ICLR 2026 Papers

Modern language models generate chain-of-thought traces by autoregressively sampling tokens from a finite vocabulary. While this discrete sampling has achieved remarkable success, conducting chain-of-thought with continuously-valued tokens (CoT2) offers a richer and more expressive alternative. Our work provides new theoretical guarantees and algorithms for CoT2, motivated by logical reasoning tasks that inherently require search capabilities. Theoretically, we establish how CoT2 facilitates the model to track multiple discrete traces in parallel; and quantify the level of achievable parallelism and its benefits for inference efficiency. We also provide a CoT2-based one-layer transformer construction that solves the combinatorial ``subset sum problem'' given a sufficient embedding dimension. These insights arise from a novel and effective supervision strategy where we match the language model outputs to the empirical token distributions of a set of target traces. Complementing this, we introduce sampling strategies that unlock policy optimization methods for CoT2. Our primary strategy samples and composes $K$ discrete tokens at each decoding step to control the level of parallelism. Experiments confirm that (i) the optimal level of parallelism is governed by the embedding dimension, (ii) our continuous supervision strategy can outperform alternative methods, and (iii) policy optimization with CoT2 indeed improves the performance of the model beyond its initial discrete or continuous supervision.

Pretraining large language models (LLMs) on high-quality, structured data such as mathematics and code substantially enhances reasoning capabilities. However, existing math-focused datasets built from Common Crawl suffer from degraded quality due to brittle extraction heuristics, lossy HTML-to-text conversion, and the failure to reliably preserve mathematical structure. In this work, we intro- duce Nemotron-CC-Math, a large-scale, high-quality mathematical corpus constructed from Common Crawl using a novel, domain-agnostic pipeline specifically designed for robust scientific text extraction. Unlike previous efforts, our pipeline recovers math across various formats (e.g., MathJax, KaTeX, MathML) by leveraging layout-aware rendering with lynx and a targeted LLM-based cleaning stage. This approach preserves the structural integrity of equations and code blocks while removing boilerplate, standardizing notation into L A T EX representation, and correcting inconsistencies. We collected a large, high-quality math corpus, namely Nemotron-CC-Math-3+(133B tokens) and Nemotron-CC-Math-4+ (52B tokens). Notably, Nemotron-CC-Math-4+ not only surpasses all prior open math datasets-including Mega-Math, FineMath, and OpenWebMath-but also contains 5.5× more tokens than FineMath-4+, which was previously the highest-quality math pretraining dataset. When used to pretrain a Nemotron-T 8B model, our corpus yields +4.8 to +12.6. gains on MATH and +4.6 to +14.3 gains on MBPP+ over strong baselines, while also improving general-domain performance on MMLU and MMLU-Stem. We present the first pipeline to reliably extract scientific content—including math—from noisy web-scale data, yielding measurable gains in math, code, and general reasoning, and setting a new state of the art among open math pretraining corpora. To support open-source efforts, we release our code1 and datasets 2 .

Reinforcement Learning from Verifiable Rewards (RLVR) is a promising method for enhancing the complex problem-solving abilities of large language models (LLMs). This is particularly evident in domains requiring long-horizon reasoning and precise execution, such as solving complex mathematical problems where solutions hinge on a fragile sequence of tool-based actions. However, current approaches are often crippled by two interconnected issues: the near-miss problem, where sparse rewards nullify the learning signal for almost-correct attempts, and the resulting exploration stagnation, which prevents the model from discovering better solutions. To address these challenges, we introduce HiPO (Hint-guided Policy Optimization), a novel RLVR framework that enables the agent to learn from its own rare successes. Our core insight is to capture an occasional successful trajectory within a training batch and repurpose its initial correct steps as an on-policy “hint”. This process transforms a single, stochastically-found success into a dense contrastive learning signal, effectively allowing the model to teach itself how to overcome the near-miss problem and break exploration stagnation. On a challenging suite of five mathematical reasoning benchmarks, HiPO improves the average avg@32 by +5.0 percentage points (pp) over the strong GRPO baseline. This improvement is driven by substantial absolute point gains on challenging datasets, including +10.3 pp on CMIMC 2025, +4.9 pp on BRUMO 2025, +4.6 pp on AIME 2024, and +3.1 pp on AIME 2025. Furthermore, HiPO demonstrates a new exploration paradigm, repurposing rare successes into reusable guidance to significantly accelerate skill acquisition for complex tasks, establishing a more efficient and scalable path for models to autonomously master intricate reasoning.

