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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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Gyrification begins around Mid-gestation

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Dr. Rishabh Pathak

Gyrification, the process of forming the characteristic folds and grooves on the surface of the cerebral cortex, initiates around mid-gestation during human brain development. This crucial phase typically begins around week 23 of gestation and continues throughout prenatal and postnatal development. The timing of gyrification coincides with the period when the brain undergoes significant growth and structural organization, leading to the formation of gyri and sulci that increase the surface area of the cortex within the confines of the skull.


During mid-gestation, primary sulci start to emerge, marking the onset of gyrification. As the brain continues to develop, secondary and tertiary sulci form, creating a complex pattern of folds that characterize the convoluted surface of the cerebral cortex. The process of gyrification is intricately linked to neuronal connectivity, cortical expansion, and the establishment of functional neural circuits essential for cognitive functions.


The timing of gyrification around mid-gestation is significant as it sets the stage for the structural maturation of the brain and the organization of cortical regions. The folding of the cortex through gyrification allows for increased neuronal density, efficient communication between brain regions, and the specialization of different functional areas. Variations in the timing and extent of gyrification can influence brain structure and function, contributing to individual differences in cognitive abilities and neurological outcomes.


Understanding the timeline and mechanisms of gyrification is essential for unraveling the complexities of brain development and for studying the impact of disruptions in this process on neurodevelopmental disorders and cognitive function. By studying the initiation and progression of gyrification during mid-gestation and beyond, researchers can gain insights into the dynamic interplay of genetic, environmental, and epigenetic factors that shape the intricate folding patterns of the human brain.

 

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