You might already know this, but a large part of test-time compute / 'overthinking' is just letting the model do more passes, and refine its activation residuals more.

For example, even if you make thinking tokens literally just '....' (absolutely meaningless; zero information), you still see significant performance improvements: https://arxiv.org/abs/2404.15758 and https://arxiv.org/abs/2607.22925 for some starters.

Treat thinking more like a "loading screen message" that's been RL'd to somewhat resemble its actual internal state; which happens in its activations, not tokens.