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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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Explain quantitative growth and development of human brain?

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Dr. Rishabh Pathak

Quantitative growth and development of the human brain involve the systematic measurement and analysis of various physical and biochemical parameters to understand how the brain changes in size, structure, and composition over time. This quantitative approach provides valuable insights into the patterns of growth, maturation, and plasticity that occur during different stages of development, from prenatal to postnatal years. Here are some key aspects of quantitative growth and development of the human brain:


1.     Measurement of Brain Parameters: Researchers quantify parameters such as brain weight, volume, surface area, cortical thickness, neuronal density, synaptic connectivity, DNA content, cholesterol levels, and water content in different brain regions. These measurements help track changes in brain structure and composition across developmental stages.


2.     Growth Trajectories: By analyzing quantitative data over time, researchers can map out growth trajectories of the human brain, identifying periods of rapid growth (growth spurts) and slower maturation. Understanding these trajectories is essential for characterizing normal brain development and detecting deviations from typical growth patterns.


3.     Critical Periods: Quantitative analysis helps identify critical periods during brain development when specific processes, such as neurogenesis, synaptogenesis, myelination, and pruning, are most active. These critical periods play a crucial role in shaping the structural and functional organization of the brain.


4.   Vulnerability and Resilience: Quantitative studies can reveal vulnerabilities in brain development, such as the impact of nutritional deficiencies, environmental toxins, genetic factors, and early-life stressors. Understanding these vulnerabilities can inform interventions to support healthy brain development and resilience.


5.  Individual Differences: Quantitative analysis allows for the examination of individual differences in brain growth and development, including variations in developmental trajectories, genetic influences, environmental factors, and the effects of interventions or treatments.


6.   Clinical Applications: Quantitative assessments of brain growth and development have clinical implications for diagnosing neurodevelopmental disorders, monitoring treatment outcomes, and predicting long-term cognitive and behavioral outcomes in individuals.


Overall, quantitative growth and development studies provide a comprehensive understanding of the dynamic changes that occur in the human brain from early prenatal stages through adulthood. By quantifying various aspects of brain development, researchers can uncover the underlying mechanisms driving neurodevelopmental processes and inform strategies to promote healthy brain growth and function.

 

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