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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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What is Connectomics?

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Dr. Rishabh Pathak


 Connectomics is a field of neuroscience that focuses on the comprehensive mapping and study of neural connections in the brain at various scales, ranging from the microscale of individual neurons and synapses to the macroscale of functional and structural connectivity between different brain regions. Here are some key points about connectomics:

 1. Definition:

   - Connectomics is the production and analysis of connectomes, which are detailed maps of neural connections within the nervous system of an organism, including the brain.

   - Connectomics aims to understand the structural and functional wiring of the brain, elucidating how neural circuits are organized, how information flows between brain regions, and how connectivity patterns relate to brain function and behavior.

 2. Scale:

   - Connectomics can be studied at multiple scales, encompassing the microscale of individual neurons and synapses, the mesoscale of neural circuits and brain regions, and the macroscale of large-scale brain networks and functional connectivity.

   - Techniques such as electron microscopy, diffusion tensor imaging (DTI), functional magnetic resonance imaging (fMRI), and electroencephalography (EEG) are used to investigate connectivity patterns at different scales.

 3. Structural Connectomics:

   - Structural connectomics focuses on mapping the anatomical connections between brain regions, revealing the physical pathways of neural communication and information transfer in the brain.

   - Techniques like diffusion MRI and tractography are used to trace white matter pathways and reconstruct the structural connectivity matrix of the brain, providing insights into the organization of neural circuits.

 4. Functional Connectomics:

   - Functional connectomics examines the dynamic patterns of neural activity and functional connectivity between brain regions during different cognitive tasks, resting states, or behavioral states.

   - Functional imaging techniques like fMRI and EEG are employed to study how brain regions interact and communicate functionally, revealing the coordinated activity within functional brain networks.

 5. Applications:

   - Connectomics research has implications for understanding brain development, neural plasticity, learning and memory, sensory processing, motor control, and cognitive functions.

   - Connectomics approaches are also used to investigate neurological and psychiatric disorders, identify biomarkers of disease, and develop targeted interventions for brain-related conditions.

 

In summary, connectomics is a multidisciplinary field that integrates neuroscience, imaging technologies, and computational methods to map, analyze, and interpret the complex network of neural connections in the brain. By unraveling the structural and functional connectivity of the brain, connectomics provides valuable insights into brain organization, information processing, and the mechanisms underlying brain function and dysfunction.

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