Yes, there are a lot of modells designed to work okay on mobile. Though you'd typically train in the cloud and only use the trained model on the phone. Alternatively, you can train over many phones, which brings a lot of extra challenges but is definitely possible.
Google's very new Reformer[0] would likely be your best bet if you want both something truly cutting-edge and have less compute, even as little as a mobile's. As far as I know, it hasn't been used on phones yet (again, it's very new) but I bet it can be done.
I don’t mind training on a desktop and use it on both desktop and mobile. We kinda already have that problem since we parse Google data for a given android phone, but it doesn’t have the memory or compute for the amount of data the phone has generated over the years. The user will background the app too quickly. So we need to ask the desktop app to do it, process there, and sync results back.
Google's very new Reformer[0] would likely be your best bet if you want both something truly cutting-edge and have less compute, even as little as a mobile's. As far as I know, it hasn't been used on phones yet (again, it's very new) but I bet it can be done.
0. https://ai.googleblog.com/2020/01/reformer-efficient-transfo...