Understanding Diversity Collapse in RLVR via the Lens of Overtraining

• URL: http://arxiv.org/abs/2606.15455v1
• Date: Sat, 13 Jun 2026 20:13:37 GMT
• Title: Understanding Diversity Collapse in RLVR via the Lens of Overtraining
• Abstract summary: Reinforcement learning with verifiable rewards (RLVR) has become a key approach for enhancing the reasoning abilities of large language models.<n>We formalize this diversity collapse through the lens of emphovertraining<n>We propose emphBayesian Boundary Gating (BBG) which redirects optimization away from overtraining by estimating each problem's marginal contribution to the reasoning boundary.
• Score: 78.37408098404312
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Reinforcement learning with verifiable rewards (RLVR) has become a key approach for enhancing the reasoning abilities of large language models. However, RLVR often suffers from \emph{diversity collapse}: Pass@$1$ improves while high-$k$ Pass@$k$ degrades, which is viewed as a narrowing of the model's reasoning boundary. We formalize this diversity collapse through the lens of \emph{overtraining}: once a problem's contribution to the reference metric has effectively saturated, further updates no longer expand what the model can solve but still concentrate probability mass on the trajectories favored by on-policy sampling. Under a standard setup with few rollouts per problem, even a single observed success places a problem in a nearly saturated regime for high-$k$ Pass@$k$, so most updates in standard RLVR are overtraining from the boundary perspective. This perspective also suggests a reading of whether RLVR can expand the model's reasoning abilities beyond the base model: since RLVR is structurally biased against high-$k$ Pass@$k$, its aggregate decline does not by itself mean that no new reasoning gains occurred. Interventionally, restricting updates to problems with zero observed success lifts Pass@$256$ above the base model on difficult benchmarks; observationally, a non-trivial fraction of initially unsolvable problems become solvable during standard RLVR training. Building on these findings, we propose \emph{Bayesian Boundary Gating} (BBG), which redirects optimization away from overtraining by estimating each problem's marginal contribution to the reasoning boundary. Across multiple reasoning benchmarks, BBG improves average Pass@$k$ across a wide range of $k$.

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