Comment by llm_nerd
Apple's VO2Max measures are not based upon that deep neural network development, and empirical seems to be conflating a few things. And FWIW, just finding the actual paper is almost impossible as that same site has SEO-bombed Google so thoroughly you end up in the circular-reference empirical world where all of their pages reference each other as authorities.
Apple and Columbia did recently collaborate on a heart rate response model -- one which can be downloaded and trialed -- but that was not related to the development of their VO2Max calculations.
Apple is very shrouded about how they calculate VO2Max, but it likely is a pretty simple calculation (e.g. how much is your heart responding based upon the level of activity assumed based upon your motion, method of exercise and movements). The most detail they provide is in https://www.apple.com/healthcare/docs/site/Using_Apple_Watch..., which mostly is a validation that it's providing decent enough accuracy.
What’s your source on Apple not using the neural network for VO2Max estimation? They’ve been using on-device neural networks for various biomarkers for several years now (even for seemingly simple metrics like heart rate).
FWIW, the article above links directly to both the paper and a GitHub repo with PyTorch code.