Recent trends in test-time scaling for reasoning models (e.g., OpenAI o1, DeepSeek-R1) have led to remarkable improvements through long Chain-of-Thought (CoT). However, existing benchmarks mainly focus on immediate, single-horizon tasks, failing to adequately evaluate models’ ability to understand and respond to complex, long-horizon scenarios. To address this incomplete evaluation of Large Reasoning Models (LRMs), we propose R-HORIZON, a method designed to stimulate long-horizon reasoning behaviors in LRMs through query composition. Based on R-HORIZON, we construct a long-horizon reasoning benchmark, comprising complex multi-step reasoning tasks with interdependent problems that span long reasoning horizons. Through comprehensive evaluation of LRMs using the R-HORIZON benchmark, we find that even the most advanced LRMs suffer significant performance degradation. Our analysis reveals that LRMs exhibit limited effective reasoning length and struggle to allocate thinking budget across multiple problems appropriately. Recognizing these limitations, we use R-HORIZON to construct long-horizon reasoning data for reinforcement learning with verified rewards (RLVR). Compared to training with single-horizon data, RLVR with R-HORIZON not only substantially improves performance on the multi-horizon reasoning tasks, but also promotes accuracy on standard reasoning tasks (+7.5 on AIME2024). These results position R-HORIZON as a scalable, controllable, and low-cost paradigm for enhancing and evaluating the long-horizon reasoning capabilities of LRMs.

Recent advancements in Large Language Models (LLMs) have shifted from explicit Chain-of-Thought (CoT) reasoning to more efficient latent reasoning, where intermediate thoughts are represented as vectors rather than text. However, latent reasoning can be brittle on challenging, out-of-distribution tasks where robust reasoning is most critical. To overcome these limitations, we introduce Latent Thought Policy Optimization (LTPO), a parameter-free framework that enhances LLM reasoning entirely at test time, without requiring model parameter updates. LTPO treats intermediate latent "thought" vectors as dynamic parameters that are actively optimized for each problem instance. It employs an online policy gradient method guided by an intrinsic, confidence-based reward signal computed directly from the frozen LLM's own output distributions, eliminating the need for external supervision or expensive text generation during optimization. Extensive experiments on five reasoning benchmarks show that LTPO not only matches or surpasses strong baselines on standard tasks but also demonstrates remarkable robustness where others fail. Most notably, on highly challenging AIME benchmarks where existing latent reasoning baselines collapse to near-zero accuracy, LTPO delivers substantial improvements, showcasing a unique capability for complex reasoning.

Reinforcement learning (RL) with group relative policy optimization (GRPO) has become a widely adopted approach for enhancing the reasoning capabilities of multimodal large language models (MLLMs). While GRPO enables long-chain reasoning without a traditional critic model, it often suffers from sparse rewards, arising from the scarcity of positive feedback on difficult problems, and from advantage vanishing, which occurs when group-level rewards exhibit high consistency for problems that are too easy or too hard. Existing solutions fall into three categories: sample enhancement and expansion, which may aggravate vanishing advantage due to poor control of difficulty distribution; selective sample utilization, which fails to fully leverage the value of all data; and indirect reward design, which may introduce biased optimization directions due to misalignment between reasoning and the final outcome. However, these approaches overlook a fundamental question: for a given problem, how can we ensure that the within-group reward distribution of responses exhibits enough variance to yield clear optimization signals for each response? To address these issues, we propose DIVA-GRPO, a difficulty-adaptive variant augmentation advantage method that dynamically adjusts the difficulty distribution of variants for each problem from a global perspective. Our method dynamically assesses problem difficulty, samples variants with appropriate difficulty levels, and advantages are computed within both local and global(a problem and its variants) groups using difficulty-weighted and normalized scaling. This design alleviates reward sparsity and advantage vanishing, minimizes data waste, and improves training stability. Extensive experiments on six reasoning benchmarks demonstrate that DIVA-GRPO outperforms existing approaches in both training efficiency and reasoning performance.

