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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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Human postnatal Neuroanatomical development

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Dr. Rishabh Pathak

Human postnatal neuroanatomical development refers to the process of structural growth and maturation of the human brain after birth, continuing through infancy, childhood, and adolescence. This period is characterized by significant changes in the size, shape, and connectivity of brain structures, which play a crucial role in shaping cognitive, motor, and perceptual abilities. Here are key points related to human postnatal neuroanatomical development :


1.  Brain Growth: From birth to teenage years, there is a fourfold increase in the volume of the human brain. This growth is not uniform, with variations in growth rates between different brain regions, such as subcortical and cortical areas.


2.  Neuronal Migration: By the time of birth, most neurons have migrated to their appropriate locations within the cortex, hippocampus, and other brain regions. However, some neurogenesis continues into adulthood, particularly in the hippocampus.


3.     Synaptogenesis: Synapse formation, the connections between neurons, undergoes rapid changes during postnatal development. Different brain regions exhibit varying rates of synapse formation, with peak densities reached at different ages.


4. Cortical Development: The cerebral cortex, responsible for higher cognitive functions, undergoes significant changes during postnatal development. The maturation of cortical regions is essential for the emergence of complex cognitive abilities.


5.     Connectivity: The development of inter- and intraregional connectivity within the brain is a critical aspect of postnatal neuroanatomical development. The establishment of neural connections influences information processing and functional specialization.


6.     Plasticity: The postnatal brain exhibits a high degree of plasticity, allowing it to adapt and reorganize in response to experiences and environmental stimuli. This plasticity plays a crucial role in shaping brain development and functional outcomes.


7.     Implications: Understanding human postnatal neuroanatomical development has implications for clinical, educational, and social policies. It can inform interventions for neurodevelopmental disorders, educational practices, and policies aimed at supporting healthy brain development in children.


In summary, human postnatal neuroanatomical development is a dynamic and complex process that involves structural changes in the brain, including neuronal migration, synaptogenesis, cortical maturation, and connectivity development. This period of growth and maturation lays the foundation for cognitive, motor, and perceptual abilities, highlighting the importance of studying brain development in understanding human behavior and function.

 

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