ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models
Authors: Mingjie Liu
Shizhe Diao
Ximing Lu
Jian Hu
Xin Dong
Yejin Choi
Jan Kautz
Yi Dong
Venue: NeurIPS 2025 poster ()
Keywords: Large Languge Models
Reasoning
Reinforcement Learning
Primary area: deep_learning

Abstract: Recent advances in reasoning-centric language models have highlighted reinforcement learning (RL) as a promising method for aligning models with verifiable rewards. However, it remains contentious whether RL truly expands a model’s reasoning capabilities or merely amplifies high-reward outputs already latent in the base model’s distribution, and whether continually scaling up RL compute reliably leads to improved reasoning performance. In this work, we challenge prevailing assumptions by demonstrating that prolonged RL (ProRL) training can uncover novel reasoning strategies that are inaccessible to base models, even under extensive sampling. We introduce ProRL, a novel training methodology that incorporates KL divergence control, reference policy resetting, and a diverse suite of tasks. Our empirical analysis reveals that RL-trained models consistently outperform base models across a wide range of pass@$k$ evaluations, including scenarios where base models fail entirely regardless of the number of attempts. We further show that reasoning boundary improvements correlates strongly with task competence of base model and training duration, suggesting that RL can explore and populate new regions of solution space over time.  These findings offer new insights into the conditions under which RL meaningfully expands reasoning boundaries in language models and establish a foundation for future work on long-horizon RL for reasoning. We will release model weights and data to support further research.

ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models
Mingjie Liu
Shizhe Diao Yejin Choi
Ximing Lu Jan Kautz NVIDIA
Jian Hu Xin Dong
Yi Dong
{mingjiel, sdiao, ximingl, jianh, xind, yejine, jkautz, yidong)@nvidia.com
Abstract
Recent advances in reasoning- centric language models have highlighted reinforce- ment learning (RL) as promising method for aligning models with verifiable rewards. However, it remains contentious whether RL truly expands model's s reasoning capabilities merely amplifies high-reward outputs already latent in the base model's ss distribution, and whether continually scaling up RL compute reliably leads to improved reasoning performance. this work, we challenge prevailing assumptions by demonstrating that prolonged RL (ProRL) training can uncover novel reasoning strategies that are inaccessible to base models, even under exten- sive sampling. We introduce ProRL, novel training methodology that incorporates KL divergence control, reference policy resetting, and a diverse suite of tasks. Our empirical analysis reveals that RL-trained models consistently outperform base models across a wide range of pass @ & evaluations, including scenarios where base models fail entirely regardless of the number of attempts. We further show that reasoning boundary improvements correlates strongly with task competence base model and training duration, suggesting that RL explore and populate new regions of solution space over time. These findings offer new insights into the conditions under which RL meaningfully expands reasoning boundaries in language models and establish foundation for future work on long-horizon RL for reasoning. We release model weights support further research:
1.5B
Introduction
Recent advances in reasoning-focused language models, exemplified by OpenAI-O1 [ and DeepScek-R1 (2), have marked paradigm shift in artificial intelligence by scaling test-time com- putation. Specifically, test-time scaling enables long-form Chain-of- Thhough (CoT) thinking and induces sophisticated reasoning behaviors, leading to remarkable improvements
complex tasks such as mathematical problem solving [3 and code generation 77 8). By continuously expending compute throughout the reasoning process via exploration, verification, and backtracking muetracking-models models boost their performance at the cost of generating longer reasoning traces.
At the heart of these advances lies reinforcement learning (RL), which has become instrumental in developing sophisticated reasoning capabilities. By optimizing against verifiable objective rewards rather than learned reward models, RL-based systems can mitigate the pitfalls of reward hacking 19] I1 and align more closely with correct reasoning processes. However, a fundamental question remains under active debate within the research community: Does reinforcement learning truly
39th Conference on Neural Information Processing Systems (NeurIPS 2025).

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Passd] Reset PoRk
0.6
0.4
02
Guegtan
10
Training Stepe (Lag Scale)
Deadiot 10
Figure 1: Benefits of prolonged reinforcement learning (ProRL). Left: Pass@ and Pass@ 16 scales with ProRL training. Middle: ProRL leads to more novel solutions reflected by higher Creativity Index 12 Right: Our model greatly surpass base model across diverse tasks.
unlock new reasoning capabilities from base model, or does it merely optimize the sampling efficiency of solutions already embedded in the base model?
Recent studies [3 argues for the latter, claiming that RL-trained models do not acquire new reasoning capabilities beyond what exists in their base models based on pass @ k metrics. We posit that these conclusions may stem from methodological constraints rather than fundamental limitations of RL approaches themselves. Specifically, we identify two key limitations in existing research: (1)
an overreliance on specialized domains like mathematics, where models are often overtrained during both pre-training and post-training phases, thereby restricting the potential for exploration; and (2)
the premature termination of RI training before models can fully explore and develop new reasoning capabilities based on limited amount of RL training. typically no more than hundreds of steps [13
In this study, we address these limitations through several key contributions. First, we introduce ProRL, recipe designed to enable extended RL training periods that facilitate deeper exploration of reasoning strategies. It enables more than 2k training steps and scale the training data across diverse masks-from traditional math and code tasks to STEM problems, logical puzzles, and in- struction following, which, we hypothesize, are crucial for generalization. Using ProRL, we de- veloped SenetroonnReseeah--Reeess
-.r.iin-..ee....B.. the world's best 1.5B reasoning model and matches or even surpasses
that significantly outperforms its base model, SeepSeek--R11-55 the performance of DeepSeek-R1177 across diverse range of benchmarks. Notably, compared to DeepSeck-RI-1.55 we achieve average pass @1 improvements of 14.7% on math benchmarks. 13.9% on coding, 54.8% on logic puzzles, 25.1% on STEM reasoning, and 18.1 1 % on instruction followinng tasks (Figure Right), More importantly. ProRL demonstrates continued performance improvements after an unprecedented 2k training steps (Figure Left), suggesting that RL training scales effectively with increased compute.
Furthermore, Nemotron- Researche-eee-eeeeee--eeeeeeeeee Reaaarchn--a Qwen- 1.5B offers surprising new insights RL can indeed discover genuinely new solution pathways entirely absent in base models, when given sufficient training time and applied novel reasoning lasks. Through comprehensive analysis, show that our model generates novel insights and performs exceptionally well on tasks with increasingly difficult and out-of-domain tasks, suggesting a genuine expansion of reasoning capabilities beyond its initial training. Most strikingly, we identify many tasks where the base model fails to produce any correct solutions regardless of the amount of sampling, while our RL-trained model achieves 100% pass rates (Figure 4). Interestingly, we find the amount of gain from RL on each task is predictable given the base model's performance RLL expands model's 's reasoning boundary most effectively in domains where the base model initially struggles. Moreover, we quantify the novelty of the model's s reasoning trajectories using the Creativity Index [12], which measures the amount of overlap with pretraining corpus. We find that prolonged RL training leads to trajectories with higher novelty (Figure I Middle), indicating the emergence of new reasoning patterns during RI.
Our findings hold significant implications for the broader Al community, demonstrating that RI. approaches can indeed enhance model capabilities without requiring additional training data. Through sustained exploration, models can develop new knowledge and reasoning strategies that potentially exceed human insights. This work reaffirms the value of reinforcement learning as pathway toward more capable and generalizable Al systems, challenging previous assumptions about the inherent limitations of these approaches.

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2 ProRL: Prolonged Reinforcement Learning
We begin with brief overview of the GRPO [66] algorithm. We then address key challenges in prolonged RL training, such as entropy collapse and instability, by introducing a KL divergence penalty and periodic resets of the reference policy. This ensures stable training across many epochs and continued performance improvement.
2.1 Background: Group Relative Policy Optimization
We adopt Group Relative Policy Optimization (GRPO) [16] the core RL algorithm. Compared with Proximal Policy Optimization (PPO) [17], it removes the value model and instead use baseline estimates based on group scores. Formally the GRPO maximizes the following objective:
(o) ET min (ro(T)A(T), clip(ro(7), sip(oo(t).--_1++eA))))))))))
(1)
where 7 is the response sampled from the current policy Tg. ro(T)
Tota(T) is the probability ratio
se(r)
between the current policy and old policy before each actor update. The advantage used in GRPO
foregoese the critic model of PPO, and instead estimates baseline from group scores (Rehe))))
A(r) Ps -mean (Ra
std( Ra hEa(t))
2.2 Prolonged Reinforcement Learning (ProRL)
2.2.1 Mitigating Entropy Collapse
A key challenge in prolonged policy optimization is entropy collapse, phenomenon where the model's output distribution becomes overly peaked early training, resulting in sharply reduced entropy. When entropy collapses, the policy prematurely commits to narrow set of outputs, severely limiting exploration. This is particularly detrimental in methods like GRPO, where the learning signal depends on having a diverse set of sampled outputs to effectively estimate relative advantages. Without sufficient exploration, policy updates become biased, leading to stagnation in training.
common mitigation strategy is to increase the sampling temperature during rollouts. However, we find that this approach only delays the onset of entropy collapse rather than preventing altogether, as entropy continues to decline steadily as training progresses. Nonethenless, we did employ high rollout temperature since encourages exploration by increasing the initial entropy.
2.3 Decoupled Clip and Dynamic Sampling Policy Optimization (DAPO)
To address entropy collapse, we adopt several components from the DAPO algorithm 4 which are specifically designed to maintain exploration and output diversity, First, DAPO introduces decoupled clipping, where the lower and upper clipping bounds in the PPO objective are treated as separate hyperparameters:
clip(ra(T), 1 Cow, + Chigh).
(3)
By setting higher value for Ehigh, the algorithm promotes 'clip-higher,, uplifting the probabilities of previously unlikely tokens encouraging broader exploration. We find that this modification helps retain entropy and reduces premature mode collapse.
Additionally, DAPO employs dynamic sampling. filtering out prompts for which the model consis- tently succeeds or fails (i.e., accuracy 1 or 0), as these provide no learning signal. This focus on intermediate difficulty examples further helps maintain a diverse learning signal during training.
2.3.1 KL Regularization and Reference Policy Reset
While DAPO and temperature adjustment help slow entropy collapse, we find that explicit regular- ization via KL divergence penalty provides stronger and more stable solution. Specifically, incorporate KL penalty between the current policy σe and a reference policy Tref:
LKL-RL(O) LGRPO (0) 3Dxl (Ta ( Tre)))
(4)
3

