Understanding Diversity Collapse in RLVR via the Lens of Overtraining
Authors: Suqin Yuan, Jinkun Chen, Jiyang Zheng, Muyang Li, Lei Feng, Dadong Wang, Tao Xiang, Tongliang Liu, +1 more
Organizations: Sydney AI Centre, The University of Sydney · Southeast University · Microsoft · Data61, CSIRO · Chongqing University · Nanyang Technological University
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.
Reinforcement Learning with Verifiable Rewards (RLVR) has achieved substantial gains in single-attempt accuracy (Pass@1) on reasoning tasks, yet often suffers from reduced multi-sample coverage (Pass@K), indicating diversity collapse. We identify a structural cause for this degradation: common RLVR objectives, such as GRPO, are indifferent to how probability mass is distributed among correct solutions. Combined with stochastic training dynamics, this indifference induces a self-reinforcing collapse, in which probability mass concentrates on a narrow subset of correct outputs while alternative valid solutions are suppressed. We formalize this collapse mechanism and further characterize the optimal policy structure under two complementary criteria: robustness and entropy-regularized optimality, which identify the Uniform-Correct Policy as uniquely optimal. Motivated by this analysis, we propose Uniform-Correct Policy Optimization (UCPO), a modification to GRPO that adds a conditional uniformity penalty on the policy's distribution over correct solutions. The penalty redistributes gradient signal toward underrepresented correct responses, encouraging uniform allocation of probability mass within the correct set. Across three models (1.5B-7B parameters) and five mathematical reasoning benchmarks, UCPO improves Pass@K and diversity while maintaining competitive Pass@1, achieving up to +10% absolute improvement on AIME24 at Pass@64 and up to 45% higher equation-level diversity within the correct set. The code is available at https://github.com/AnamikaLochab/UCPO.
Reinforcement Learning with Verifiable Rewards (RLVR) trains reasoning models without labeled trajectories, relying on grouped rollouts to expose the policy to alternative reasoning paths and a verifier to score them. Rollout diversity has accordingly emerged as a central bottleneck in RLVR, with most existing methods broadening exploration through temperature, prefix, or rollout-selection adjustments. We identify a structurally distinguished but overlooked position for broadening this diversity: the first token after the reasoning marker. The policy's first-token distribution exhibits a sharply peaked yet correctness-decoupled phenomenon, and this first token position can broaden the regions a rollout group covers without altering the correctness signal. We introduce REFT (Rollout Exploration with First-Token Diversification), a light addition to the RLVR pipeline that samples first tokens uniformly from the policy's own top-N candidates and allocates rollouts evenly, leaving every other component unchanged. Trained on the resulting diversified rollouts, REFT improves aggregate Pass@1, Pass@8, and Pass@64 over DAPO and GRPO baselines across four base models (0.5B-7B) and three difficulty regimes.
Recent studies observe that reinforcement learning with verifiable rewards (RLVR) reliably improves pass@1 on reasoning tasks, yet often fails to yield comparable gains in pass@k, raising the question of whether RLVR genuinely enables large language models to acquire novel reasoning abilities or merely enhances the efficiency of sampling reasoning modes already present in the base model. Prior analyses largely support the latter view, attributing this limitation to structural properties of standard RLVR objectives that result in insufficient exploration pressure. In this work, we argue that a central structural constraint arises from reverse-KL regularization, which stabilizes training but inherently anchors the policy to the reference distribution, thereby suppressing the emergence of alternative reasoning modes. However, we show that neither removing the KL term nor replacing it with forward-KL provides a satisfactory solution, as both disrupt the efficiency-coverage trade-off by either inducing reward hacking or allocating probability mass to off-target regions. To resolve this tension, we propose SAGE, a principled framework that enables controllable empirical support expansion by reshaping the reverse-KL anchor distribution itself through a guide function q(x,y), achieving consistent improvements in both pass@1 and pass@k across challenging mathematical reasoning benchmarks. Our code is available at https://github.com/tally0818/SAGE.