How well does LLM performance on frontier math benchmarks generalize outside of the sort of tasks that they've been RLVR'd on? For example, could a model, after solving an unsolved Erdős problem, explain its solution to a Math undergrad in a way that is both correct and useful? I know that the original DeepSeek math paper alternated between RLVR and supervised training to prevent the model from drifting into a language that was perfectly fine for generating correct solutions but was not easily human-readable.

I feel like a solid answer here would have broad implications for how well other things picked up in RLVR training carry over^[1], and potentially, in the inverse, how well e.g. alignment training will carry over to task behavior that isn't easily human-checkable once superhuman performance has been reached on some narrow, computationally-verifiable task^[2].

1. ^{^}

   For instance, just how much software engineering performance can we get by training LLMs to write code that passes unit tests? Will we hit a brick wall on more subtle aspects of the profession?

2. ^{^}

   For instance, would a model that's been through RLVR training to let it maximize throughput in service industry settings, when assigned to manage a hospital, rule out solutions that involve discharging a patient that will die if discharged in order to treat additional patients using his hospital bed?