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...
Non-Invasive Brain-Computer Interfaces (BCIs) are systems that facilitate direct communication between the brain and external devices without the need for surgical procedures. They primarily rely on techniques that measure brain activity externally, such as electroencephalography (EEG). Principles of Non-Invasive BCIs 1. Signal Acquisition : Non-invasive BCIs capture brain signals using external sensors placed on the scalp. The most common method employed is: Electroencephalography (EEG) : This method detects electrical activity produced by neuronal firing via electrodes attached to the scalp. 2. Signal Processing : Once the brain signals are acquired, they undergo signal processing, which includes filtering, amplification, and feature extraction. The aim is to enhance signal quality and isolate relevant neural signatures associated with specific thoughts or commands. 3. ...