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...
Epileptiform bursts are a specific EEG pattern characterized by a series of rapid, repetitive spikes or sharp waves that indicate abnormal electrical activity in the brain, typically associated with seizure activity. 1. Definition : o Epileptiform bursts consist of brief, high-frequency discharges that can appear as spikes or sharp waves. These bursts are indicative of underlying epileptic activity and can occur in various seizure types. 2. EEG Characteristics : o The bursts are often more monomorphic and stereotyped compared to non-epileptic bursts, exhibiting greater rhythmicity, especially in the faster frequency ranges. This distinct waveform helps differentiate them from other types of EEG activity, such as those seen in non-epileptic conditions. o Epileptiform bursts can vary in duration and frequency, and they may evolve into more complex patterns, such as ge...