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...
Functional Magnetic Resonance Imaging (fMRI) is a non-invasive neuroimaging technique that measures brain activity by detecting changes in blood flow and oxygen levels in response to neural activity. fMRI is widely used in neuroscience and cognitive psychology to study brain function and connectivity during various tasks, behaviors, and resting states. Key features of fMRI include: 1. Principle of fMRI : o fMRI is based on the principle that changes in neural activity are accompanied by changes in blood flow and oxygenation levels in the brain. o When a specific brain region becomes active, it requires more oxygenated blood to support the increased metabolic demands of neural activity. o The fMRI scanner detects these changes in blood oxygen level-dependent (BOLD) signals, providing a measure of brain activity in different regions. 2. Task-Based fMRI : o ...