Large reasoning models (LRMs) excel on complex problems but face a critical barrier to efficiency: reinforcement learning (RL) training requires long rollouts for outcome-based rewards, where autoregressive decoding dominates time and memory usage. While sliding-window cache strategies can bound memory, they disrupt long-context reasoning and degrade performance. We introduce Progressive Thought Encoding, a parameter-efficient fine-tuning method that enables LRMs to reason effectively under fixed-size caches. By progressively encoding intermediate reasoning into compact representations, our approach eliminates the need to backpropagate through full-cache rollouts, thereby reducing training-time memory usage, while maintaining constant memory during inference. Experiments on three models, including Qwen2.5-3B-Instruct, Qwen2.5-7B-Instruct, and DeepSeek-R1-Distill-Llama-8B, across six widely used challenging mathematical benchmarks show consistent gains: our method achieves +19.3\% improvement over LoRA and +29.9\% over the baseline on average, with up to +23.4 absolute gains on AIME2024/2025 under tight cache budgets. These results demonstrate that Progressive Thought Encoding not only improves reasoning accuracy but also makes RL training of LRMs substantially more efficient and scalable under real-world memory constraints.

Large language models (LLMs) have demonstrated remarkable progress in coding and mathematical problem-solving; however, evaluation on advanced research-level problems in the hard sciences remains scarce. To fill this gap, we present \cmt, a dataset of 50 original problems covering condensed matter theory (CMT) at the level of an expert researcher. The topics cover analytical and computational approaches commonly used in quantum many-body physics as well as classical statistical mechanics. This dataset was designed and verified by a panel of expert researchers from around the world. We built the dataset through a collaborative environment that challenges the panel to write and refine difficult problems that the panel would like their research assistants to be able to solve, with topics including Hartree-Fock mean-field theory, exact diagonalization, quantum Monte Carlo, density matrix renormalization group, quantum statistical mechanics, classical statistical mechanics, and model building. We evaluate different LLMs by programmatically checking LLM-generated solutions against expert-supplied ground truth. For this, we developed machine-grading mechanisms that are suitable for advanced physics research problems. For example, we handle non-commuting operators that are essential for quantum many-body problems by symbolic manipulation and normal ordering. Our evaluations show that frontier models struggle with all of the problems in the dataset, highlighting a gap in the physical reasoning skills of current LLMs. Notably, experts identified strategies for creating increasingly difficult problems by interacting with the LLMs and exploiting common failure modes. While the highest-performing model, GPT5, correctly solves 30\% of the problems, average performance across 17 models (GPT, Gemini, Claude, DeepSeek, and Llama classes) is only 11.4$\pm$2.1\%. Moreover, our benchmark contains 18 problems that {\it not a single one} of the 17 models can correctly solve, and 26 problems that are solved by {\it at most} one model. These currently unsolvable problems span the fields of Quantum Monte Carlo, Variational Monte Carlo, and Density Matrix Renormalization Group. The answers sometimes violate fundamental symmetries or have unphysical scaling dimensions. We believe that this benchmark set provides valuable guidance for the future development of language models, aiming to achieve the goal of AI research assistants and tutors.

Large language models (LLMs) often solve drill-style math exercises yet fail to apply the concept right when the problem requires genuine understanding. Popular outcome-based RL pipelines reinforce final answers but provide little fine-grained conceptual signal, so models improve at pattern reuse rather than concept selection and use. We introduce $\textit{CORE}$ (Concept-Oriented REinforcement), an algorithm-agnostic training framework that turns explicit concepts into a controllable supervision signal. Starting from a high-quality, low-contamination textbook resource that links verifiable exercises to concise concept descriptions, we run a sanity probe showing LLMs can restate definitions while missing concept-linked quizzes, quantifying the conceptual reasoning gap. $\textit{CORE}$ then (i) synthesizes additional concept-aligned quizzes, (ii) injects concept snippets into rollouts, and (iii) reinforces trajectories that correctly apply the injected concept while constraining drift with a lightweight divergence penalty; the procedure is compatible with standard policy-gradient methods (e.g., GRPO). On a 7B-class model, $\textit{CORE}$ yields consistent gains over a vanilla baseline and reinforcement-only training across in-domain concept–exercise suites and diverse out-of-domain math benchmarks (GSM8K, SVAMP, MAWPS, SAT-Math, OlympiadBench, Gaokao, Minerva-Math, CounterMath, TheoremQA). Improvements are largest on concept-heavy categories while maintaining or modestly improving drill performance. $\textit{CORE}$ demonstrates that concept-injected, outcome-regularized rollouts supply the missing fine-grained supervision needed to bridge drill competence and true conceptual reasoning—without committing to a particular RL algorithm or certain process-based verifiers.

