The key quantity of interest here is the Riemannian metric, which characterizes the Riemannian geometry and defines straight lines and derivatives on the manifold.

"Robot, make me a chair" Computer-aided design (CAD) systems are tried-and-true tools used to design many of the physical objects we use each day. But CAD software requires extensive expertise to master, and many tools incorporate such a high level of detail they don't lend themselves to brainstorming or rapid prototyping. In an effort to make design faster and more accessible for non-experts, researchers from MIT and elsewhere developed an AI-driven robotic assembly system that allows people to build physical objects by simply describing them in words. Their system uses a generative AI model to build a 3D representation of an object's geometry based on the user's prompt. Then, a second generative AI model reasons about the desired object and figures out where different components should go, according to the object's function and geometry.

Project page is available at https://ku-cvlab.github.io/DaRF/ .

Algebraic varieties are the geometric shapes defined by systems of polynomial equations; they are ubiquitous across mathematics and science.

Deep learning methods have gained popularity in high energy physics for fast modeling of particle showers in detectors.

A neural radiance field (NeRF) enables the synthesis of cutting-edge realistic novel view images of a 3D scene. It includes density and color fields to model the shape and radiance of a scene, respectively. Supervised by the photometric loss in an end-to-end training manner, NeRF inherently suffers from the shape-radiance ambiguity problem, i.e., it can perfectly fit training views but does not guarantee decoupling the two fields correctly.

However, current methods are impeded by requiring long-time per-scene optimizations and cannot generalize to new scenes.