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This penalty not only helps maintain entropy but also serves as regularizer to prevent the online policy from drifting too far from stable reference, stabilizing learning and mitigating overfitting to spurious reward signals.
Recent works 4 18] have argued for the removal of the KI. penalty, citing that models naturally diverge during training on chain-of -ftouughtthhhht reasoning tasks. We observe that this perspective often applies base models prior to any supervised fine-tuning. In contrast, begin from a well-initialized checkpoint (DeepSeek-RI SeepSeee-RI-Distlllle --iistill--wenn---- 1.5B) already capable of generating coherent CoT outputs. In this context, retaining KL penalty is still beneficial for both stability and sustained entropy.
We further observe that as training progresses, the KL term may increasingly dominate the loss, leading to diminishing policy updates. To alleviate this, we introduce simple yet effective technique: reference policy reset. Periodically, we hard-reset the reference policy Tref to a more recent snapshot of the online policy Te, and reinitialize the optimizer states. This allows the model to continue improving while maintaining the benefits of KI. regularization. We apply this reset strategy throughout training avoid premature convergence and encourage prolonged training.
3
The World's Best 1.5B
Reasoning Model
We present Nemotron Reshonnn-eeeeechh--ee Research-Reasooingg Qwen- 1.5B, a generalist model trained via reinforcement learning diverse, verifiable dataset of 136K problems across math, code, STEM, logic puzzles, and instruction following. Leveraging stable reward computation, improved GRPO, and prolonged training, our model achieves strong generalization across domains. It outperforms DeepSeek-R. -11 Distill-Qwen-1.3 by +15.7% on math, + 14.4% on code, +25.9% on STEM, +22.0% on instruction following, and +54.8% text-based logic puzzles, Reasoning Gym [19]. It also surpasses domain- specialized baselines in both math (+4.6%) and code (+6.5%), demonstrating the effectiveness of generalist prolonged RL training.
3.1 Training Dataset
We construct a diverse and verifiable training dataset spanning 136K examples five task domains, math, code, STEM, logical puzzles, and instruction following, to enable robust reinforcement learning from a wide range of reasoning problems. Each task type is paired with a clear reward signal (binary or continuous), allowing for reliable feedback during training. This broad task coverage encourages generalization beyond narrow domains and enables meaningful comparison of RL. algorithms across diverse reward structures. Details on the composition of training dataset is presented in Appendix E
3.2 Training Setup
We use verl 20 for reinforcement learning training. We adopt enhancements of GRPO (16) proposed
by DAPO 4 decoupling clipping hyperparameters with clow 0.2, Enigh 0.4, and dynamic sampling for filtering prompts that are too easy or difficult (with accuracy equal rollout, we sample n = 16 responses for each prompt with context window limit of 8096 and use high sampling temperature of 1.2. We set batch size to 256 and mini-batch size 64 (equating to gradient updates per rollout step). For training we use the AdamW W (2T) optimizer with a constant learning rate of 10-6 We conduct training on 4 x NVIDIA- 80GB nodes, and the whole training runs for approximately 16k GPUs hours.
and 0). For
3.3 ProRL Training Dynamics
To enable effective long-horizon reinforcement learning, we monitor training progress using a blended validation set derived from the evaluation benchmark. When validation performance stagnates or degrades, we perform hard reset of the reference model and optimizer. This not only restores training stability but also facilitates greater policy divergence from the base model. Throughout most of training, we cap response length at 8k tokens to maintain concise and stable generations. In the final stage (-200 steps), we increase the context window to 16k tokens, observing that the model adapts quickly and achieves measurable improvements. We detail our training recipe in Appendix F

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Table 1: Performance (pass @ comparison for benchmarks across Math domain. The best results are highlighted in bold. The results of DeepSeek-RI RI-Distill Peiisiil-QQee---- 7B are marked as gray and are provided as a reference (same in following tables).
Model
AIME24
AIME25
AMC
Math
Minerva
Olympiad
Avg
DeepSeck- R1- R1-Distill-O S1--Dstll-QQen--.33
28.54
22.71
62.58
82.90
26.38
43.58
44.45
DeepScaleR-1.55
40.21
31.46
73.04
89.36
41.57
$1.63
54.54
DeepSeek RI- 1--istill--ween-7
53.54
40.83
82.83
93.68
50.60
57.66
63.19
Nemotron Research Rewearch-RRassennngg-eeeee- -eeasnning-Qwen-..88
48.13
33,33
79.29
91.89
47.98
60.22
60.14
Table 2: Performance (pass @ 1) comparison across benchmarks for Code. We abbreviate benchmarks names for codecontests (cc), codeforces (cf), humanevalplus (human), and livecodebench (LCB).
Model
apps
cc
cf
taco
human
LCB
Avg
-aais---ttiitssli--eeeeeee DeepCoder-1.55 DeepSeek-RL-Disttil--Weeee
20.95
16.79
14.13
8.03
61.77
16.80
23.08
30.37
23.76
21.70
13.76
73.40
22.76
30.96
42.08
32.76
33.08
19.08
83.32
38.04
41.39
Nemotton-Reeaarc--Rccssonnnnnng
41.99
31.80
34.50
20.81
72.05
23.81
37.49
Table 3: Performance comparison STEM reasoning (GPQA Diamond), instruction following (IFEval), and logic puzzles (Reasoning Gym) tasks. We also present results on OOD tasks: acre, boxnet, and game of life halting (game).
Model
GPQA
IFEval
Reasoning
acre
boxnet
DeepScek-RI R1- 1-DistilDl 1-iiiiill--lll-
15.86
44.05
4.24
5.99
0.00
3.49
DeepSeek- I-Distill -wenr-BB
35.44
58.01
28.55
20.21
1.71
12.94
Nemotron- Somotron-Rescarch -wattg---een5555
41.78
66.02
59.06
58.57
7.91
52.29
Figure 2 illustrates key statistics on training dynam- ies over the course of extended reinforcement learn- ing across multiple stages. The application of var- ious enhancements proposed by DAPO 4 along with the inclusion of KL divergence loss, helped the model avoid entropy collapse. Although we observe positive correlation between average response length and validation scores, this factor does not ap- pear to be decisive, as there are training stages where performance improves without requiring longer re- sponses. Meanwhile, the validation performance, measured by both pass@1 and pass@ 16, consis- tently improved and scaled with increased training computation.
Runa
7003
Resporsio Lenighh
5003
Entrops
5003
600
2500
Training Steps
Figure ProRL training dynamics.
3.4 Evaluation
Evaluation Benchmarks. We evaluate models the breadth of various tasks across math, coding, reasoning, and instruction following. For math, we follow DeepScaleR K and SimpleRL, [22). and
evaluate on AIME2024 (23), AIME2025 24 AMC (25 (composed of AMC2022 and AMC2023),
MATH 26). Minerva Math (27). and Olympiad Bench (28 For coding, we use the validation set
from PRIME 22 consisted of APPS [30]. Codecontests [1]], Codeforee and TACO [32]. We also
include benchmarks HumanevalPlus
33 and LiveCodeBenchh [34], For logic puzzles, we reserved
100 samples from each reasoning gym
tasks test datasets for evaluation. addition, we use
curated subse from GPQA Diamond
35 and IFEval
33 to evaluate the capability of our models
in STEM reasoning and instruction following
[37
http://waggaaccccce/eeee///sssss Srt Submissions
http:r/wwngggageeecccc///sttetts ClaudeRR1

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Evaluation Settings. We use vllm [3] as the inference backend, with a sampling temperature of 0.6, nucleus sampling (39 with top_p- 0.95 and maximum response length of 32k. For math, coding. and STEM reasoning tasks, we obtain estimates of pass@I from 16 samples for each benchmark prompt from strictly binary rewards. For other tasks (logical puzzles and instruction following), we calculate the average continuous reward score from our rule-based verifiers. We evaluate and report benchmark results for open-source models using our own evaluation settings.
Evaluation Results. We provide a detailed comparison between -eeeSeee-RI--isiil-ONee- 1wen-1.5B and our final model Nemotron- -emmtrro-Researcch-ee Research-Reasoning Qwen-1.5B across multiple domains. the math domain shown in T our model consistently outperforms the base model across benchmarks, showing an average improvement of 15.7%. For code domain results shown in Table our final model surpasses the base model in competitive programming tasks as measured by pass@1 1 accuracy by 14.4%. Our model also demonstrates substantial gains in STEM reasoning and instruction following, with improvements of 25.9% on GPQA Diamond and 22.0% on IFEval. Our model achieves high accuracy on Reasoning Gym logic puzzles after training. despite the base model struggles with formatting and challenging subtasks, improving reward by 54.8%. Even compared to much larger model, DeepSeek-RR -wr-SSee-----isill----- 1--issill--Qen-77B, our model achieves comparable or even better performance across multiple domains.
Generalization OOD Tasks. In Table we also present results on out out-of-disttibution (OOD) tasks in Reasoning Gym. Our model shows significant improvements on three OOD tasks, demonstrating stronger generalization beyond the training distribution. This highlights the effectiveness of our training approach in enabling the model to adapt and perform well on unseen challenges.
Comparision with Domain-Specializzd Models. We compare the performance of Nemotron- with two domain-specializeed baselines: DeepScaleR-I.5B (3], tailored for mathematical reasoning, and DeepCoder-I.5B (7). focused on competitive programming tasks. Our ProRL trained model enables strong generalization, achieving superior pass@ I scores on both math (+4.6%) and code (+6.5%) benchmarks. Additionaly, ProRL enables deeper exploration and refinement within limited response length, where prior works often increase training response length too early, causing "overthinking" [40] with verbose reasoning.
4 Analysis: Does ProRL Elicit New Reasoning Patterns?
To evaluate whether prolonged ProRL training enhances reasoning beyond the base model, we increase inference sam- ples to 256 and re-evaluate performance. Due to compute limits, we randomly se- lect 18 Reasoning Gym tasks (out of 96) and re-run all other benchmarks: math, code, STEM reasoning. and instruction following. We compare the base model (DeepSeck-RI-De 1-Distilled-1155D diate checkpoint, and Nemotron-Reseer Research- Reasoning-
Oul morie
Cok
elive rings
Lnver (.833)
Basa Model Phr10133
an interme-
Figure 3: Left: ProRL expands a model's 's reasoning boundary most effectively tasks where the base model initially struggles. Right: Tasks with minimal gains Post-RL. highlighted in the eircle tend to have lower creativity index, indicating higher overlap with pretraining data.
Qwen-1.5B Muasoning-Qwen--.BBB ter extended training).
(the final model af-
4.1 The Weaker the Start, the Stronger the Gain with ProRL
A key finding from our study is that the effectiveness of RL in expanding a model's reasoning boundary (measured by pass @ 128) is strongly influenced by the base model's initial capabilities. As shown in Figure3) 3 we observe a significant negative correlation between the base model's reasoning boundary and the extent of reasoning improvement after RL training. Specifically, tasks where the base model already performs well (i.e., high pass@ @ 128) tend to exhibit minimal or even negative gains in reasoning breadth RL. This indicates a narrowing of the reasoning boundary, where the model becomes more confident in subset of solutions it already understands, rather than exploring new reasoning patterns. In contrast, in domains where the base model struggles, particularly those with low initial pass@ @ 128, RL training is most effective. Here, ProRL not only improves pass @ 1,

