Matt Golden
552 posts
@GoldnMatt
Postdoctoral Fellow at Georgia Tech. I like tensors a lot. 5 ⭐️ Lyft passenger
As an aside: In the usual ML and DL setup, "tensors" perhaps should have just been called hypermatrices (which are just multi-dimensional arrays and don't correspond to specific transformation rules). The terminology never caught on, but "tensor" sounds cool I guess.
If you think OpenAI Sora is a creative toy like DALLE, ... think again. Sora is a data-driven physics engine. It is a simulation of many worlds, real or fantastical. The simulator learns intricate rendering, "intuitive" physics, long-horizon reasoning, and semantic grounding, all by some denoising and gradient maths. I won't be surprised if Sora is trained on lots of synthetic data using Unreal Engine 5. It has to be! Let's breakdown the following video. Prompt: "Photorealistic closeup video of two pirate ships battling each other as they sail inside a cup of coffee." - The simulator instantiates two exquisite 3D assets: pirate ships with different decorations. Sora has to solve text-to-3D implicitly in its latent space. - The 3D objects are consistently animated as they sail and avoid each other's paths. - Fluid dynamics of the coffee, even the foams that form around the ships. Fluid simulation is an entire sub-field of computer graphics, which traditionally requires very complex algorithms and equations. - Photorealism, almost like rendering with raytracing. - The simulator takes into account the small size of the cup compared to oceans, and applies tilt-shift photography to give a "minuscule" vibe. - The semantics of the scene does not exist in the real world, but the engine still implements the correct physical rules that we expect. Next up: add more modalities and conditioning, then we have a full data-driven UE that will replace all the hand-engineered graphics pipelines. openai.com/sora
A useful integral formula, derived with an assist from the Pythagorean trig identity.
Here's an application of birdtrack notation to prove a curvature tensor identity. It is identical to the [abstract] index notation, but I find the diagrammatic proof easier to follow once I picked up the rules. This is a solution to exercise [14.10] in Penrose's Road to Reality.
Wheeler’s vivid analogy for spacetime curvature measurement based on measuring the shape of an iceberg in a tossing rowboat gets me every time.
🤖 oopsie in a 2023 @ElsevierConnect journal paper: “Please note that as an AI language model, I am unable to generate specific tables or conduct tests, so the actual results should be included in the table.” 🤡 #ChatGPT
