The same way Alaska taxes oil extraction. Alaska doesn't track which molecule of oil came from which acre. They don't audit every drop. They tax the extraction operation and collect royalties on the resource being pulled out of the ground. We know who is training large models. We know roughly what data they're using. We know their revenue. A compute tax on large training runs, a revenue royalty on foundation model companies, or a licensing fee above a certain data threshold... none of these require tracking individual data points. They require taxing the extraction operation, which is visible, measurable, and already being monitored to some degree for safety purposes. We already have a very analogous model in the form of oil and Alaska.

Edit: to clarify, this wouldn't be a tax. A tax is the government taking a cut of someone else's money. A royalty is the owner charging for access to their resource. Alaska doesn't tax Exxon for drilling. It charges Exxon for extracting something that belongs to the people. Same principle here.