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but also expands the model's ability to explore and succeed in broader range of reasoning paths. To further confirm our intuition that tasks with minimal gains post-RL are those the base model is familiar with, we compute the creativity index [41] of the base model's responses for each task against the largest open-soure pretraining corpus, DOLMA [42]. The creativity index quantifies the degree of overlap between model's responses and the some math and code tasks highlighted in the
circle-tend to have lower creativity indices, suggesting the base model has seen large amount of similar data during pretraining.
4.2 Unpacking ProRL's 's Reasoning Boundaries: Diminish, Plateau, and Sustained Gains
We analyze performance trends on individual benchmarks and categorize them based on how pass @ evolves throughout training. Our analysis reveals that reinforcement learning can meaningfully expand a model's reasoning capacity, particularly on challenging tasks that extend beyond the capability of the base model. While some tasks exhibit early saturation or even regressions in reasoning breadth, we also observe clear instances where the model's reasoning capabilities expand with continued training. Most notably, on some domains such as code generation, ProRL enables continued gains, suggesting that prolonged training allows the model to explore and internalize more sophisticated reasoning patterns. This demonstrates that, under the right conditions, ProRL can push the frontier of a model's reasoning abilities beyond what the base model achieves.
muth pe
destcade beccddeech bords
Reacting
Diminish
Cra
120
Plateau
Desaless Crenial
Eoep ppont
600
Sustained
cls 1:8 Pradion costome1
Seaarin by 1-8 Sirrrmniio
Figure Pass @ comparison of the base model, an intermediate checkpoint, and the final RL-trained models. Trends are grouped into three regimes: (1) Diminish: reduced diversity due to narrow output distributions; (2) Plateau: early RL saturation of gains in reasoning boundary; and (3) Sustained: continued reasoning boundary improvement with prolonged training.
Diminished Reasoning Boundary In some benchmarks (particularly in the math domain). Nemotron- Rescarch-Reasoning Reasoning-Qweerrr 1.5B exhibit decreased unchanged reasoning capacity compared to the base model, aligning with observations of prior work [3]. Although pass@ improves, the pass @ 128 score, which reflects broader reasoning ability. often declines. These tasks tend to have high baseline pass @ 128, suggesting that the base model already possesses sufficient reasoning ability, and RL training merely sharpens the output distribution the expense of exploration and generality.
Gains Platcau with RL For these tasks, RL training boosts both pass@ and pass@ 128, indicating improved reasoning. However, these gains are largely achieved early in training. Comparing the intermediate and final checkpoints shows that ProRI. offers negligible additional benefit, implying that the model quickly saturates its learning potential for these tasks.
7

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Sustained Gains from ProRL In contrast, some benchmarks, particularly more complex ones such as coding, Nemotron-Reseann
Deassning--wwen-LSBB Qwen- show continued improvements in reasoning capacity with prolonged RI. training. These tasks likely require extensive exploration of diverse problem instances during training to generalize effectively to the test set. In such cases, ProRI. expands the model's reasoning boundaries.
4.3 ProRL Enhances Out-of- Distriiittiittionn Reasoning
We focus on how ProRL influences the model's ability to generalize beyond the distribution of its training data. These studies aim to isolate the role of extended RL updates in expanding the model's reasoning boundaries, especially structurally novel semantically challenging tasks that encountered during initial training.
Out-of-Distributie (OOD) Task We evaluate the model Reasoning Gym task boxeet, which was not seen during training. As shown in Figure (Check Appendix D.3 for example), the base model exhibits no capability of solving the task. In contrast, the model trained with ProRL demonstrates significant ability to solve the problem, indicating clear expansion in the model's ' rea- soning boundary, generalizing
beanet Da
1-B leck
zxc
-i-----ddisiitttionn tasks unseen during training. Furthermore, when comparing an intermediate RI. checkpoint with the final prolonged RI. model, we observe that extended training sustains and amplifies performance gains consistently across all values of k. These results further support the conclusion that ProRL enables the model to internalize ab- stract reasoning patterns that generalize beyond specific training distributions or complexity levels.
0201
105
550
500
1.59
1000
Figure 5: Expanded reasoning boundary for OOD task boxnet.
Increased Task Difficulty We evaluate performance across vary- ing levels of task difficulty for graph_coll task (Check Ap- pendix [ for an example) by generating graph problems with different numbers of graph nodes. While the training data only includes graphs of size 10, we test on larger graphs assess generalization beyond the training regime. Figure 6 plots the pass@ I (solid lines) and pass@ 128 (dashed lines) across differ- ent models. The results reveal consistent decline in performance as task difficulty increases, which is expected given the combi- natorial growth in solution space. However, our prolonged RL model maintains significantly higher accuracy across all graph sizes compared to both the base and intermediate models. This indicates that extended RI updates not only enhance pass@1 on in-distribution tasks but also improve the model's 's robustness to more complex, unseen scenarios.
Figure 6: ProRL generalizes to increased task difficulty on graph_colas
4.4 How Does @ @1 1 Distributions Evolve as ProRL Progresses?
Dang derived mathematical upper bound for pass @ k as:
Er [pass@k]] < 1 ((1 (e.))=)l==)) + Var(p=)) 4/2
(5)
where Pa represents the pass@) accuracy for task æ. While increasing expected pass@) 1 raises this upper bound, higher variance reduces it. In contrast 114 's observation of declining pass @ during training, our results in Figure I demonstrate ddgunredeeoosttrate continuous improvement in both pass 1 and pass@ 16, reproducing the scaling law patterns reported for OpenAI Ol's RL training 443 Our ProRL approach generates substantial performance gains across diverse tasks. Figures a) and b illustrate significant rightward distribution shifts in code and logic puzzle tasks. Initially concentrated near zero with extended tails, the pass@) @ distributions evolved markedly after training. Codeforces problems exhibit broader distribution patterns post-training, while the family_red relationships task (Appendix
Drrendix(D.2fieee D.2 for an example), which is a novel reasoming challenge, demonstrate a dramatic shift from predominantly zero accuracy to peaking at perfect accuracy, indicating successful solution discovery across the majority of prompts. These pronounced distribution changes, driven by extended RI. training, produce sufficient improvement expected pass @ to overcome any negative effects from increased variance.
8

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(a) Codeforces
familyy relationships
Figure Distribution shifts pass accuracy following prolonged RL training across two representative tasks. The figure illustrates the evolution of pass@) probability distributions for selected tasks from code (a) codeforees, and reasoning domains (b) family relationships.
Related Work
Reasoning Models Reasoning models represent specialized category of Al systems that engage in detailed, long chain-of- of-thought before generating final answers, a concept first introduced by OpenAl's series models [4]. Subsequently, DeepSeek [2 and Kimi 455 detail methodologies for training reasoning models using reinforcement learning with verifiable rewards (RLVR). Both approaches have popularized RL algorithms like GRPO [16), Mirror Descent[46), RLOO and other variants. While numerous open-source efforts have attempted to reproduce ol-like models,
6 or study test-time compute scaling [48), with few addressing prolonged reinforcement learning training examining RL training time scaling laws. As widely acknowledged in the reinforcement learning community, RL training presents significant challenges due to its sensitivity to hyperparameters [49]. Various reinforcement learning techniques [5] have been studied enhance training stability for sustained optimization periods. Our research demonstrates that achieving prolonged RL training substantially expand the boundaries of reasoning capabilities these models.
most focus on single domains 3
RL Reasoning Boundary Achieving superhuman performance has been the holy grail of machine learning, with reinforcement learning algorithms successfully delivering on this expectation, starting with DeepQ networks for Atari games [50|5] 51). More recently, AlphaGo and AlphaZero [52) have
demonstrated that AI agents can enhance their performance indefinitely by continuously iterating between data collection via Monte Carlo Tree Search and policy improvement. These examples show that RL training helps agents develop novel techniques not present in their base models (53)57]. However, challenging this perspective, several recent studies question whether RL training genuinely enhances the reasoning capacity of LLMs. One work 13 argue that the RLVR method fails to extend this capacity, as evidenced by pass @ k metrics showing improvement and in some cases deterioration. compared to the base model, a trend echoed by other researchers [4]. Similarly, another work [15] finds that RI algorithms tend converge toward dominant output distribution, merely amplifying existing pretraining patterns. Beyond pass@1 k metrics, alternative measurements like creativity index [12) also determine whether models learn ideas through RL training,
which we employ during our studies.
Conclusion
In this work, we address whether reinforcement learning can truly expand language models' reasoning boundaries. Through our introduction of ProRL, we provide compelling evidence that extended, stable RL training develops novel reasoning patterns beyond a base model's initial capabilities. ProRL incorporates KL divergence penalties and periodic reference policy resets to maintain training stability over long durations. Using this approach, we developed sfate-of-the generalist reasoning model trained on diverse datasets spanning mathematics, coding, STEM, logical puzzles, and instruction following tasks. Our analysis reveals ProRL is particularly effective tasks where the base model initially struggles. Most importantly, ProRI. enables strong generalization to duit---diittibuttoo tasks and increasingly complex problems, demonstrating that extended RI. training helps models internalize abstract reasoning patterns transferable beyond the training distribution.
1.5B parameter

