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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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Human Connectome Project

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Dr. Rishabh Pathak

The Human Connectome Project (HCP) is a large-scale research initiative that aims to map the structural and functional connectivity of the human brain. Launched in 2009, the HCP utilizes advanced neuroimaging techniques to create detailed maps of the brain's neural pathways and networks in healthy individuals. The project focuses on understanding how different regions of the brain communicate and interact with each other, providing valuable insights into brain function and organization.


1.     Structural Connectivity: The HCP uses diffusion MRI to map the white matter pathways in the brain, revealing the structural connections between different brain regions. This information helps researchers understand the physical wiring of the brain and how information is transmitted between regions.


2.     Functional Connectivity: Functional MRI (fMRI) is employed to study the patterns of brain activity and connectivity while individuals are at rest (resting-state fMRI) or engaged in specific tasks (task-based fMRI). By analyzing these functional networks, researchers can identify brain regions that are synchronized in their activity and study how these networks support various cognitive functions.


3.     Multi-Modal Imaging: The HCP integrates data from multiple imaging modalities, including structural MRI, diffusion MRI, and functional MRI, to create comprehensive maps of the human brain's connectivity at different levels. This multi-modal approach provides a more complete understanding of brain structure and function.


4.     Open Data Sharing: One of the hallmarks of the HCP is its commitment to open science and data sharing. The project makes its datasets freely available to the scientific community, allowing researchers worldwide to access and analyze the rich neuroimaging data generated by the HCP.


5.     Impact on Neuroscience: The Human Connectome Project has significantly advanced our understanding of the human brain's organization and connectivity. By providing detailed maps of brain networks and connections, the HCP has contributed to research in areas such as cognitive neuroscience, neuroimaging, and neurology.


Overall, the Human Connectome Project plays a crucial role in advancing our knowledge of the human brain's complex architecture and functioning. It serves as a valuable resource for researchers studying brain connectivity, neural circuits, and brain disorders, ultimately leading to new insights into brain health and disease.

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