From https://metaculus.com/questions/17096/us-tracks-training-runs-by-2026/

As of May 2023, US law does not restrict training of large AI models in any capacity. Current state-of-the-art AI projects require immense computational resources to develop. One way US policymakers may address risks from AI is to require those who train large models to report this training, and to audit such reports.

A similar regime exists for labor - firms must report how many employees they have (and have various obligations resulting from that). Another parallel might be reporting for the amount of CO2 the company emits. Such regulation may be tied to taxes or statements of public disclosure.

A list of large AI training runs can be found here. See also Epoch for much more information about AI training resource costs.