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These results challenge previous assumptions about RL's limitations and establish that sufficient training time with appropriate techniques can meaningfully expand reasoning boundaries, providing valuable direction for development of more capable reasoning models.
Acknowledgments
We sincerely thank Shrimai Prabhumoye for the insightful discussions that significantly inspired our work. We are also grateful Sahil Jain for sharing his perspectives on addressing entropy collapse. Additionally, we thank Makesh Narsimhan Sreedhar and David Mosallanezhad for their assistance with running several model evaluations.
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A Detailed Ablation Studies
We refer readers to our technical report 58 for detailed ablation studies, including analyses of hyperparameters and policy resets. Additional results on training with different base models and scaling larger models and compute are provided our updated blog post (59].
B Limitations
Despite the impressive results achieved by our ProRL approach, several important limitations should be acknowledged:
Computational Resources The extended RL training process requires substantial computational resources, which may be prohibitive for smaller organizations or researchers with limited budgets. Our approach involves multiple training stages with periodic resets, long reasoning chains sampling further intensifying these requirements.
Scalability Concerns While we demonstrate effective training of 1.5B parameter model, remains unclear how well our approach scales to larger models. The increase in computational requirements becomes more pronounced with larger parameter counts.
Training Process Challenges Our approach requires periodic hard-resets of the reference policy and optimizer parameters to maintain training stability. This introduces additional complexity to the training process and may lead to inconsistent results compared to more stable training methods.
Limited Task Scope While our evaluation covers diverse domains, the training dataset still repre- sents only subset of possible reasoning tasks. The performance certain cuttr--distribution tasks shows promising generalization, but we cannot guarantee similar improvements across all potential reasoning domains not explicitly included in our training evaluation.
C Societal Impacts
The development of Prolonged Reinforcement Learning (ProRL) has significant implications for both the Al research community and society at large. By enhancing reasoning capabilities of language models across domains, this approach creates both opportunities and challenges that warrant careful consideration.
Potential Benefits and Opportunities ProRL demonstrates that current RL methodology can po- tentailly achieve superhuman reasoning capabilities when provided with sufficient compute resources. Our trained smaller 1.5B parameter models, democratizes access to advanced AI capabilities for individuals, researchers, and organizations with limited computational resources. This accessibility is particularly valuable in educational settings where resource constraints often limit the adoption of large-scale AI systems. Our approach offers significant social benefits through its cost-effectiveness, reduced energy consumption, and lower computational requirements compared larger models, making advanced reasoning capabilities available to a much wider audience. As shown in our analysis, tasks with low initial performance often exhibit sustained gains through extended training, creating opportunities to address reasoning challenges in critical domains like healthcare, climate science, and accessibility technologies. Small but powerful models can be deployed on-premises with enhanced security and privacy protections, making them suitable for sensitive applications in financial, legal, and healthcare sectors. Furthermore. these models' adaptability and lower latency make them ideal for real-time applications like AI teaching assistants, scientific research support, and specialized problem-solving tools that can significantly enhance human productivity across multiple domains.
Ethical Considerations and Challenges Despite these opportunities, ProRL introduces important ethical considerations that require careful governance. The substantial training computational require- ments may exacerbate resource inequality in Al development, while enhanced reasoning capabiliitess could enable more sophisticated misuse deployed without appropriate safeguards. As these sys- tems transition from no capability to high capability in certain reasoning tasks, ongoing monitoring
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becomes essential to anticipate emergent behaviors and potential risks. Future work should combine ProRL techniques with explicit value alignment approaches, while developing dynamic evaluation benchmarks that evolve alongside model capabilities to ensure comprehensive assessment of both progress and risks across different contexts and communities.
D Example Prompts
D.1 Graph Color Example
Graph Color Example:
Question: Please provide coloring for this graph such that every vertex is not connected to vertex of the color. The graph has these properties:
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] Edges: [(o, 1), (0, 7), (0, 9), (1, 4), (2, 4), (3, 5)
(3, 6), (6, 8), (7, 9)]
Possible colors: [1, 2, 3]
Return your solution as a JSON map of vertices to colors.
(For example: {"0": 1, "1": 2, "2": 3}.)
D.2 Family Relationships Example
Family Relationships Example: Question: John is married to Isabella. They have child called Edward. Edward is married to Victoria.
What is Isabella to Edward? Respond only with the word that describes their relationship.
D.3 Boxnet Example
Question:
You are a central planner tasked with directing agents in grid-like field to move colored boxes to their corresponding color-coded targets.
Each agent occupies ix1 square and can only interact with objects within its square. Agents can move a box to an adjacent square or directly to target square of the same color. A square may contain multiple boxes and targets. The squares are identified by their center coordinates (e.g., square(0.5, 0.5l). Actions move (box_color, destination), where vox_color is the color of the box and destination is either target of the same color an adjacent square. Your objective is to create a sequence of action plans that instructs each agent to match all boxes to their color-coded targets in the most efficient manner.
formatted as:
Please adhere to the following rules when specifying your action plan: Single Action per Agent: Assign only action each agent at time. However, the final ansver shoule be a list of action plans for multiple steps
1.
2. Unique Agent Keys: Use unique keys for each agent the JSON format action plan. The key should be the agent's coordinates in the format "Agent(x [x, y]".
3. Prioritize Matching Boxes to Targets: Always prioritize actions that will match box to its target over moving box to an adjacent square.
4. Sequential Action Planning: The whole returned answer should be list of action plans for multiple steps, do not just return one step plan. Clear Formatting: Ensure the action plan clearly formatted in JSON, with each agent's action specified as a key-value pair.
Conflict Resolution: Ensure that no two agents are assigned actions that would interfere with each other.
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7. Optimize Efficiency: Aim to minimize the number of moves required to match all boxes with their targets.
Here format for your action plan:
Please provide your final answer as a list of action dictionaries. For example: 'sjsonn
[{"Agent [0.5, 0.5]": "move blue, square 1.5])",
"Agent[1.3 (1.5, 0.5]": "move (box target_red) ("Agent [0.5, 1.5] "; "move bbuu_blue, target_blue)", "Agent [2.5, 0.5] ": "move...); [.......]
Include agent in the action plan only if it has task to perform next.
The current left boxes and agents are:
Agent(o.3. 0.5] I am in [0.5r 0.5], I can observe ['boo_red', 'target_red', 'box_blue" 'target_blue blue', 'box_green', Starget_green'ss I can do (box__ee__ square (0.5, 1.5])', 'move (box_red, target_red) 'move bboe_blue, square[0.5, 1.5])', 'move (box_ blue, target_blue)', 'move (box_green, square[0.8 5, 1.5)),, 'move (box_green, target_green)
Agent 5, 1.5] I am in square (0.5, 1.5], I can observe [], I can do 0
E Training Dataset
We scale training across a wide spectrum of tasks that provide verifiable reward signals with details in Table 4 These tasks span from traditional reasoning domains, such as mathematical problem solving and code generation, to more complex and open-ended domains, including STEM-related problem solving, logical puzzles, and instruction following. The inclusion of such diverse task set serves two key purposes. First, it broadens the model's exposure to wide distribution of reasoning patterns, encouraging generalization beyond narrow, domain domain-specific behaviors. This especially critical for developing models of adapting to new unseen task formulations. Second, the task diversity enables more rigorous evaluation of RL algorithms, as it tests their ability to learn robust decision-making strategies across fundamentally different environments and reward structures.
Table 4: Overview of training data used in our experiments, categorized by domain, reward type (binary or continuous), dataset size, and source. The datasets span a range of reasoning, coding, STEM, and mnstruction-followee tasks.
Data Type
Reward Type
Quantity
Data Source
Math
Binary
40k
DeepScaleR Dataset
Code
Continuous
24k
Eurus-2-RL. Dataset
STEM
Binary
25k
SCP-116K Dataset
Logical Puzzles
Continuous
37k
Reasoning Gym
Instruction Following
Continuous
10k
Llama-Nemotron
E.1 Math
We use high-quality. community-curated datasets made available through DeepScaleR B.. The training set consists of 40K math problems sourced from diverse range of national and international math competitions. We adopt DeepScaleR's 's original verifier and further augment with an improved math-verify[] We obtain the LLM's answers by prompting the model with Let's think step by step and output the final answer within \boxed(). We use a binary reward signal, assigning a score of if the LLM's response passes either the original or the enhanced math- math-verify. and 0 otherwise (for incorrect or improperly formatted answers).
