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A Decomposition Perspective to Long-context Reasoning for LLMs

Yanling Xiao, Huaibing Xie, Guoliang Zhao, Shihan Dou, Shaolei Wang, Yiting Liu, Nantao Zheng, Cheng Zhang, Pluto Zhou, Zhisong Zhang, Lemao Liu

Year: 2026Venue: arXiv preprintArea: cs.CLType: PreprintEmbeddings: 53

Intelligence

Status: succeeded | Model: google/gemini-3.1-flash-lite-preview | Prompt: intel-v1 | Confidence: 96%

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Summary

The paper introduces a decomposition perspective to long-context reasoning for LLMs, breaking down the monolithic task into five fundamental atomic skills: Foundational Retrieval, Anti-Interference, Global Integration, Relational Reasoning, and Dynamic State Tracking. The authors propose the Anchor-based Reasoning (AbR) framework to automatically synthesize pseudo-datasets for these skills and demonstrate that targeted reinforcement learning on these datasets significantly improves general long-context reasoning performance across multiple benchmarks.

Entities (7)

Anti-Interference · atomic-skill · 99%Dynamic State Tracking · atomic-skill · 99%Foundational Retrieval · atomic-skill · 99%Global Integration · atomic-skill · 99%Relational Reasoning · atomic-skill · 99%DeepSeek-R1-distill-32B · llm · 98%Anchor-based Reasoning (AbR) · framework · 95%

Relation Signals (3)

Atomic Skills → correlateswith → Long-context reasoning performance

confidence 97% · Our empirical analysis confirms that proficiency in these atomic skills is strongly correlated with general long-text reasoning performance.

Reinforcement Learning → improves → Long-context reasoning ability

confidence 96% · we employ reinforcement learning on these pseudo datasets to sharpen the model's atomic skills, in the hope of boosting its general long-context reasoning ability.

AbR framework → decomposes → Long-context Reasoning

confidence 95% · we move beyond this holistic view and decompose long-context reasoning into a set of fundamental atomic skills

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Abstract

Abstract:Long-context reasoning is essential for complex real-world applications, yet remains a significant challenge for Large Language Models (LLMs). Despite the rapid evolution in long-context reasoning, current research often overlooks the internal complexity of the long-context reasoning task itself. In this paper, we move beyond this holistic view and decompose long-context reasoning into a set of fundamental atomic skills, and we then automatically synthesize a suite of pseudo datasets, each explicitly targeting a specific atomic skill. Our empirical analysis confirms that proficiency in these atomic skills is strongly correlated with general long-text reasoning performance. Building on this insight, we employ reinforcement learning on these pseudo datasets to sharpen the model's atomic skills, in the hope of boosting its general long-context reasoning ability. Extensive experiments across multiple benchmarks demonstrate the effectiveness of our approach: it outperforms a strong baseline by an average margin of 7.7\% (improving from 46.3\% to 54.0\%) across Loogle, Loong, LongBench-v2, BrowscompLong, Ruler-qa2, and MRCR.

