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...
Abnormal slowing of the alpha rhythm refers to deviations from the typical frequency range and characteristics of the alpha waves observed in EEG recordings. 1. Characteristics : o Abnormal slowing of the alpha rhythm is characterized by a decrease in frequency, typically falling below the normal range of 8-13 Hz. o The alpha rhythm may exhibit frequencies in the range of 6-8 Hz, indicating a slower oscillation pattern compared to the typical alpha activity. 2. Appearance : o The abnormal slowing of the alpha rhythm may manifest as extended anterior distribution of the alpha waves. o In some cases, abnormal slowing may occur without other accompanying signs of drowsiness, distinguishing it from the normal alpha rhythm in drowsiness. 3. Diagnostic Considerations : o Identifying abnormal slowing of the alpha rhythm requires comparison with age-appropriate norms and considera...