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...
A connectome is a comprehensive map of neural connections in the brain, representing the intricate network of structural and functional pathways that facilitate communication between different brain regions. 1. Definition: - A connectome is a detailed representation of the wiring diagram of the brain, illustrating the complex network of axonal projections, synaptic connections, and communication pathways between neurons and brain regions. - The connectome encompasses both the structural connectivity, which refers to the physical links between neurons and brain areas, and the functional connectivity, which reflects the patterns of neural activity and information flow within the brain. 2. Structural Connectome: - The structural connectome provides a map of the anatomical connections in the brain, showing how neurons are physically linked through axonal projections, white matter pathways, and synaptic contacts. - Techniques ...