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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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Gyrogenesis

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Dr. Rishabh Pathak

Gyrogenesis refers to the process of gyrus formation in the brain, specifically the development of the characteristic folds and grooves (gyri and sulci) on the surface of the cerebral cortex. This intricate process of cortical folding is essential for maximizing the surface area of the brain within the constraints of the skull, allowing for increased neuronal density and enhanced cognitive capabilities. Here is an overview of gyrogenesis and its significance in brain development:


1.  Timing of Gyrogenesis: Gyrogenesis begins around mid-gestation in human brain development, typically around week 23 of gestation. Primary sulci start to form, followed by the development of secondary and tertiary sulci as the brain continues to grow and mature. The process of gyrification continues throughout prenatal and postnatal development, shaping the convoluted surface of the cerebral cortex.


2.     Relationship to Neural Connectivity: Gyrogenesis is closely linked to neuronal connectivity and the establishment of functional neural circuits in the brain. The folding of the cortex allows for the spatial organization of different brain regions and facilitates efficient communication between neurons by reducing the distance over which signals need to travel. The convolutions created by gyrogenesis increase the surface area available for synaptic connections, supporting complex cognitive processes.


3. Regulation of Brain Function: The pattern of gyri and sulci formed during gyrogenesis is not random but follows a specific developmental trajectory that is influenced by genetic, environmental, and epigenetic factors. The unique folding patterns of individual brains contribute to variations in brain structure and function, including differences in cognitive abilities, sensory processing, and motor skills. Disruptions in gyrogenesis can impact brain connectivity and function, potentially leading to neurodevelopmental disorders.


4. Computational Modeling: Computational models have been developed to simulate the process of gyrogenesis and understand the underlying mechanisms that drive cortical folding. These models incorporate factors such as differential growth rates, mechanical forces, and genetic influences to predict the formation of gyri and sulci patterns observed in the human brain. By studying gyrogenesis computationally, researchers can gain insights into the complex interplay of biological and physical processes that shape brain morphology.


5. Clinical Implications: Abnormalities in gyrogenesis can manifest as cortical malformations, such as lissencephaly (smooth brain) or polymicrogyria (excessive small folds). These conditions are associated with developmental delays, intellectual disabilities, and epilepsy, highlighting the importance of proper cortical folding for normal brain function. Understanding the mechanisms of gyrogenesis and its disruptions is crucial for diagnosing and treating neurodevelopmental disorders.

In summary, gyrogenesis is a fundamental process in brain development that shapes the convoluted structure of the cerebral cortex, influencing neural connectivity, brain function, and cognitive abilities. The intricate folding patterns generated during gyrogenesis optimize the brain's capacity for information processing and are essential for normal brain development and function.
 

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