http::///gtabbbooo//hgggggggggg
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E.2
Code
We utilize publicly available reinforcement learning datasets comprising 24K coding problems 22 sourced from various programming competitions. To support continuous reward feedback, we improve code execution environment to run all test cases rather than terminating on the first error and assign rewards based on the fraction of test cases passed. Submissions that fail to compile, contain syntax errors, or exceed a second total timcout are assigned a reward of zero. We also include instructions for the LLM to enclose its final code response with triple backticks.
E.3 STEM
We use SCP-116K 160. a large-scale dataset containing 274k scientific problem-solution pairs spanning diverse fields such physics, chemistry, biology, and mathematics. Each problem is accompanied by a corresponding solution extracted from the original source text, along with model- generated responses and reasoning paths produced by DeepSeek-RI. Given that CCP-116K was automatically extracted from heterogeneous and potentially noisy sources, we applied rigorous data filtering. First, removed problems lacking retrievable ground-truth solution from the source text. Then, we employed GPT-4o as judge to assess whether the DeepSeck-RR R1 response aligned with the ground truth answer. Only problems with consistent answers were retained, reducing the dataset from the original entries to 25K.
E.4 Logical Puzzles (Reasoning Gym)
The logical puzzles are well-suited for reasoning model training due to their broad coverage of different reasoning skills, well as their clear objectives and evaluation metrics. We utilize the Reasoning Gym projec which offers approximately 100 tasks across various domains, including algebra, arithmetic, computation, cognition, geometry, graph theory, logic, and popular games. To facilitate model training and evaluation, we generate a large dataset consisting 37K synthetic training samples and 9600 validation samples, spanning 96 tasks. Notably, solution, whereas others, such as the Rubik's 's Cube and Countdown, admit multiple correct solutions. We employ the verifier provided by the Reasoning Gym repository for both model evaluation and reinforcement learning training signals. We use recommended default prompts which instruct models enclose answers between <answer> </answer> tags.
tasks have unique
E,5 Instruction Following
To enhance our model's 's cnttuuctionfollowiiin capabilities, we leverage synthetic generated data from Alama-Nemotron [6] which data format is similar to IFEval (37). Specifically the dataset contains synthetic prompts that pair tasks with randomly chosen instructions. For instance, a prompt may ask the model to "Write an essay about machine learning", while the instruction specifies, "Your response should have three paragraphs." We do not add further instructions on formatting and obtain the models response after thinking (</think> token).
F Training Recipe
Training Monitoring. We construct validation data blend to closely monitor training progress across steps. This validation set includes subsets from evaluation benchmark, specifically AIME2024, Codeforces, GPQA-diamont IFEval, and the logic puzzle graph _cclorrcorrroooo from Reasoning Gym. We evaluate model performance using similar sampling parameters as in evaluation settings (other than we use the same context window as in training).
Reference Model and Optimizer Reset. Occasionally, we perform a hard reset of the reference model and optimizer, described in Section Se3tion particularly when validation metrics significantly degrade when improvements plateau. Interestingly, the hard reset not only restores training stability but also provides an opportunity to adjust training hyperparameters and introduce enhancements such as additional training data and reward shaping. Figure presents KI. divergence across training runs. The final training recipe comprises several sequential stages, described the following.
gym
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0.32
Tesset fo
Fioi addidd
0.20
Read
Ran?
Rand
Bard
Divergence
0:04
0.62
0.20
500
2000
1500
2000 2500
Training Steps
Figure 8: KL divergence across training runs. We periodically reset the reference policy and optimizer
state during training.
Run 1: We begin training on four tasks from Appendix E. We did not include instruction- following data as it was not available to us initially. In this phase, we limit the response length 8k where the base model's sequential length is 128k to avoild long sequence rollouts. As shown in Figure 2 increasing along with improved validation scores. Toward the end of this stage, we observe instability and degradation in validation performance.
model response length first decreases shortly and then keeps
We perform hard reset of the reference policy and resume training with the same setup as Run 1. Unlike DeepScaleR [3. which proposes increasing the maximum response length, maintain the maximum response length as 8k because we observe that 8k maximum length is sufficient for the model to learn and improve its validation scores.
Run 2:
Run 3: We incorporate instruction-folllnt following data into the training mix and continue training. This stage proceeds until we observe sudden increase in response length, primarily due to the model repeating answers and failing terminate with <eos> token.
We introduce reward shaping by penalizing responses that do not terminate correctly. This encourages proper generation behavior, resulting in a modest reduction in response length.
Run and 5:
Runs 6 and 7: We increase the rollout count from 16 to 32, performing two hard resets in the process. Interestingly, response length begins to rise again alongside improvements in validation metrics.
Run 8: We extend the context window to 16k tokens and reduce rollout count to 16. Despite the model being trained on an 8k context window for most the time, it quickly adapts to the extended context window. We observe marginal improvements in hard math tasks like AIME, with more substantial gains coming from other domains.
G
Results Details
G.1
Reasoning Gym
For logic puzzles in the Reasoning Gym suite, we adopt the categorization of 96 tasks as defined by the official GitHub repository. We show category performance details of our model in Table 5 Notably,
underperforms even on relatively simple mathematical tasks such algebra and arithmetic. Closer inspection reveals that the model consistently formats its answers using \boxed{(] rather than adhering to the instruction to use <answer> </answer> tags. Despite poor initial formatting behavior, the model able to achieve high accuracy on these easier tasks post training, suggesting that formatting is relatively easy to learn. Our models still exhibit room for improvement on more challenging categories, including tasks from arc, code, cognition, and games. In these cases, the model often fails to make meaningful progress. Further analysis indicates that these failures stem from either a lack of core reasoning skills necessary to solve specific subtasks or insufficient background knowledge related to the problem domains. Addressing these limitations
RI-Distilll-Qwe
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Table 5: Detailed Reasoning Gym performance across all subcategories. Our model demonstrates superior performance across all reasoning tasks compared to both DeepSeek models.
Reusoning Gym Performance (Part
algebra
algorithmic
arc
arithmetic
cognition
games
DeepSeck RI Distill Qwen-1.50
0.73
3.56
1.53
5.36
1.22
6.47
2.34
DeepSeek-RR Riei---RRDDDDiii---- EEt-iitiil--wee---- Qw
21.75
55.43
Nemotron Research Reasoning Qwen-I. 1.5B
97.21
53,90
2.52
82.81
29.84
40.16
26.38
Reasoning Gym Performance (Part 2)
Model
geonehry
graphs
induction
logic
Avg
DeepSeck-RR & R1-Distil-Qwea-1.53
1.05
6.64
1.32
10.90
4.24
DeepSeck RI Distill Qwen-
17.38
33,29
29.31
34.96
28.55
Nemotron Research Reasoning- Qwen- 1,5B
89.84
66.49
73.50
82.94
59.06
may require additional finetuning data better support model from cold start, which we leave these enhancements to future work.
G.2
Pass @k Comparisions
We share pass@k k comparision plots across 3 models for all evaluated tasks. Due to compute resource limitations, we randomly select subset of tasks from reasoning gym.
G.3
Pass@1 Distribution Shifts
We share pass @1 I distribution shifts for all evaluated tasks. Due to compute resource limitations, randomly select subset of tasks from reasoning gym.
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Figure Pass@k for tasks in Math.
google B3553
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Figure 10: Pass@k for IFEval, GPQA, and Out-of-Distribuiit (OOD) tasks.
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codelbmee pArKRE
120
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211
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830
Compteab Ower 100
360
150
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Figure 11: Pass@k for tasks in Code.
911 cope PANNO
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gnph cibo 18 passes
Bathh cdlir 20 p3500k
Reabon caarsdaion uas
100
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1000
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080
Figure 12: Pass for additional varying difficulty (number of nodes) in graph__clor. Default used training 10 nodes.
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advanced OrOO OA
CAAD PAL
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283
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10
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100
baystokk D3024
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2114
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440
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Figure 13: @ass@k for tasks in Reasoning Gym.
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Figure 14: @ distribution for tasks Math.
Figure 15: @ass@1 distribution for IFEval, GPQA, and Out-of- titt----istrbutiin (OOD) tasks.
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Figure 16: Pass distribution for tasks Code.
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Figure 17: P distribution for tasks Reasoning Gym.
34