Large Language Models (LLMs) are increasingly applied to complex tasks that require extended reasoning. In such settings, models often benefit from diverse chains-of-thought to arrive at multiple candidate solutions. This requires two competing objectives: to inject enough stochasticity to explore multiple reasoning chains, and to ensure sufficient accuracy and quality in each path. Existing works pursue the first objective by increasing exploration at highly uncertain steps with higher temperature or larger candidate token sets, while others improve reliability by rejecting samples with low confidence post generation, implying that low confidence correlates with low answer quality. These two lines of thought are in conflict, as they conflate different sources of uncertainty. To resolve this, we argue that the decoding rule should be calibrated by *correctness*, not confidence alone. We should sample from tokens with higher estimated correctness, and reduce sampling where expected correctness is low. We propose simple strategies that achieve this goal: **Greedy-Threshold** makes sampling greedy at very low confidence steps. **Calibrated-TopK** and **Calibrated-ε** set truncation threshold based on estimated rank-wise correctness. Together, our findings challenge prevailing heuristics about decoding under uncertainty, showing consistent gains across math and general reasoning benchmarks.

Scaling inference-time compute for Large Language Models (LLMs) has unlocked unprecedented reasoning capabilities. However, existing inference-time scaling methods typically rely on inefficient and suboptimal discrete search algorithms or trial-and-error prompting to improve the online policy. In this paper, we propose $\nabla$-reasoner, an iterative generation framework that integrates differentiable optimization over token logits into the decoding loop to refine the policy on the fly. Our core component, Differentiable Textual Optimization (DTO), leverages gradient signals from both the LLM’s likelihood and a reward model to refine textual representations. $\nabla$-reasoner further incorporates rejection sampling and acceleration design to robustify and speed up decoding. Theoretically, we show that performing inference-time gradient descent in the sample space to maximize reward is dual to aligning an LLM policy via KL-regularized reinforcement learning. Empirically, $\nabla$-reasoner achieves over 20% accuracy improvement on a challenging mathematical reasoning benchmark, while reducing number of model calls by approximately 10-40% compared to strong baselines. Overall, our work introduces a paradigm shift from zeroth-order search to first-order optimization at test time, offering a cost-effective path to amplify LLM reasoning.

Reasoning on Temporal Knowledge Graphs (TKGs) is essential for predicting future events and time-aware facts. While existing methods are effective at capturing relational dynamics, their performance is limited by a closed-world assumption, which fails to account for emerging entities not present in the training. Notably, these entities continuously join the network without historical interactions. Empirical study reveals that emerging entities are widespread in TKGs, comprising roughly 25\% of all entities. The absence of historical interactions of these entities leads to significant performance degradation in reasoning tasks. Whereas, we observe that entities with semantic similarities often exhibit comparable interaction histories, suggesting the presence of transferable temporal patterns. Inspired by this insight, we propose TransFIR (Transferable Inductive Reasoning), a novel framework that leverages historical interaction sequences from semantically similar known entities to support inductive reasoning. Specifically, we propose a codebook-based classifier that categorizes emerging entities into latent semantic clusters, allowing them to adopt reasoning patterns from similar entities. Experimental results demonstrate that TransFIR outperforms all baselines in reasoning on emerging entities, achieving an average improvement of 28.6\% in Mean Reciprocal Rank (MRR) across multiple datasets. The implementations are available at https://anonymous.4open.science/r/TransFIR-C72F.

