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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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Patterns of Change in White Mater

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Dr. Rishabh Pathak

White matter undergoes significant changes throughout development, reflecting the maturation and refinement of neural connections in the brain. Here are some key patterns of change in white matter:


1.  Increase in White Matter Volume: During early development, there is a rapid increase in white matter volume, reflecting the growth of myelinated axons and the establishment of neural pathways. This period of white matter expansion is crucial for enhancing connectivity between different brain regions.


2.   Myelination: Myelination, the process of insulating axons with myelin sheaths, continues throughout childhood and adolescence, leading to increased white matter integrity and faster neural transmission. Myelination enhances the efficiency of neural communication and supports cognitive functions.


3.     Pruning and Refinement: As the brain matures, there is a process of pruning and refinement in white matter connectivity. Unused or inefficient neural connections are eliminated, while stronger connections are reinforced through synaptic pruning and plasticity. This selective pruning optimizes neural networks for efficient information processing.


4.     Frontal Lobe Development: White matter changes in the frontal lobes, including the prefrontal cortex, are particularly pronounced during adolescence and early adulthood. The maturation of white matter tracts in the frontal lobes is associated with the development of executive functions, cognitive control, and decision-making abilities.


5.     Long-Distance Connections: White matter pathways that facilitate long-distance communication between brain regions show continued development and specialization across the lifespan. These long-range connections support complex cognitive processes, such as language, spatial reasoning, and social cognition.


6.  Age-Related Changes: While white matter volume generally increases during childhood and adolescence, there may be age-related declines in white matter integrity in older adulthood. Factors such as vascular health, inflammation, and neurodegenerative processes can contribute to white matter changes in aging brains.


Understanding the patterns of change in white matter provides insights into the dynamic nature of brain development and the role of white matter in supporting cognitive functions and neural communication. The maturation and plasticity of white matter pathways contribute to the structural foundation of the brain and underlie the complex network of connections that enable diverse cognitive abilities.

 

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