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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 the growth spurt period of the human brain differ from previous beliefs?

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Dr. Rishabh Pathak

The growth spurt period of the human brain differs from previous beliefs in several key aspects, as revealed by more recent research and quantitative analyses. Here are some ways in which the understanding of the human brain growth spurt has evolved:


1.   Duration and Timing: Previous beliefs suggested that the human brain growth spurt was primarily a perinatal phenomenon, similar to that of pigs, characterized by rapid growth in the early postnatal period. However, more recent studies have shown that the human brain growth spurt begins in mid-pregnancy and extends well into the second postnatal year and beyond. This extended duration indicates that a significant portion of the human brain growth spurt is postnatal, lasting longer than previously thought.


2.   Cell Division and Growth: Earlier assumptions stated that the phase of cell division in the human brain was completed by about 5 postnatal months. However, current research indicates that the human brain continues to undergo substantial growth and development beyond this timeframe, with a significant portion of the growth spurt occurring postnatally. This prolonged period of growth suggests that humans resemble rats more closely in terms of brain development than previously believed.


3.  Implications for Intervention: The revised understanding of the human brain growth spurt offers new opportunities for promoting optimal brain development by establishing the best environmental conditions during this critical period. Recognizing the extended postnatal growth phase allows for targeted interventions and support to enhance brain growth and function during infancy and early childhood.


4.     Research Contributions: The shift in understanding the duration and timing of the human brain growth spurt is attributed to quantitative studies that have systematically measured and analyzed various parameters of brain development. These studies have provided a more accurate depiction of the growth trajectories and critical periods in human brain development.


In summary, the updated understanding of the human brain growth spurt challenges previous beliefs by highlighting the prolonged postnatal growth phase, the importance of environmental influences on brain development, and the need for targeted interventions to support optimal brain growth and function. This revised perspective underscores the dynamic and extended nature of human brain development, emphasizing the significance of early life experiences in shaping cognitive and neurological outcomes.

 

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