Reinforcement Learning with Verifiable Rewards (RLVR) offers a robust mechanism for enhancing mathematical reasoning in large models. However, we identify a systematic lack of emphasis on more challenging questions in existing methods from both algorithmic and data perspectives, despite their importance for refining underdeveloped capabilities. Algorithmically, widely used Group Relative Policy Optimization (GRPO) suffers from an implicit imbalance where the magnitude of policy updates is lower for harder questions. Data-wise, augmentation approaches primarily rephrase questions to enhance diversity without systematically increasing intrinsic difficulty. To address these issues, we propose a two-dual MathForge framework to improve mathematical reasoning by targeting harder questions from both perspectives, which comprises a Difficulty-Aware Group Policy Optimization (DGPO) algorithm and a Multi-Aspect Question Reformulation (MQR) strategy. Specifically, DGPO first rectifies the implicit imbalance in GRPO via difficulty-balanced group advantage estimation, and further prioritizes harder questions by difficulty-aware question-level weighting. Meanwhile, MQR reformulates questions across multiple aspects to increase difficulty while maintaining the original gold answer. Overall, MathForge forms a synergistic loop: MQR expands the data frontier, and DGPO effectively learns from the augmented data. Extensive experiments show that MathForge significantly outperforms existing methods on various mathematical reasoning tasks. The code and augmented data are all available at https://github.com/AMAP-ML/MathForge.

Agents in the real world must make not only logical but also *timely* judgments. This requires continuous awareness of the dynamic environment: hazards emerge, opportunities arise, and other agents act, while the agent's reasoning is still unfolding. Despite advances in language model reasoning, existing approaches fail to account for this dynamic nature. We introduce *real-time reasoning* as a new problem formulation for agents in evolving environments and build **Real-Time Reasoning Gym** to demonstrate it. We study two paradigms for deploying language models in agents: (1) **Reactive agents**, which employ language models with *bounded reasoning computation for rapid responses*. (2) **Planning agents**, which allow *extended reasoning computation for complex problems*. Our experiments show that even state-of-the-art models struggle with making logical and timely judgments in either paradigm. To address this limitation, we propose **AgileThinker**, which simultaneously engages *both reasoning paradigms*. **AgileThinker** consistently outperforms agents engaging only one reasoning paradigm as task difficulty and time pressure rise, effectively balancing reasoning depth and response latency. Our work establishes real-time reasoning as a critical testbed for developing practical agents and provides a foundation for research in temporally constrained AI systems, highlighting a path toward real-time capable agents.

As single-center computing approaches power constraints, decentralized training becomes essential. However, traditional Reinforcement Learning (RL) methods, crucial for enhancing large model post-training, cannot adapt to decentralized distributed training due to the tight coupling between parameter learning and rollout sampling. For this, we propose HeteroRL, a heterogeneous RL architecture that decouples these processes, enabling stable training across geographically distributed nodes connected via the Internet. The core component is Group Expectation Policy Optimization (GEPO), an asynchronous RL algorithm robust to latency caused by network delays or heterogeneity in computational resources. Our study reveals that high latency significantly increases KL divergence, leading to higher variance of importance weights and training instability. GEPO mitigates this issue by using group expectation weighting to exponentially reduce the variance of importance weights, with theoretical guarantees. Experiments show GEPO achieves superior stability—only a 3\% performance drop from online to 1800s latency—and reduces the best-to-last gap by 85\% versus GSPO ($\Delta$=1.8 vs. 12.0) while attaining the highest scores, highlighting its effectiveness in decentralized, resource-heterogeneous environments.

Evaluating language models fairly is becoming harder as static benchmarks available on the internet risk contamination by training data. This makes it unclear whether models are truly reasoning or just recalling answers. In this paper, we introduce $\textbf{BeyondBench}$, an evaluation framework that avoids this problem by using $\textbf{algorithmic problem generation}$. Unlike traditional benchmarks that risk contamination from internet-scale training data, $\textbf{BeyondBench}$ creates mathematically grounded problems on the fly, ensuring each test remains fresh and uncontaminated. Our framework covers $\textbf{44 algorithmic tasks}$ with a total of $\textbf{117 variations}$, grouped into three difficulty levels: the $\textit{Easy Suite}$ (29 tasks) for basic arithmetic and statistics, the $\textit{Medium Suite}$ (5 tasks, 49 variations) for sequence patterns and reasoning, and the $\textit{Hard Suite}$ (10 tasks, 68 variations) tackling NP-complete and constraint satisfaction problems. Each task generates problems from a combinatorial space larger than $10^{15}$ unique instances, with solutions verified deterministically by mathematical proofs. We evaluated $\textbf{101 language models}$, including 85 open-source and 16 closed-source models, spanning sizes from 0.5B to 141B parameters and multiple quantization schemes. All evaluations use three-fold cross-validation to ensure statistical robustness. Our results show consistent reasoning deficiencies across model families, with performance degrading sharply as problem complexity increases from polynomial to exponential. In our Hard Suite evaluations, models such as Gemini-2.5-pro, Llama-3.3-70B, and Qwen2.5-72B achieved average accuracies of 56.38%, 26.91%, and 33.60%, respectively. Moreover, we observe that performance drops drastically without tool usage, with GPT-5, GPT-5-mini, and GPT-5-nano showing a $\textbf{decline}$ of 16.81% 28.05%, and 47.59% accuracy on the hard suite. The contamination resistance of $\textbf{BeyondBench}$ rests on three guarantees: (i) the problem space is vastly larger than any static dataset, (ii) every instance has a unique, verifiable solution, and (iii) isomorphic transformations generate semantically equivalent but syntactically new problems. $\textbf{BeyondBench}$ redefines reasoning evaluation through genuine algorithmic problem-solving capability, ensuring a fair and meaningful evaluation.

