Principled detection of unreliable extrapolation

Develop a principled method for detecting when linear extrapolation in RISE becomes unreliable during training, despite the use of beta-decay scheduling and an exponential-moving-average anchor for empirical robustness.

Background

RISE constructs a future teacher by extrapolating the model’s own RLVR training trajectory in either parameter space or logit space. The method assumes that the trajectory is sufficiently low-dimensional and locally linear for extrapolation at moderate values of the extrapolation factor beta to remain meaningful. The paper uses a decaying beta schedule and an EMA anchor to reduce the risk of overshooting, but these safeguards are empirical rather than principled.

The unresolved problem is to determine, during training, when the extrapolation assumption has ceased to be reliable. Such a detection mechanism would help identify when RISE’s self-extrapolated teacher may become misleading or harmful and could support adaptive control of the extrapolation process.

References

The $\beta$-decay schedule and EMA anchor provide empirical robustness, yet principled detection of when extrapolation becomes unreliable remains open.

— RISE: Recursive Improvement via Self-Extrapolating Policy Distillation  (2609.05295 - Li et al., 4 Sep 2026) in Section 6, “Limitations”