BIOENGINEER

New Lie-Algebraic Framework Separates Task Signal From Gradient Geometry in Quantum Machine Learning

Researchers at the Universidad de Salamanca have developed a Lie-algebraic framework that separates task-relevant signal from ...
BIOENGINEER

COSMOS Learns Neural Representations as Gauge Dynamics on the Grassmannian

The COSMOS framework trains orthonormal subspace frames with conjugation-based gauge-style updates, holding geometric ...
Nature

Gradient Ricci Solitons in Riemannian Geometry

Gradient Ricci solitons are self-similar solutions to the Ricci flow, characterised by a Riemannian manifold (M,g) endowed with a smooth potential function f satisfying the equation Ric + ∇²f = λg for ...
TES

Coordinate Geometry and Gradients of Linear Graphs - Lesson and Worksheet

This is the second lesson on Coordinate Geometry. This lesson focuses on how to find the Gradient and Gradient Problems as well as rearranging the equations of lines into the form ax + by + c = 0.
newswise

When Geometry Matters: Gradient-Wall Microresonators Enable Large-Scale Optical Trapping

Newswise — Near-field optical trapping has transformed particle manipulation in biology, chemistry, and nanotechnology, enabling contact-free control of objects ranging from nanoparticles to living ...
umass

Geometry of sliced optimal transport and projected-transport gradient flows

We will discuss two types of objects that can be approximated in high-dimensions. Recent results have established that sliced-Wasserstein (SW) distance can be approximated accurately in high ...