Multimodal reasoning is a dynamic process that requires synergistic coordination of language and vision. However, current approaches to multimodal interleaved generation fall short of providing a generalizable recipe that productively engages text and vision to advance reasoning. We introduce ThinkMorph, a unified thinking model capable of effective interleaved reasoning. By constructing a high-quality pipeline for generating interleaved reasoning data for training unified models, we enable ThinkMorph to generate multimodal reasoning traces where language and vision mutually advance each other. ThinkMorph delivers substantial gains on vision-centric reasoning, including +11.53\% on visual search and +38.75\% on jigsaw assembly over the base model. It also reaches 80.33\% on MMVP and 52.67\% on SAT, indicating strong generalization. The improvements are large enough to close the gap with, and in some cases even surpass, leading large-scale or proprietary VLMs. Moreover, ThinkMorph reveals \emph{emergent properties} indicative of higher-level multimodal intelligence. These include unseen visual manipulation skills during finetuning, such as zoom-in and image inpainting, as well as autonomous reasoning mode switching, wherein a model trained exclusively on interleaved data chooses to engage in text-only reasoning due to the nature of the task, for instance. We show that this ability to think in text, vision, and multimodality opens new avenues for test-time scaling, allowing ThinkMorph to \textit{effectively scale and aggregate thoughts across three reasoning modes}. These findings suggest promising directions for future work to characterize the emergent capabilities of unified models for multimodal reasoning.

Neural methods are transforming automated reasoning for proof assistants, yet integrating these advances into practical verification workflows remains challenging. A $\textit{hammer}$ is a tool that integrates premise selection, translation to external automatic theorem provers, and proof reconstruction into one overarching tool to automate tedious reasoning steps. We present LeanPremise, a novel neural premise selection system, and we combine it with existing translation and proof reconstruction components to create LeanHammer, the first end-to-end domain general hammer for the Lean proof assistant. Unlike existing Lean premise selectors, LeanPremise is specifically trained for use with a hammer in dependent type theory. It also dynamically adapts to user-specific contexts, enabling it to effectively recommend premises from libraries outside LeanPremise's training data as well as lemmas defined by the user locally. With comprehensive evaluations, we show that LeanPremise enables LeanHammer to solve 21\% more goals than existing premise selectors and generalizes well to diverse domains. Our work helps bridge the gap between neural retrieval and symbolic reasoning, making formal verification more accessible to researchers and practitioners.

Large reasoning models (LRMs) trained with *Reinforcement Learning with Verifiable Rewards* (RLVR) have achieved remarkable progress on complex reasoning tasks. However, RLVR heavily relies on on-policy rollout generation, whose cost grows rapidly with rollout length and model size, eventually becoming the training bottleneck. Our empirical analysis reveals that independent rollouts for the same query often share similar early steps, indicating substantial redundancy. To address this, we propose **Pros** (**P**refix **R**euse for **O**n-policy **S**ampling), a paradigm that reuses promising prefixes of historical rollouts in RLVR training. **Pros** appends these self-generated partial rollouts to the original queries to form *Augmented Queries*, which are then used as regular training inputs in subsequent iterations, thereby reducing redundant computation. To select training batch from augmented queries, **Pros** adopts a hierarchical Bayesian model to estimate their pass rates and prioritize those with the highest reward uncertainty. Experiments across diverse settings show that **Pros** consistently improves training efficiency and achieves higher accuracy than strong baselines. These results highlight **Pros** as a practical path toward scalable and compute-efficient RLVR.