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 prefrontal cortex (PFC) is a critical brain region associated with higher-order cognitive functions, including executive function, decision-making, social behavior, and emotional regulation. The PFC undergoes significant development across the lifespan, with distinct regions contributing to various aspects of cognitive control and behavior. Here are the key regions of the prefrontal cortex and their functions: 1. Orbitofrontal Cortex (BA 11) : o Location : Located in the ventromedial part of the PFC. o Function : The orbitofrontal cortex is involved in decision-making, reward processing, emotional regulation, and social behavior. It plays a role in evaluating the emotional and motivational significance of stimuli and guiding adaptive behavior based on reward outcomes. 2. Ventrolateral PFC (BA 44, 45, 47) : o Location : Situated in the lower lateral aspects of the PFC. o Functi...