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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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How does prenatal brain development differ from postnatal development?

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Dr. Rishabh Pathak

Prenatal brain development and postnatal brain development differ in several key aspects:


1. Genetic Control vs. Experience-Dependent: Prenatal brain development is largely under genetic control, with the basic structure of the brain being laid down primarily during the prenatal period. In contrast, postnatal brain development is more experience-dependent, with the environment playing a crucial role in shaping neural networks and brain functions.


2.   Timing of Myelination: The timing of myelination, which is essential for neural communication, varies across different brain regions. Sensory and motor areas are myelinated earlier, typically completing around the preschool period. However, regions involved in higher cognitive abilities, such as the prefrontal cortex, may not complete myelination until adolescence or early adulthood.


3. Developmental Patterns: While basic sensation and perception systems are typically fully developed by kindergarten age, other systems involved in memory, decision-making, and emotion continue to develop well into childhood. The foundations for many of these abilities are established during the early years, highlighting the importance of early childhood in brain development.


4.     Hierarchical Process: Brain research suggests that development is a hierarchical process, where higher-level processes build upon a foundation of lower-level processes. For example, language development depends critically on sensory and perceptual development, emphasizing the interconnected nature of brain development.


In summary, prenatal brain development is more genetically driven and focuses on laying down the basic structure of the brain, while postnatal brain development is influenced by experiences and interactions with the environment, leading to the refinement of neural networks and the development of various cognitive abilities.

 

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