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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 the development of human brain places evidence?

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Dr. Rishabh Pathak


The development of the human brain is supported by various lines of evidence, including neuroimaging studies, histological analyses, genetic research, and clinical observations. These different approaches provide valuable insights into the structural, functional, and molecular changes that occur during brain development. Here are some key pieces of evidence supporting the development of the human brain:

1.   Neuroimaging Studies: Techniques such as magnetic resonance imaging (MRI) and functional MRI (fMRI) allow researchers to visualize the structural and functional changes in the human brain across different developmental stages. These studies provide detailed information about brain maturation, connectivity patterns, and regional changes over time.


2.  Histological Analyses: Histological studies involve examining brain tissue samples under a microscope to observe cellular structures, neuronal connections, and developmental changes. These analyses help researchers understand the cellular processes involved in brain development, such as neurogenesis, synaptogenesis, and myelination.


3.  Genetic Research: Genetic studies have identified key genes and molecular pathways that play crucial roles in brain development. Mutations in these genes can lead to neurodevelopmental disorders, highlighting the importance of genetic factors in shaping the developing brain.


4.  Clinical Observations: Observations of brain development in clinical settings, such as pediatric neurology and developmental psychology, provide valuable insights into typical and atypical patterns of brain maturation. Clinical assessments help identify developmental milestones, cognitive abilities, and potential delays or disorders affecting brain development.


5. Comparative Studies: Comparative studies across different species provide insights into evolutionary aspects of brain development and help researchers understand common principles of neurodevelopment across diverse organisms.


By integrating evidence from these various sources, researchers can build a comprehensive understanding of human brain development, from prenatal stages through infancy, childhood, adolescence, and into adulthood. This multidisciplinary approach enhances our knowledge of the complex processes that shape the human brain and underpins cognitive, emotional, and behavioral functions throughout life.

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