Beyond the Sampled Token: Preserving Candidate Support in RLVR
read the original abstract
We revisit exploration collapse in reinforcement learning with verifiable rewards (RLVR), from the perspective of the \emph{candidate distribution} for next-token prediction. We formally show that as probability concentrates on the top-$1$ candidate, the expected number of distinct responses collapses to one regardless of the sampling budget $K$. This theoretical implication is further verified by our empirical tracking of top-$N$ candidate probabilities during training, where the top-$1$ candidate progressively dominates while plausible alternatives are suppressed. These findings suggest a key desideratum for effective exploration: \emph{preserving non-negligible probability mass on the top-$N$ candidates}. To this end, we propose Candidate-aware Support Preservation (CaSP), with two complementary designs. Specifically, CaSP redistributes positive gradients among top-$N$ candidates for correct responses, and applies a stronger penalty to the top-$1$ candidate for incorrect responses. Unlike many exploration-oriented methods that improve pass@$K$ at the cost of pass@1, CaSP improves pass@$K$ across the full $K$ spectrum. These gains generalize to 6 math, 2 logical-reasoning, and 2 coding benchmarks, and scales to 32B-parameter models and sampling budgets up to $K=1024$, positioning it as a principled, candidate-level approach for RLVR exploration.
This paper has not been read by Pith yet.
Forward citations
Cited by 10 Pith papers
-
VISD: Enhancing Video Reasoning via Structured Self-Distillation
VISD improves VideoLLM reasoning performance and training efficiency by combining structured multi-dimensional self-distillation feedback with RL via direction-magnitude decoupling, curriculum scheduling, and EMA stab...
-
ResRL: Boosting LLM Reasoning via Negative Sample Projection Residual Reinforcement Learning
ResRL decouples shared semantics between positive and negative responses in LLM reinforcement learning via SVD-based projection residuals, outperforming baselines including NSR by up to 9.4% on math reasoning benchmarks.
-
On Advantage Estimates for Max@K Policy Gradients
Proposes MaxPO using a Leave-Two-Out baseline for centered unbiased advantages in max@K policy gradients, with a unified derivation of finite-batch estimators.
-
ResRL: Boosting LLM Reasoning via Negative Sample Projection Residual Reinforcement Learning
ResRL boosts LLM reasoning by modulating negative gradients with SVD-based projection residuals from negative samples, outperforming NSR by 9.4% Avg@16 on math benchmarks while preserving diversity across 12 tasks.
-
From $P(y|x)$ to $P(y)$: Investigating Reinforcement Learning in Pre-train Space
PreRL applies reward-driven updates to P(y) in pre-train space, uses Negative Sample Reinforcement to prune bad reasoning paths and boost reflection, and combines with standard RL in Dual Space RL to outperform baseli...
-
Calibration-Aware Policy Optimization for Reasoning LLMs
CAPO improves LLM calibration by up to 15% while matching or exceeding GRPO accuracy through logistic AUC loss and noise masking, enabling better abstention and scaling performance.
-
The Geometric Reasoner: Manifold-Informed Latent Foresight Search for Long-Context Reasoning
TGR performs manifold-informed latent foresight search to boost trajectory coverage in long-context reasoning tasks by up to 13 AUC points with minimal overhead.
-
VISD: Enhancing Video Reasoning via Structured Self-Distillation
VISD improves VideoLLM reasoning by adding multi-dimensional diagnostic self-distillation and RL decoupling, yielding higher accuracy, better grounding, and nearly 2x faster training convergence.
-
VISD: Enhancing Video Reasoning via Structured Self-Distillation
VISD adds structured privileged feedback from a judge model and a direction-magnitude decoupling trick to let VideoLLMs learn token-level credit assignment while keeping RL stable, yielding higher accuracy and roughly...
-
VISD: Enhancing Video Reasoning via Structured Self-Distillation
VISD proposes structured self-distillation with a multi-dimensional judge model and direction-magnitude decoupling to improve token-level credit assignment and convergence speed in VideoLLM reasoning training.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.