Reviews:
[{"review_id": "IWc86UV8x6", "reviewer": "Reviewer_TrB6", "summary": "Authors demonstrate that with prolonged tuning LM using RL with verifiable rewards can actually lead to better generalization in a wide range of domains. Tuned model demonstrates higher performance, bigger amount of novel solutions and better generalizability to OOD tasks.", "questions": "1) Please address as many weaknesses as possible. I hope I provided enough guidance for that. The core one is the weakness (1).\n2) Figure 1 (middle) demonstrates that base model produces some amount of outliers which score much higher in terms of creativity compared to samples after RL finetuning. What are those outliers? Are those just random garbage? And do you have any hypothesis why we don't see those for RL model?\n3) Is any weight decay used? AdamW is used as optimizer, however no weight decay parameter is mentioned. I would also recommend to report all the hyperparamters in the form of a table in Appendix and not as parts of the text.", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "# Strengths \n1) Authors provide recipe for stable prolonged RL finetuning which includes KL regularization with hard update of the reference model, decoupled $\\epsilon$ parameters for GRPO objective and specific schedule which involves various alterations over the training process.\n2) Tuned model significantly outperforms base model on a wide range of tasks and better adapts to the OOD problems. It is worth mentioning that tuned 1.5B model (based on 1.5B DeepSeek-R1) works on-par with 7B DeepSeek-R1.\n3) The work challenges claims from recent works which say that RL does not actually improve reasoning capabilities of the base model but only improves sampling. This work shows that in domains different from math this might not be the case.\n\n# Weaknesses\n1) The main goal of the work is to demonstrate that tuning LMs using RL with verifiable rewards is a good methodology. And it is demonstrated that for the challenging setups (where the base model struggled) RL tuning actually helps. I personally would be much more surprised if it was not the case. However, authors do not provide any additional baselines. If I understand correctly, base model was not trained on the data which is used for finetuning. But what if improvements come from just seeing the novel tasks during finetuning? I think that adding experiments with other tuning techniques is a **must-have** part of such research. E.g. using supervised tuning if reference reasoning trails are available for benchmarks, running language modeling over just the input tasks if reference solutions are not available or generating reasoning samples from stronger model, using DPO with things mentioned before. I doubt that supervised tuning or DPO with limited samples will demonstrate that strong performance, however those are more stable and much less cheaper in terms of compute. Anyway, I will struggle a lot to recommend this paper for publication without such baselines.\n2) No ablation study is presented for the proposed approach. Authors alternate several things in GRPO pipeline such as decoupling $\\epsilon$ hyperparameters, adding reference model (and optimizer reset) hard reset and non-trivial changes over the course of the training. That many changes should be carefully analyzed so further works could use pipeline confidently. No analysis on hyperparameters sensitivity as well.\n3) No analysis on the various model sizes. While I understand that it potentially requires a lot of compute it would be nice to see the same behavior over varying base model sizes, e.g. DeepSeek-R1 7B and 14B.\n4) It would be also interesting to see whether RL saturates at some point or not. Figure 1 (left) demonstrates that performance improvement requires exponential training time scale. But I would highly appreciate to see further tuning results (starting from the latest available checkpoint) if authors have resources for that.\n5) (Formating) Font sizes should be increased for the most of the figures. It is hard to read figures now.", "was_revised": true, "final_justification": "Authors resolved most of my concerns", "rebuttal": "Thank you for your review and suggestions. We hope the following responses could clarify your concerns.\n\n\n1. *Additional baseline request such as SFT or DPO*\n\n\nThank you for the suggestion. Our main contribution is to provide empirical analysis in demonstrating the benefits of prolonged reinforcement learning in expanding the reasoning boundary and uncovering novel reasoning strategies inaccessible to the base model. Such results are in fact not as straightforward, especially works targeting RLVR, since numerous concurrent works have argued otherwise. We hope our paper can bring forth more discussion within the research community on the benefits (or lack thereof) of prolonged RL on LLMs.\n\n\nWe do agree that providing additional baselines would greatly strengthen our argument on the increased benefit of scaling Reinforcement Learning. Since the concern seems to be particularly centered on novel tasks outside the capabilities of the base model, we decide to focus on tasks within the Reasoning Gym suite. As per your recommendations, we used a stronger base model DeepSeek-R1-Distilled-Qwen-32B model to generate reasoning traces and used verifiers to filter negative samples. We constructed a finetuning dataset of ~200k verified responses. We further collected additional negative responses across the same dataset, constructing a preference dataset of ~200k entries for DPO finetuning. We conduct SFT and DPO for ~2 epochs using DeepSeek-R1-Distilled-Qwen-1.5B as the base model. We will make sure to include these additional baselines in our paper and details on the training setups etc. We provide only the following results for brevity:\n\n\n|       Model      | algebra | algorithmic |  arc | arithmetic |  code | cognition | games | geometry | graphs | induction | logic |  Avg  |\n|:----------------:|:-------:|:-----------:|:----:|:----------:|:-----:|:---------:|:-----:|:--------:|:------:|:---------:|:-----:|:-----:|\n| DeepSeek-R1-1.5B |   0.73  |     3.56    | 1.53 |    5.36    |  1.22 |    6.47   |  2.34 |   1.05   |  6.64  |    1.32   | 10.90 |  4.24 |\n|  ProRL-1.5B (2k) |  97.21  |    53.90    | 2.52 |    82.81   | 29.84 |   40.16   | 26.38 |   89.84  |  66.49 |   73.50   | 82.94 | 59.06 |\n|     SFT-1.5B     |  51.18  |    25.65    | 1.48 |    64.18   |  1.35 |   39.13   | 17.64 |   65.13  |  35.63 |   60.59   | 41.21 | 35.81 |\n|     DPO-1.5B     |  48.61  |    24.29    | 1.53 |    62.76   |  0.88 |   37.37   | 15.64 |   64.12  |  32.92 |   58.47   | 38.63 | 34.15 |\n\n\n\n\n\n\n\n\n2. *No ablation study is presented for the proposed approach.*\n\n\nWe did conduct careful small scale ablation studies on our alternations of the GRPO pipeline, including decoupling  hyperparameters, adding reference model (and optimizer reset) hard reset. We apologize for not including such experiment details.\n\n\n**We will be providing an additional detailed technical report alongside the final version of the paper.** Unfortunately the conference review process prohibits sharing additional documents or figures, thus we are only able to provide brief text descriptions on the ablation studies and key observations as follows:\n\n\n2.1 Rollout Sampling Temperature\n\n\nAblations with temperatures {0.6, 1.2} show that low temperature (0.6) causes early instability, reduced diversity, and overexploitation, hurting reward and validation. High temperature (1.2) yields steadier improvement, better generalization, and avoids mode collapse even in late-stage training, so we use 1.2 throughout.\n\n\n2.2 Decoupled Clipping\n\n\nWe vary ϵlow {0.1, 0.2} and ϵhigh​ {0.2, 0.3, 0.4}; ϵlow=0.2 better handles negative advantage, and ϵhigh=0.4 prevents entropy collapse, giving best validation. Smaller ϵlow increases entropy but not learning, so we adopt (0.2, 0.4).\n\n\n2.3 Dynamic Sampling\n\n\nWe further verified that dynamic sampling led to faster improvements than static sampling by filtering out prompts with zero advantage. This increases reward signal density in each batch, thereby improving the overall sample efficiency of training.\n\n\n2.4 Resetting Reference Policy\n\n\nWe observe that extending training with the same setting and training hyperparameters does not always lead to consistent improvements. We observed that by simply extending the training or Run1 (this is the DAPO baseline) without reference policy reset, it encounters a sharp drop in validation scores on the Codeforces benchmark. We were not able to scale RL training beyond 600 steps with DAPO, and in contrast resetting the reference policy allowed us to scale training to beyond 2k steps.\n\n\n2.5 Mitigating Entropy Collapse\n\n\nWe conducted a series of ablation studies evaluating the training dynamics under different strategies to mitigate entropy collapse. We investigated the following settings:\n\n\n- GRPO-KL=0: We employ standard GRPO training without KL divergence penalty or entropy bonus.\n\n\n- GRPO-KL=1e-4: We apply a small KL regularization term 1e-4 to control the divergence between the online policy and a reference policy. This helps prevent the model from drifting too far and encourages continued exploration.\n\n\n- DAPO: This is the DAPO baseline with decoupled clipping and dynamic sampling. No KL divergence penalty or entropy bonus.\n\n\nWe observe that GRPO-KL=0 suffers from entropy collapse and the validation score stops improving after the entropy degrades to ~0 in ~500 steps. In contrast, DAPO and KL penalty both can mitigate entropy collapse as the validation scores continue to improve. Based on these findings, we adopt a combination of DAPO and a KL penalty in our final training setup.\n\n\n3. *No analysis on the various model sizes.*\n\n\nWe conduct further experiments by applying our training recipe to a larger model and different base model. We use Llama-3.1-Nemotron-Nano-8B-v1, which is a derivative based on llama-3.1-8B-Instruct, further finetuned on diverse reasoning tasks. Due to time constraints and compute limitations, we only scale training to ~1.4k steps. We provide detailed comparison with the base model across tasks as follows\n| Model                         | Math  | Code  | GPQA  | IFEval | Reasoning Gym |  \n|-------------------------------|-------|-------|-------|--------|---------------|\n| Llama-3.1-Nemotron-Nano-8B-v1 | 68.26 | 61.20 | 52.76 |  66.88 |     12.15     |\n| ProRL-8B                      | 71.98 | 72.80 | 55.52 |  70.94 |     77.23     |\n\n\nNote: The above reported results on Code only consists of {apps, condecontests, codeforces, taco} and report the obtained continuous reward. All other benchmarks are the same as in the paper.\n\n\n4. *Further scaled training results*\n\n\nWe were able to further scale training for an additional 1k steps to a total 3k steps. We compare the new model with the original 2k model in our paper as follows:\n| Model                         | Math  | Code  | GPQA  | IFEval | Reasoning Gym |  \n|-------------------------------|-------|-------|-------|--------|---------------|\n| ProRL-2k  | 60.14 | 37.49 | 41.78 |  66.02 |     59.06     |\n| ProRL-3k  | 61.69 | 41.03 | 41.32 |  70.85 |     62.49     |\n\n\nAs shown above, prolonged RL continues to bring improved performance across most tasks, with only GPQA as an exception.\n\n\n5. *Font sizes should be increased for the most of the figures*\n\n\nWe apologize for the inconvenience and will take this into consideration when revising the final paper.\n\n\n6. *Figure 1 (middle) demonstrates that base model produces some amount of outliers which score much higher in terms of creativity compared to samples after RL finetuning. What are those outliers? Are those just random garbage? And do you have any hypothesis why we don't see those for RL model?*\n\n\nThanks for the great observation! The base model sometimes produces outliers with much higher creativity indices, likely because these tasks are highly out-of-distribution—unseen during the base model’s training and unfamiliar to it, such as the dice task in Reasoning Gym, which has near-zero pass@1 accuracy. After RL training, the model learns to handle these tasks (e.g., the dice task's pass@1 accuracy improves to 39.9%), making them more in-domain for the model.\n\n\n7. *Is any weight decay used? AdamW is used as an optimizer, however no weight decay parameter is mentioned. I would also recommend to report all the hyperparameters in the form of a table in Appendix and not as parts of the text.*\n\n\nWe use a weight decay of 0.01. We will include detailed hyperparameter configurations in the Appendix for our final version."}, {"review_id": "VkJt5545EW", "reviewer": "Reviewer_Dkqj", "summary": "This work examines reinforcement learning for reasoning and attempts to show that it does indeed genuinely extend the base model's reasoning ability. The authors goal is to question a number of recent papers which claim that reinforcement learning merely improves search of the existing base model's reasoning space.  The authors show that there are a number of methodological problems with these other papers (they have overfit on pretraining/finetuning and their RL and crucially they have terminated prematurely) They then propose a prolonged RL recipe ProRL which fixes these problems.  Elements of this recipe include diverse training data, and mitigating entropy collapse with high sampling temperature and more flexible clipping of the PPO objective, and finally KL regularisation with hard resets.  They then show that with this recipe they can train in a stable fashion for much longer, reaching up to 2000 steps. The have extensive experiments where they show that with ProRL they can increase the boundary of the model's reasoning ability (as measured by accuracy @ 128). They show improvements in overall reasoning accuracy across many tasks covering maths, code and stem problems. The provide interesting analyses on when this extended RL training helps and when it does not.", "questions": "Questions\n\t1) DeepScaler, DeepCoder in Tables 1 and 2 are not explained. \n\t2) I suggest you use the same colours for the models in both Figure 5 and Figure 6 for easing understanding - a somewhat ironic suggestion for a task called \"graph colour\" :)", "limitations": "Yes - Limitations were well described and indeed there are a number of significant limitations including limited model size - we don't know how well this will scale to larger models.