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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 EEG?

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Dr. Rishabh Pathak



 

Electroencephalography (EEG) is a technique used to record the electrical activity of the brain. It involves placing electrodes on the scalp to detect and measure the electrical signals produced by brain cells, known as neurons. These electrodes pick up the electrical impulses generated by the brain's neurons, which communicate with each other through electrical activity.

The EEG signals are then amplified and recorded, allowing researchers and clinicians to analyze the brain's electrical patterns. EEG is a non-invasive method that provides real-time information about brain activity. It is commonly used in various fields, including neuroscience, clinical neurology, psychology, and cognitive science.

By studying EEG signals, researchers can investigate brain function, cognitive processes, and neurological disorders. Different brain wave patterns, such as alpha, beta, delta, and theta waves, are associated with different states of consciousness, cognitive tasks, and brain functions. Analyzing these patterns can provide valuable insights into brain activity, cognitive processes, and neurological conditions.

Overall, EEG is a powerful tool for studying the brain's electrical activity, understanding cognitive processes, diagnosing neurological disorders, and monitoring brain function in various contexts.



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