This paper is less dramatic than you think it is and really just re-explains what RLVR does. Let's stipulate that what pretraining does is train next token pre

This paper is less dramatic than you think it is and really just re-explains what RLVR does. Let's stipulate that what pretraining does is train next token prediction over a gigantic corpus. You can then sample from this distribution repeatedly (cf the Large Language Monkeys paper) and count how often it passes some deterministic verifier. What GRPO-style RLVR does is precisely this, but then reward the trajectories which passed the verifier. These distributions are _by construction_ within the accessible output space of the pretrained model; you're reweighting the distribution so that pass@k goes up, because that's (for applications like programming) very useful. RLVR is about making sampling more efficient; the only new information being added to the system is the presence of the verifier, and note that you only get a reward when the verifier passes, so there's essentially no mechanism for "teaching new facts" here.