Among the methods, hint-guided exploration -- not UFT's auxiliary loss -- drives hint gains, and replacing the critic's MSE loss with HL-Gauss cross-entropy is worth +14.4 points in-domain.
Abstract
Reinforcement learning for vision-language math reasoning starves under sparse reward: on a pool of 20,830 visual-math problems where Qwen2-VL-2B answers 3.6% of rollouts correctly, 85-97% of GRPO rollout groups are entirely wrong and contribute zero gradient. We train eleven methods under identical conditions in this regime, each injecting a different prior: text (reference-solution hints), distribution (on-policy distillation from a 7B teacher), and value (a value-pretrained critic with an MSE or HL-Gauss categorical loss). A prior helps exactly when it is delivered: the six arms whose prior effectively reaches the policy separate with no overlap from the remaining five -- the no-prior baseline and four arms whose prior is teacher-capped, gated away, or lost to a mis-parameterized critic -- both on the pooled in-domain metric and on cross-domain transfer (DynaMath). The central finding, however, concerns evaluation: one slice of the in-domain pool -- long used as this project's general-distribution check -- anti-correlates with genuine cross-domain transfer (Spearman rho = -0.74, n = 11 arms, permutation p = 0.011), while the hardest in-domain slice predicts it closely (rho = +0.89, p<0.001). We attribute the inversion to a near-chance multiple-choice subset that rewards models for not having changed; read through it, the best cross-domain method looked mediocre and the worst looked like the champion. Among the methods, hint-guided exploration -- not UFT's auxiliary loss -- drives hint gains, and replacing the critic's MSE loss with HL-Gauss cross-entropy is worth +14.4 points in-domain. All accuracies are blind-judged, with paired exact tests.
Noise-Contrastive GRPO is introduced, which injects scale-calibrated Gaussian noise into the last hidden layer of the prompt-encoding pass for half of each rollout group, branching those rollouts from a displaced departure state and integrates into a standard RLVR pipeline as a ~50-line change to the inference engine.
Michael M. Jerge, Joseph Pelczar, J. Downes· 0 citations
RSTG (Recovering Learning Signals via Adaptive Teacher Guidance), which applies distillation selectively and precisely where it matters most, and substantially outperforms naive GRPO+OPD.
Zhuo-Wen Han, Jinwei Xiao, Zhengxi Lu et al.· 4 citations
Desc descriptive evidence is provided that long-horizon multi-tool post-training can change ways of working that transfer beyond its training domain, and both software-engineering benchmarks improve despite the training collection containing no software-engineering tasks.
Sushant Mehta, Logan Ritchie, Liudas Panavas et al.· 0 citations
Reinforcement learning with verifiable rewards (RLVR) and on-policy distillation (OPD) have emerged as two dominant methods for post-training reasoning LLMs. Prior work uses OPD's dense token-level supervision to complement the sparse RL reward, fusing the two signals within a single step: either as a \emph{weighted-additive combination} or a \emph{teacher-modulated rescaling} of the RL advantage. In this paper, we show that a simple two-stage scheme, OPD-then-RL, consistently outperforms pure OPD, pure RLVR, and all such joint baselines across logic and math reasoning benchmarks. Beyond the empirical results, we further provide a systematic understanding of this through pass@$k$ behavior, learning dynamics, and parameter updates, yielding a consistent explanation: OPD expands the student's coverage of teacher-supported solutions and RL sharpens within that support, while jointly optimizing the two signals causes them to interfere. To provide a practical recipe, we find that the OPD validation score is the key signal for when to switch to RL, and that OPD is a better cold start for RL than SFT. Together, our results establish OPD-then-RL as a simple yet strong way to combine the two methods, turning two entangled signals into complementary stages.
Bo-Yang Li, Bingsen Chen, Cheng-Hao Yang et al.· 0 citations
Reinforcement learning from verifiable rewards (RLVR) drives chain-of-thought reasoning in large language models, yet its binary outcome reward cannot distinguish among correct trajectories. Existing dense reward alternatives, from surface heuristics to process reward models, either ignore the expert solutions already present in training corpora or require expensive offline annotation. We propose Gradient-Aligned Reward (GAR), which operates in the policy's own gradient space: truncated backpropagation through the output projection layer extracts a compact gradient vector for each rollout, and cosine similarity with an expert-anchor gradient yields a dense, reasoning-aware reward with less than 9% wall-clock overhead. We prove that this cosine admits a multiplicative decomposition into prediction-error and activation-pattern factors, providing a concrete characterization of what the alignment signal measures. On Qwen3-4B and Qwen3-8B, GAR consistently improves over GRPO and other baselines on competition-level math benchmarks and transfers to GPQA Diamond and MMLU-Pro without domain-specific data. Code and data are available at https://github.com/LQgdwind/GAR.
Le-Qi Zheng, Jin-Bo Su, Fang Niu et al.· 2 citations
Extensive experiments show that Distilled RL substantially outperforms standard RL and OPD in terms of both pass@1 and pass@k, and can effectively transfer previously unavailable knowledge from a teacher model to a student model.
Chen Wang, Zhaochun Li, Jionghao Bai et al.· arXiv.org· 2 citations
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