The Invisible Leash: Why RLVR May Not Escape Its Origin
Authors: name: Fang Wu, name: Weihao Xuan, name: Ximing Lu, name: Zaid Harchaoui, name: Yejin Choi

Recent advances in large reasoning models highlight Reinforcement Learning
with Verifiable Rewards (RLVR) as a promising method for enhancing AI's
capabilities, particularly in solving complex logical tasks. However, it
remains unclear whether RLVR truly expands a model's reasoning boundary or
merely amplifies high-reward outputs that the base model already knows for
improved precision. This study presents a theoretical and empirical
investigation that provides fresh insights into the potential limits of RLVR.
First, we offer a new theoretical perspective that RLVR is constrained by the
base model's support-unable to sample solutions with zero initial
probability-and operates as a conservative reweighting mechanism that may
restrict the discovery of entirely original solutions. We also identify an
entropy-reward tradeoff: while RLVR reliably enhances precision, it may
progressively narrow exploration and potentially overlook correct yet
underrepresented solutions. Extensive empirical experiments validate that while
RLVR consistently improves pass@1, the shrinkage of empirical support generally
outweighs the expansion of empirical support under larger sampling budgets,
failing to recover correct answers that were previously accessible to the base
model. Interestingly, we also observe that while RLVR sometimes increases
token-level entropy, resulting in greater uncertainty at each generation step,
answer-level entropy declines, indicating that these seemingly more uncertain
paths ultimately converge onto a smaller set of distinct answers. Taken
together, these findings reveal potential limits of RLVR in extending reasoning
horizons. Breaking this invisible leash may require future algorithmic
innovations such as explicit exploration mechanisms or hybrid strategies that
seed probability mass into underrepresented solution regions.