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A Decomposition Perspective to Long-context Reasoning for LLMs Yanling Xiao 1 Huaibing Xie 1 Guoliang Zhao 1 2 Shihan Dou 1 3 Shaolei Wang 1 Yiting Liu 1 Nantao Zheng 4 Cheng Zhang 1 Pluto Zhou 1 Zhisong Zhang 5 Lemao Liu 3 Abstract Long-context reasoning is essential for complex real-world applications, yet remains a significant challenge for Large Language Models (LLMs). Despite the rapid evolution in long-context rea- soning, current research often overlooks the in- ternal complexity of the long-context reasoning task itself. In this paper, we move beyond this holistic view and decompose long-context rea- soning into a set of fundamental atomic skills, and we then automatically synthesize a suite of pseudo datasets, each explicitly targeting a spe- cific atomic skill. Our empirical analysis confirms that proficiency in these atomic skills is strongly correlated with general long-text reasoning per- formance. Building on this insight, we employ reinforcement learning on these pseudo datasets to sharpen the model’s atomic skills, in the hope of boosting its general long-context reasoning ability. Extensive experiments across multiple benchmarks demonstrate the effectiveness of our approach: it outperforms a strong baseline by an average margin of 7.7% (improving from 46.3% to 54.0%) across Loogle, Loong, LongBench-v2, BrowscompLong, Ruler-qa2, and MRCR. 1. Introduction The rapid evolution of Large Language Models (LLMs) (Guo et al., 2025; Liu et al., 2025; Comanici et al., 2025) has ushered in a new era of artificial intelligence, where the ability to handle extensive context windows is increas- ingly critical. From analyzing multi-document repositories to synthesizing legal contracts and financial reports (Meyur et al., 2025; Reddy et al., 2024), real-world applications demand that the large language models not only “compre- hend” massive amounts of text but also reason over them 1 Large Language Model Department, Tencent 2 Xi’an Jiao- tong University, Xi’an, China 3 Fudan University, Shanghai, China 4 Tencent 5 City University of Hong Kong. Correspondence to: Yanling Xiao<lynniexiao@tencent.com>, Pluto Zhou<plu- tozhou096@foxmail.com>, Lemao Liu<lemaoliu@gmail.com>. Preprint. April 10, 2026. By how much did the revenue share of the top ten pharmaceutical products of Sanofi in the first half of 2024 increase compared to the same period last year (without excluding the impact of exchange rate fluctuations)? Please retain one decimal place in the final calculation result. Sanofi's 2024 half-year financial report Figure 1. Decomposition of a complex task into atomic capabili- ties. The process necessitates Global Integration for aggregating distributed figures and Dynamic State Tracking for holding inter- mediate values during multi-step computation, rather than simple retrieval. effectively. Although recent advancements have expanded the maximum context window of LLMs to 1 million tokens (Team et al., 2024; GLM et al., 2024), a pronounced chasm persists between the scale of context that models can ac- commodate and the efficacy of reasoning they can deliver (Paulsen, 2025). To bridge this critical gap, extensive research efforts have been dedicated to advancing the long-context reasoning ca- pabilities of LLMs (Chen et al., 2023; Li et al., 2024d; Bai et al., 2024). Conventional approaches typically entail cu- rating specialized training datasets tailored for long-context reasoning tasks (Chen et al., 2023; Zhang et al., 2025; Bai et al., 2024), followed by fine-tuning (Li et al., 2024a; Zhang et al., 2025) or reinforcement learning (Wan et al., 2025; Wang et al., 2025) on these datasets to boost model perfor- mance. Nevertheless, long-context reasoning constitutes a monolithic and inherently complex task, rendering the direct construction of high-quality data fraught with chal- lenges (Yang et al., 2025b). Key challenges include the risk of misinformation stemming from inadequate verification protocols (Li et al., 2024c) and the potential for latent knowl- edge conflicts within curated datasets (Xu et al., 2024). In this paper, we propose a paradigm shift from a mono- lithic view of long-context reasoning to a decomposition perspective. We argue that, from a cognitive standpoint, long-context reasoning is a hierarchical spectrum composed of fundamental atomic skills. For instance, as illustrated in Figure 1, the task of calculating Sanofi’s revenue share growth cannot be solved by simple retrieval. Instead, it ne- 1 arXiv:2604.07981v1 [cs.CL] 9 Apr 2026 Submission and Formatting Instructions for ICML 2026 cessitates Global Integration to synthesize distributed finan- cial data across different reporting periods (e.g., aggregating figures from H1 2024 and H1 2023), followed by Dynamic State Tracking to execute multi-step reasoning—holding these intermediate values in memory to compute the final percentage increase. We decompose long-context reason- ing into five atomic skills including Foundational Retrieval, Anti-Interference, Global Integration, Relational Reasoning, and Dynamic State Tracking (§2.1). Unlike the complex long-context reasoning task, each atomic task is compara- tively straightforward; thus, we