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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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Basic Model of Human Connectome Project

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Dr. Rishabh Pathak


 The Human Connectome Project (HCP) employs a comprehensive and multi-modal approach to map the structural and functional connectivity of the human brain. The basic model of the HCP involves the following key components:

  1. Data Acquisition:
    • The HCP collects neuroimaging data from a large cohort of healthy individuals using state-of-the-art imaging techniques.
    • Structural MRI: High-resolution structural MRI scans are acquired to visualize the anatomical features of the brain, such as gray matter, white matter, and cortical thickness.
    • Diffusion MRI: Diffusion MRI is used to map the white matter pathways in the brain by tracking the diffusion of water molecules along axonal fibers.
    • Functional MRI: Resting-state fMRI and task-based fMRI are employed to study the functional connectivity and activity patterns of the brain at rest and during specific cognitive tasks.
  2. Data Processing and Analysis:
    • The acquired neuroimaging data undergoes extensive processing and analysis to extract meaningful information about brain connectivity.
    • Structural Connectivity Analysis: Diffusion MRI data is processed to reconstruct white matter tracts and create maps of structural connectivity in the brain.
    • Functional Connectivity Analysis: Resting-state fMRI data is used to identify functional networks and correlations between different brain regions, providing insights into how the brain's functional networks are organized.
  3. Integration of Data:
    • The HCP integrates data from multiple imaging modalities, including structural MRI, diffusion MRI, and functional MRI, to create a comprehensive model of the human connectome.
    • By combining information from different imaging techniques, researchers can study the relationships between brain structure, function, and connectivity in a holistic manner.
  4. Connectome Mapping:
    • The primary goal of the HCP is to map the human connectome, which refers to the complete set of neural connections in the brain.
    • This mapping includes identifying structural connections (anatomical pathways) and functional connections (synchronized activity) between different brain regions.
    • The connectome maps generated by the HCP provide a detailed understanding of how information is processed and transmitted within the brain's network.
  5. Open Science and Data Sharing:
    • A fundamental principle of the HCP is open science and data sharing, where the generated datasets and connectome maps are made freely available to the scientific community.
    • This open access approach allows researchers worldwide to explore the rich neuroimaging data and contribute to advancing our understanding of the human brain.

Overall, the basic model of the Human Connectome Project involves acquiring, processing, and integrating neuroimaging data to create detailed maps of the human connectome, with a focus on structural and functional connectivity in the brain.

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