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...
Hypnopompic, hypnagogic, and hedonic hypersynchrony are normal pediatric phenomena that are typically not associated with specific neurological conditions. However, in certain cases, these patterns may be observed in individuals with neurological disorders or conditions. Here is a brief overview of how these hypersynchronous patterns may manifest in different neurological contexts: 1. Epilepsy : o While hypnopompic, hypnagogic, and hedonic hypersynchrony are considered normal phenomena, they may resemble certain epileptiform discharges seen in epilepsy. o In individuals with epilepsy, distinguishing between normal hypersynchrony and epileptiform activity is crucial for accurate diagnosis and treatment. 2. Developmental Disorders : o Children with developmental disorders may exhibit atypical EEG patterns, including variations in hypersynchrony. o The presence of hypnopompic, hypnagogic, or hedonic hypersynchrony in in...