can relatively easily curate training data for each atomic skill through an anchor-based automatic pipeline with verification (§2.2). Our empirical experiments further demonstrate that these atomic skills are strongly correlated with long-context reasoning skill (§3). This finding indicates that enhancing these atomic skills of LLMs can ultimately boost their long-text reasoning perfor- mance. Based on the curated datasets for these atomic skills, we then present a highly efficient training strategy: we employ Reinforcement Learning (RL) (Shao et al., 2024; Yu et al., 2025) in the curated set of approximately 4,000 synthetic samples generated through our pipeline. This targeted ap- proach sharpens the model’s atomic capabilities, enabling it to generalize to complex, unseen long-context reason- ing tasks. Experimental results on six challenging bench- marks—including Loogle (Li et al., 2024b), Loong (Wang et al., 2024) and LongBench v2 (Bai et al., 2025)—show that our approach significantly improves performance, out- performing strong baselines such as DeepSeek-R1-distill- 32B (DeepSeek, 2025a) by an average margin of 7.7% (im- proved from 46.3% to 54.0%) (§4). Our contributions are summarized as follows: •Taxonomy of Atomic Skills: We decompose the long- context reasoning into five distinct, hierarchical capa- bilities, providing a anchor-based pipeline to automati- cally synthesize data for these atomic skills (§2). • Validation via Correlation: We provide an empiri- cal evidence that our proposed atomic skills are statis- tically correlated well with the general long-context reasoning capability (§3). •Efficient RL-based Enhancement: We demonstrate that targeted Reinforcement Learning on a small scale (4k) of atomic-skill data yields substantial improve- ments in general long-context reasoning, establishing a data-efficient path for model alignment (§4). 2. Atomic Skills for Long-context Reasoning In essence, long-context reasoning is not a monolithic skill but a hierarchical spectrum of cognitive requirements. Therefore, we decompose long-context reasoning into five atomic skills, ordered by increasing cognitive complexity: from foundational retrieval to robust discrimination, global aggregation, rational reasoning, and finally, dynamic state manipulation. 2.1. Atomic Skill Taxonomy Foundational Retrieval: Needle-in-a-Haystack (NIAH) The hierarchy begins with Foundational Retrieval, the most fundamental skill. Before any complex reasoning can occur, a model must first prove it can reliably locate a specific piece of information (“the needle”) anywhere within a vast sea of text (“the haystack”), overcoming the common “lost-in-the- middle” problem. This is the bedrock of all long-context capabilities. Robustness to Noise: Anti-Interference Capability Building on simple retrieval, Robustness to Noise addresses a more realistic challenge. It’s not enough to just find in- formation; a model must distinguish the correct target from similar-looking but incorrect “distractors”. This skill mea- sures the ability to maintain focus and factual accuracy when faced with deceptive or confusing information. Global Integration: Multi-Source Information Process- ing Moving beyond finding a single, correct piece of ev- idence, Global Integration requires a model to locate and synthesize information from multiple, separate locations within the context. Instead of retrieving one fact, the model must connect several scattered data points to construct a single, coherent answer, demonstrating an ability to process information in parallel. Relational Reasoning: Structure Understanding and LogicThe next level of complexity, Relational Reasoning, requires more than just gathering facts; it demands an under- standing of the logical relationships between them. A model must recognize the text’s underlying structure to perform operations like filtering, joining, or comparing different sets of information, much like executing a database query on unstructured text. Dynamic State Tracking: Long-Range Computational Reasoning At the peak of this hierarchy, Dynamic State Tracking tests a model’s ability to perform multi-step com- putational reasoning. Here, a model must not only retrieve and relate information but also use it to perform interme- diate calculations. It must derive new values from the text, hold these “states” in its working memory, and then execute a final computation using these derived results, completing a full “retrieve-solve-then-compute” workflow. 2 Submission and Formatting Instructions for ICML 2026 Stage1:Blueprint Stage2:QApair Stage3:Synthesis "Doc 1" : ["anchor4", "anchor5", "anchor3"] "Doc 2" : ["anchor1", "anchor5", "anchor2"] “Doc 3”: ["anchor4“, " anchor3"] [Noise Text....... ..................... Noise Text....... Noise Text.......] ..................... .........][...... ..................... .....................] ............... Multi-source Logic Calc-reason NIAHAnti-interfere Figure 2. The Automated Dataset Construction Pipeline of the Anchor-based Reasoning (AbR) Framework. 