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\t1) The authors identify problems with existing research methodology which claims that RL does not increase the model's ability to reason. \n\t2) They propose a recipe that allows RL to provide improvements throughout prolonged RL training. \n\t3) They have extensive experiments showing the benefit of their recipe. \n\t4) They do analysis that show what types of conditions are necessary for prologued training to help (difficult tasks) or hinder (simpler or overfitted tasks) \n\nWeaknesses: \n\t1) No ablation studies - what part of the recipe made all the difference in performance? Are all pieces equally necessary? At least some discussion of this is warrented. \n\t2) The methods proposed are not particularly novel - however the value of the paper is in the insight into the problems in methodology of other RL papers, and finding a recipe that fixes these problems. I do not this this is a major flaw. \n\t3) Why stop at 2000? Figure 1 shows continued improvement although I am sure you had a stopping criteria. Is further exploration of the reasoning space impossible? Some discussion of the limits would be good. \n\t4) How do you know if your task is going to benefit from extended RL? Would you need task specific stopping criteria? This does not seem ideal if you have many different tasks with different inherent complexities.", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for the feedback and acknowledgement of our work. We hope the following responses could clarify your concerns.\n\n\n1. *No ablation studies.*\n\n\nWe did conduct careful small scale ablation studies on our alternations of the GRPO pipeline, including decoupling  hyperparameters, adding reference model (and optimizer reset) hard reset. We apologize for not including such experiment details.\n\n\n**We will be providing an additional detailed technical report alongside the final version of the paper.** Unfortunately the conference review process prohibits sharing additional documents, thus we are only able to provide brief text descriptions on the ablation studies and key observations as follows:\n\n\n1.1 Rollout Sampling Temperature\n\n\nAblations with temperatures {0.6, 1.2} show that low temperature (0.6) causes early instability, reduced diversity, and overexploitation, hurting reward and validation. High temperature (1.2) yields steadier improvement, better generalization, and avoids mode collapse even in late-stage training, so we use 1.2 throughout.\n\n\n1.2 Decoupled Clipping\n\n\nWe vary ϵlow {0.1, 0.2} and ϵhigh​ {0.2, 0.3, 0.4}; ϵlow=0.2 better handles negative advantage, and ϵhigh=0.4 prevents entropy collapse, giving best validation. Smaller ϵlow increases entropy but not learning, so we adopt (0.2, 0.4).\n\n\n1.3 Dynamic Sampling\n\n\nWe further verified that dynamic sampling led to faster improvements than static sampling by filtering out prompts with zero advantage. This increases reward signal density in each batch, thereby improving the overall sample efficiency of training.\n\n\n1.4 Resetting Reference Policy\n\n\nWe observe that extending training with the same setting and training hyperparameters does not always lead to consistent improvements. We observed that by simply extending the training or Run1 (this is the DAPO baseline) without reference policy reset, it encounters a sharp drop in validation scores on the Codeforces benchmark. We were not able to scale RL training beyond 600 steps with DAPO, and in contrast resetting the reference policy allowed us to scale training to beyond 2k steps.\n\n\n1.5 Mitigating Entropy Collapse\n\n\nWe conducted a series of ablation studies evaluating the training dynamics under different strategies to mitigate entropy collapse. We investigated the following settings:\n\n\n- GRPO-KL=0: We employ standard GRPO training without KL divergence penalty or entropy bonus.\n\n\n- GRPO-KL=1e-4: We apply a small KL regularization term 1e-4 to control the divergence between the online policy and a reference policy. This helps prevent the model from drifting too far and encourages continued exploration.\n\n\n- DAPO: This is the DAPO baseline with decoupled clipping and dynamic sampling. No KL divergence penalty or entropy bonus.\n\n\nWe observe that GRPO-KL=0 suffers from entropy collapse and the validation score stops improving after the entropy degrades to ~0 in ~500 steps. In contrast, DAPO and KL penalty both can mitigate entropy collapse as the validation scores continue to improve. Based on these findings, we adopt a combination of DAPO and a KL penalty in our final training setup.\n\n\n2. *Why stop at 2000 steps.*\n\n\nWe stopped at 2k steps largely due to resource limitations and time constraints. We were able to further scale training for an additional 1k steps to a total 3k steps. We compare the new model with the original 2k model in our paper as follows:\n| Model                         | Math  | Code  | GPQA  | IFEval | Reasoning Gym |  \n|-------------------------------|-------|-------|-------|--------|---------------|\n| ProRL-2k  | 60.14 | 37.49 | 41.78 |  66.02 |     59.06     |\n| ProRL-3k  | 61.69 | 41.03 | 41.32 |  70.85 |     62.49     |\n\n\nAs shown above, prolonged RL continues to bring improved performance across most tasks. Since we largely observe log-linear scaling, linear growth in the performance translates to exponential training computation. Furthermore data might be another limitation, as dynamic sampling will filter easy tasks (with pass rate of 1). We also provided a Limitations section in the Appendix.\n\n\n3. *How do you know if your task is going to benefit from extended RL? Would you need task specific stopping criteria?*\n\n\nIn our experimental observations, all five tasks are generally suitable for ProRL. However, some tasks—such as those related to Code—show more noticeable and consistent improvement, while tasks in the MATH category improve more slowly. We do not impose a stopping criteria, as dynamic sampling removes too easy and too difficult problems from training. We do agree that having a stopping criteria (such as if the validation scores reach beyond a certain threshold) would greatly improve the efficiency of dynamic sampling.\n\n\n4. *DeepScaler, DeepCoder in Tables 1 and 2 are not explained.*\n\n\nWe included text descriptions under \"Comparison with Domain-Specialized Mdoels”:\n“We compare the performance of NemotronResearch-Reasoning-Qwen-1.5B with two domain-specialized baselines: DeepScaleR-1.5B [3], tailored for mathematical reasoning, and DeepCoder-1.5B [7], focused on competitive programming tasks.”\nWe will also include the related citations in the Table for clarity.\n\n\n5. *I suggest you use the same colours for the models in both Figure 5 and Figure 6 for easing understanding*\n\n\nThank you for pointing this out. We will keep colours of models consistent for Figure 5 and 6 in the final version."}, {"review_id": "ihylirqzAC", "reviewer": "Reviewer_SYom", "summary": "This paper sheds some light on the training dynamics of GRPO for reasoning models. The authors present a really comprehensive study where they first identify problems in the training dynamics due to entropy collapse during prolonged training. Previous literature have used KL regularizers to mitigate this issue, however, the authors find that this only slows the occurrence of this issue. Therefore, they propose an hard reset of the reference policy which is useful to smooth down the training. The authors apply this new training recipe to the base model DeepSeek-R1-1.5B and are able to substantially outperform it on several benchmarks. \n\nThis paper represents a great contribution to the community and provides important insights into current best practices in using RL for LLMs.", "questions": "1. I was wondering how the solution proposed by this paper compares with current real-world implementations of GRPO such as TRL (from Huggingface). For instance, they explicitly mention the following:\n\n\n> Note that compared to the original formulation in DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models, we use β = 0.0 by default, meaning that the KL divergence term is not used. This choice is motivated by several recent studies (e.g., Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model) which have shown that the KL divergence term is not essential for training with GRPO. As a result, it has become common practice to exclude it (e.g. Understanding R1-Zero-Like Training: A Critical Perspective, DAPO: An Open-Source LLM Reinforcement Learning System at Scale).\n\n2. How do you determine when the model stagnates? Do you have a way to determine this automatically? This would be interesting to understand more deeply, considering that it might have an effect on how these results can generalise to other model families.\n\n3. I find Figure 4 a bit confusing. Specifically, I'm not sure how to concretely read it considering that all the trends are very similar across the different categories. \n\n4. Did you notice any specific difference in performance between tasks that have binary or continuous rewards?", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "### Strengths\n\n1. Really well-written paper which includes a detailed background as well as a detailed analysis of the experiments. \n2. The authors present an interesting training regime that mitigates important issues in current RL training for reasoning models with a particular focus on entropy collapse. \n3. The training regime is applied only to DeepSeek-R1 and showcases an impressive boost in performance not only on mathematical reasoning but also on code, instruction following and logic puzzles. In my opinion, this represents the most important contribution of this paper. \n4. The paper provides a lot of insights into the training dynamics of these training regimes. Particularly, they study how ProRL improves the performance and the ability to elicit new reasoning patterns.\n\n### Weaknesses\n\nI really liked the paper and I think it represents an important contribution for the community. However, I would like to point out some weaknesses that this work might have and that I believe might help researchers make more informed decisions in the future. I list them below:\n\n1. It's not clear what the impact of the selection of the base model is. At the moment, the authors start from DeepSeek-R1, which presumably is already skilled in producing reasoning chains. I appreciate that running these experiments is a big endeavour and I wonder whether the authors have explored what happens when starting from a base instruction-tuned model like Llama or Qwen.\n\n2. It is not clear to me how the authors determine when the model stagnates. Based on Section 3.3, this seems to be a manual process and therefore might be very model-specific. I think it would be useful to report this point in the limitations or, in general, it would be useful to be explicit about the limitations of this training regime.", "was_revised": true, "final_justification": "I think this is a great paper which explores a really important research question in the space of reasoning models. I thank the reviewers for providing additional details on this paper. I think that the authors should focus their attention on reporting these details in their manuscript to clearly highlight the main contribution and the scope of the work. For instance, I think that it's important to highlight that this work focuses on further improving a reasoning model, so it assumes that the starting point of their training regime is already quite good. Additionally, reporting more details regarding the training and how they monitor the training is essential. I would suggest the authors implement this in two ways: 1) release your code with clear indications regarding how to reproduce your training runs; 2) release some logbooks that showcase when the authors detected specific faulty runs or situations where their model was stagnating.", "rebuttal": "Thank you for the feedback and acknowledgement of our work. We hope the following responses could clarify your concerns.\n\n\n1. *I wonder whether the authors have explored what happens when starting from a base instruction-tuned model like Llama or Qwen.*\n\n\nThank you for the question. We primarily wanted to experiment whether RL can bring improvements to already strong reasoning models. We thus leave research on scaling RL from non-reasoning models as an open question for future research.\n\n\nWe conduct further experiments by applying our training recipe to a larger model and different base model. We use Llama-3.1-Nemotron-Nano-8B-v1, which is a derivative based on llama-3.1-8B-Instruct, further finetuned on diverse reasoning tasks. Due to time constraints and compute limitations, we only scale training to ~1.4k steps. We provide detailed comparison with the base model across tasks as follows\n| Model                         | Math  | Code  | GPQA  | IFEval | Reasoning Gym |  \n|-------------------------------|-------|-------|-------|--------|---------------|\n| Llama-3.1-Nemotron-Nano-8B-v1 | 68.26 | 61.20 | 52.76 |  66.88 |     12.15     |\n| ProRL-8B                      | 71.98 | 72.80 | 55.52 |  70.94 |     77.23     |\n\n\nNote: The above reported results on Code only consists of {apps, condecontests, codeforces, taco} and report the obtained continuous reward. All other benchmarks are the same as in the paper.\n\n\n2. *It is not clear to me how the authors determine when the model stagnates. Based on Section 3.3, this seems to be a manual process and therefore might be very model-specific. I think it would be useful to report this point in the limitations or, in general, it would be useful to be explicit about the limitations of this training regime.