After Gestational week 22 the cortical plate differentiates

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Dr. Rishabh Pathak

After gestational week 22, a pivotal phase in brain development unfolds as the cortical plate undergoes significant differentiation. Here is an explanation of the importance of gestational week 22 in the context of cortical plate differentiation:


1.     Areal, Laminar, and Cytological Differentiation: The period following week 22 marks a crucial time for the differentiation of the cortical plate in terms of its areal organization, laminar structure, and cytological characteristics. This phase is characterized by the emergence of distinct cortical areas, the refinement of cortical layers, and the maturation of neuronal cell types within the developing cortex.


2.    Gyral Formation: Around week 24, gyral formation begins at specific locations such as the parieto-occipital and central sulci. Gyri are the raised folds on the brain's surface that increase its surface area, allowing for more complex neural connections and cognitive functions. The initiation of gyral formation signifies the dynamic changes occurring in the cortical architecture during this developmental period.


3.  Transition in Proliferative Zones: By week 25–27, the ventricular zone, where neural progenitor cells reside, reduces to a one-cell-thick ependymal layer. This transition indicates a shift in the proliferative zones of the developing brain, with the subventricular zone becoming the primary source of cortical neurons. The subventricular zone continues to generate neurons that contribute to the expanding cortical plate.


4.  Subplate Attenuation: During this phase, the subplate, a transient structure critical for guiding early cortical development, reaches its maximum thickness and begins to attenuate. While some residual subplate neurons persist as interstitial neurons in the white matter tissue throughout life, the overall reduction in subplate thickness reflects the maturation and refinement of the cortical plate architecture.


5.  Maturation of Cortical Circuits: The differentiation of the cortical plate after gestational week 22 is essential for the maturation of cortical circuits and the establishment of functional connectivity within the developing brain. As cortical areas become more specialized and neuronal populations mature, the foundation for complex neural processing and information integration is laid down, setting the stage for higher-order cognitive functions.


In summary, gestational week 22 marks a critical period in brain development when the cortical plate undergoes differentiation, leading to the emergence of distinct cortical areas, refined laminar organization, and maturation of neuronal cell types. The initiation of gyral formation, transition in proliferative zones, attenuation of the subplate, and maturation of cortical circuits are key events that shape the structural and functional development of the cerebral cortex during this phase. Understanding the processes that occur after gestational week 22 is essential for unraveling the complexities of cortical differentiation and the establishment of the mature brain's intricate architecture and functional connectivity.

 

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