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...
The lateral prefrontal cortex (LPFC) plays a crucial role in various cognitive functions, particularly those related to executive control, working memory, decision-making, and goal-directed behavior. Here are key functions associated with the lateral prefrontal cortex: 1. Executive Functions : o The LPFC is central to executive functions, which encompass higher-order cognitive processes involved in goal setting, planning, problem-solving, cognitive flexibility, and inhibitory control. o It is responsible for coordinating and regulating other brain regions to support complex cognitive tasks, such as task switching, attentional control, and response inhibition, essential for adaptive behavior in changing environments. 2. Working Memory : o The LPFC is critical for working memory processes, which involve the temporary storage and manipulation of information to guide behavior and decis...