*\n\n\nWe determine stagnation through manual inspection guided by quantitative signals. Specifically, we reset the reference model when (i) the KL loss exceeds a threshold (e.g., 0.2), indicating excessive policy drift, or (ii) validation performance shows a consistent downward trend. In such cases, we resume from the most recent checkpoint with the best validation score. We will explicitly note in the limitations section that this process involves manual intervention and may be model-specific.\n\n\n3. *I was wondering how the solution proposed by this paper compares with current real-world implementations of GRPO such as TRL (from Huggingface).*\n\n\nI believe both the work mentioned (Open-Reasoner-Zero and DAPO) mainly experiment with using pretraining checkpoints (no instructional finetuning) as the base model. In our case, we select already strong reasoning models as the base model. In the case of starting from a weak model, removing KL penalty could facilitate the model learning as this additional penalty term constrains the policy term potentially limiting exploration. In our case, our ablation studies still found small KL divergence to be beneficial when starting from a strong base model, since it mitigates the entropy collapse issue and enables scaling training to thousands of steps. The reference policy resets ensures stability, and also allows the policy model also to gradually diverge from the base model.\n\n\nMost popular RL frameworks (such as TRL and verl) still keep KL divergence penalty coefficient as a tunable parameter, allowing easy application of our proposed method.\n\n\n4. *Did you notice any specific difference in performance between tasks that have binary or continuous rewards?*\n\n\nThank you for the great question! We do notice differences on tasks such as coding with binary and continuous rewards. Using continuous reward during initial training stages improves the model learning since these partial rewards help guide weaker models to achieve some level of competence. Furthermore, since dynamic sampling filters instances with pass rate of 0/1, continuous reward would improve efficiency as instances with intermediate rewards still have non-zero advantage. However, we also observe that during the late stages, switching to binary rewards increases the pass@1 score (but lowers the continuous reward scores) of the model performance. Nonetheless we keep tasks to continuous reward as to keep consistency during training."}, {"review_id": "AW73VZ0udM", "reviewer": "Reviewer_nT4B", "summary": "This work introduces prolonged RL (ProRL), an optimization method that incorporates KL divergence control and reference policy resetting on policy optimization for LLMs. ProRL conducts its training over a diverse suite of tasks. Its empirical analysis shows that prolonged RL-trained models can consistently outperform the base model, suggesting that prolonged RL can discover new solution pathways that were not present in base models. This work also quantifies the model's novelty in reasoning via a creativity index for more quantitative analysis.", "questions": "Please see the concerns raised in the weakness section. I am happy to increase the score if the author is able to address my concerns.", "limitations": "Yes.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strength: \n1. The findings delivered by this work are quite insightful and beneficial to the community for post-training LLMs. ProRL shows that with appropriate extropy collapse mitigation techniques, prolonged RL training on a diverse set of tasks can elicit new abilities from even SLMs.\n\n2. The diverse and verifiable training dataset that covers 5 task domains also serves as a good contribution for eliciting SLMs reasoning capability outside of the previously dominating Math and Coding sets. \n\nWeakness:\n1. Though this work delivers useful findings on expanding the reasoning boundary, the source of the techniques that truly elicit new reasoning patterns is not analyzed thoroughly in this work. ProRL integrates KL regularization, Reference Policy Reset, and a diverse set of tasks as the training resources. However, the ablation for each component is not studied. Consequently, it is not clear from a reader's perspective whether the key ingredient came from the reference policy reset, maintaining a reasonable entropy during training, or the diversified task set appears to be more important.\n\n2. The base model is limited to DeepSeek-R1-Distill-Qwen-1.5B. Recently, different base models have been discussed to exhibit completely different post-training behaviors. It is important to include another family of base models for conducting ProRL and with a larger model larger than 1.5B.\n\n3. As described in weakness 1, the main results did not compare other training baselines, such as GRPO and DAPO, on the curated training datasets. It can also be beneficial to provide an ablation on the training data mixture.", "was_revised": true, "final_justification": "The ablation study is important for this work and for readers to understand what components enable prolonged training with diverse explorations. Given the additional details and the promised improved manuscript with all additional ablation details, I am increasing my final rating to 4.", "rebuttal": "Thank you for the feedback and acknowledgement of our work. We hope the following responses could clarify your concerns.\n\n\n1. *However, the ablation for each component is not studied.*\n\n\nWe did conduct careful small scale ablation studies on our alternations of the GRPO pipeline, including decoupling  hyperparameters, adding reference model (and optimizer reset) hard reset. We apologize for not including such experiment details.\n\n\n**We will be providing an additional detailed technical report alongside the final version of the paper.** Unfortunately the conference review process prohibits sharing additional documents, thus we are only able to provide brief text descriptions on the ablation studies and key observations as follows:\n\n\n1.1 Rollout Sampling Temperature\n\n\nAblations with temperatures {0.6, 1.2} show that low temperature (0.6) causes early instability, reduced diversity, and overexploitation, hurting reward and validation. High temperature (1.2) yields steadier improvement, better generalization, and avoids mode collapse even in late-stage training, so we use 1.2 throughout.\n\n\n1.2 Decoupled Clipping\n\n\nWe vary ϵlow {0.1, 0.2} and ϵhigh​ {0.2, 0.3, 0.4}; ϵlow=0.2 better handles negative advantage, and ϵhigh=0.4 prevents entropy collapse, giving best validation. Smaller ϵlow increases entropy but not learning, so we adopt (0.2, 0.4).\n\n\n1.3 Dynamic Sampling\n\n\nWe further verified that dynamic sampling led to faster improvements than static sampling by filtering out prompts with zero advantage. This increases reward signal density in each batch, thereby improving the overall sample efficiency of training.\n\n\n1.4 Resetting Reference Policy\n\n\nWe observe that extending training with the same setting and training hyperparameters does not always lead to consistent improvements. We observed that by simply extending the training or Run1 (this is the DAPO baseline) without reference policy reset, it encounters a sharp drop in validation scores on the Codeforces benchmark. We were not able to scale RL training beyond 600 steps with DAPO, and in contrast resetting the reference policy allowed us to scale training to beyond 2k steps.\n\n\n1.5 Mitigating Entropy Collapse\n\n\nWe conducted a series of ablation studies evaluating the training dynamics under different strategies to mitigate entropy collapse. We investigated the following settings:\n\n\n- GRPO-KL=0: We employ standard GRPO training without KL divergence penalty or entropy bonus.\n\n\n- GRPO-KL=1e-4: We apply a small KL regularization term 1e-4 to control the divergence between the online policy and a reference policy. This helps prevent the model from drifting too far and encourages continued exploration.\n\n\n- DAPO: This is the DAPO baseline with decoupled clipping and dynamic sampling. No KL divergence penalty or entropy bonus.\n\n\nWe observe that GRPO-KL=0 suffers from entropy collapse and the validation score stops improving after the entropy degrades to ~0 in ~500 steps. In contrast, DAPO and KL penalty both can mitigate entropy collapse as the validation scores continue to improve. Based on these findings, we adopt a combination of DAPO and a KL penalty in our final training setup.\n\n\n2. *It is important to include another family of base models for conducting ProRL and with a larger model larger than 1.5B.*\n\n\nWe conduct further experiments by applying our training recipe to a larger model and different base model. We use Llama-3.1-Nemotron-Nano-8B-v1, which is a derivative based on llama-3.1-8B-Instruct, further finetuned on diverse reasoning tasks. Due to time constraints and compute limitations, we only scale training to ~1.4k steps. We provide detailed comparison with the base model across tasks as follows\n| Model                         | Math  | Code  | GPQA  | IFEval | Reasoning Gym |  \n|-------------------------------|-------|-------|-------|--------|---------------|\n| Llama-3.1-Nemotron-Nano-8B-v1 | 68.26 | 61.20 | 52.76 |  66.88 |     12.15     |\n| ProRL-8B                      | 71.98 | 72.80 | 55.52 |  70.94 |     77.23     |\n\n\nNote: The above reported results on Code only consists of {apps, condecontests, codeforces, taco} and report the obtained continuous reward. All other benchmarks are the same as in the paper.\n\n\n3. *The main results did not compare other training baselines, such as GRPO and DAPO, on the curated training datasets.*\n\n\nWe apologize again for not including detailed ablation studies in the original manuscript. We hope our response to the 1st question could provide confidence in our results when comparing against other training baselines such as GRPO and DAPO. In our ablation studies, we found GRPO performance to saturate within ~600 steps, largely due to entropy collapse as the model loses the capability to explore. We also found DAPO without reference policy reset to have training stability issues, in having some validation scores degrading ~500 steps.\n\n\nAs requested from Reviewer TRB6, we further conducted ablation studies comparing with other finetuning techniques such as SFT and DPO. We decided to focus on tasks within the Reasoning Gym suite and used a stronger base model DeepSeek-R1-Distilled-Qwen-32B model to generate reasoning traces and used verifiers to filter negative samples. We constructed a finetuning dataset of ~200k verified responses. We further collected additional negative responses across the same dataset, constructing a preference dataset of ~200k entries for DPO finetuning. We conduct SFT and DPO for 2 epochs using DeepSeek-R1-Distilled-Qwen-1.5B as the base model. We provide comparisons with these additional baselines with our ProRL-1.5B model on the Reasoning Gym tasks as follows:\n|       Model      | algebra | algorithmic |  arc | arithmetic |  code | cognition | games | geometry | graphs | induction | logic |  Avg  |\n|:----------------:|:-------:|:-----------:|:----:|:----------:|:-----:|:---------:|:-----:|:--------:|:------:|:---------:|:-----:|:-----:|\n| DeepSeek-R1-1.5B |   0.73  |     3.56    | 1.53 |    5.36    |  1.22 |    6.47   |  2.34 |   1.05   |  6.64  |    1.32   | 10.90 |  4.24 |\n|  ProRL-1.5B (2k) |  97.21  |    53.90    | 2.52 |    82.81   | 29.84 |   40.16   | 26.38 |   89.84  |  66.49 |   73.50   | 82.94 | 59.06 |\n|     SFT-1.5B     |  51.18  |    25.65    | 1.48 |    64.18   |  1.35 |   39.13   | 17.64 |   65.13  |  35.63 |   60.59   | 41.21 | 35.81 |\n|     DPO-1.5B     |  48.61  |    24.29    | 1.53 |    62.76   |  0.88 |   37.37   | 15.64 |   64.12  |  32.92 |   58.47   | 38.63 | 34.15 |\n\n\n4. *It can also be beneficial to provide an ablation on the training data mixture.*\n\n\nIn regards to training data mixture, we conduct a small scale experiment with the following two data mixtures: Math-Only, consisting of only the math dataset; and Math-Code-STEM-Reasoning, consisting of the math, code, stem reasoning and logic puzzle (Reasoning Gym) data. We only train for ~600 steps with the comparison as follows:\n| Model                         | Math  | Code  | GPQA  | Reasoning Gym |  \n|-------------------------------|-------|-------|-------|---------------|\n| Base Model | 44.45 | 14.98 | 15.86 | 4.24     |\n| Math-Only | 53.37 | 17.21 | 17.48 |  4.51     |\n| Math-Code-Stem-Reasoning | 53.45 | 24.57 | 37.12 |  49.87   |\n\n\nNote: The above reported results on Code only consists of pass@1 for {apps, condecontests, codeforces, taco}.\n\n\nAs shown in the above, training only on math data does bring some level of transfer to other tasks but not as significant as directly including similar tasks in training. This highlights the importance of training on a diverse mixture of data."}]

Author rebuttal:

Meta-review: This paper challenges recent works that claim that RL fine-tuning does not improve the reasoning capabilities of the base model. They identify a number of issues with these prior works -- which essentially amounts to overfitting and early termination -- and propose a novel algorithm -- ProRL -- which mitigates these weaknesses with a KL regularization. There were concerns about whether the improved performance was due to improved reasoning or due to simply novel expose to the data, but through discussion and additional experiments, the authors successfully convinced the reviewers that the model fine-tuned with ProRL does indeed demonstrate enhanced reasoning over the base model. Additional ablations were asked for from the reviewers, and these were provided, e.g., hyper parameters, policy reset, and base model.

Given this is an active area of research (RL for fine-tuning / reasoning) and the quality of the paper, I advocate for acceptance as a poster.
Decision: Accept (poster)