2.2. Automated Dataset Construction Pipeline To systematically evaluate the hierarchical cognitive de- mands outlined in our taxonomy, we introduce the Anchor- based Reasoning(AbR) framework. The core principle of this framework is to embed algorithmically generated an- chors—unique strings paired with specific, verifiable ques- tions—into extensive, noise-laden documents. By strate- gically distributing these “anchor-question” pairs, we can then pose meta-questions that require a model to aggregate or reason over the answers to these individual embedded queries. This design transforms the ambiguous challenge of long-context reasoning into a precise, quantifiable workflow comprising three core steps: information localization, em- bedded problem-solving, and logical integration. As shown in figure 2, we establish a three-stage automated pipeline to construct scalable, controllable, and verifiable datasets. Stage 1: Logical Blueprint Generation. We first pro- grammatically generate adocmappingJSON file. This blueprint defines the “ground truth” by specifying which an- chors (ancid) are contained within each virtual document (docid). // 5 anchors across 3 docs. "doc1": ["anc4", "anc5", "anc3"], "doc2": ["anc1", "anc5", "anc2"], "doc3": ["anc4", "anc3"] Stage 2: Question-Answer Pair Generation. Based on docmapping, we then generate diverse meta-questions requiring complex reasoning via rule-based templates or LLMs. The answers are generated as an executable expres- sion, representing the procedural steps needed to arrive at the correct solution.Solve(Q(anc))denotes solving the question associated with a specific anchor. •Question (Relational): “In the document that contains both ‘anchor5’ and ‘anchor3’, what is the answer to the question associated with ‘anchor4’?” • solve (Q (anc 4 , in doc (docs(anc 5 )∩ docs(anc 3 )))) •Question (Computational): “Calculate the sum of the answers to the questions for ‘anchor3’ in all documents that contain it.” • P [solve(Q(doc 1 , anc 3 )), solve(Q(doc 3 , anc 3 ))] Stage 3: Multi-Document Context Synthesis.We assem- ble the final sample by: 1) selecting unrelated background texts for eachdocid; 2) inserting anchor-question pairs at random positions based on thedocmapping; and 3) pairing the meta-question with the full synthesized context. Skill-Specific Task ConstructionWe tailor AbR tasks for each atomic skill: (1) Foundational Retrieval inserts specific pairs requiring the model to locate distributed anchors for objective answers. (2) Robustness to Noise employs two interference patterns: Similarity Discrimination uses highly similar anchors for fine-grained distinction, while Conflict- ing Information Resolution distributes identical anchors to enforce contradiction resolution. (3) Global Integration fragments clues across separate documents, compelling the model to aggregate dispersed data points into coherent logi- cal chains. (4) Relational Reasoning imposes logical con- straints on structural positions, requiring set operations (e.g., intersection, union) on document locations to identify tar- gets. (5) Dynamic State Tracking necessitates a multi-stage process deriving numerical values from distributed anchors to execute sequential mathematical operations. Detailed showcases for each skill are provided in the Appendix A. Controllable Difficulty and Curriculum A key advan- tage of our methodology is the precise control of training difficulty across a continuous complexity spectrum. By sys- tematically tuning parameters such as context length, anchor density, noise similarity, and reasoning depth, we establish a controlled environment for generating diverse challenges. This granularity facilitates the creation of a fine-grained training curriculum, enabling models to progressively ad- vance their long-context capabilities. 3. Validating the Role of Atomic Skills in Long-context Reasoning With the AbR pipeline enabling the precise generation of datasets targeting specific atomic skills, we proceed to ver- ify the ecological validity of our taxonomy. We aim to confirm that the atomic skills are not merely theoretical con- structs but foundational drivers of performance in complex, real-world scenarios. By conducting rigorous analyses, we 3 Submission and Formatting Instructions for ICML 2026 Figure 3. Spearman Correlation Analysis. The heatmap com- pares the correlation of our proposed atomic capabilities against real-world long-context benchmarks. demonstrate that the proposed atomic skills serve as critical indicators of the model’s overall capability. 3.1. Setup In these analyses, we evaluate LLMs with both standard real-world long-context benchmarks and atomic skill evalu- ation sets. The real-world benchmarks are used to mea- sure models’ general long-context capability, including Loogle (Li et al., 2024b), LongBench-v2 (Bai et al., 2025) and Loong (Wang et al., 2024). The atomic evaluation sets are based on our proposed atomic skills: Needle-in-a- Haystack (NIAH), Anti-Interference, Multi-Source, Logic, and CalcReason. We additionally introduced existing open- source benchmarks focusing on computational reasoning and information aggregation capabilities as a control group. We selected 11 open-source models with parameter sizes ranging from 7B to 32B. To quantify the relationship be- tween atomic skill proficiency and long-context reasoning, we employed the Spearman rank correlation coefficient (ρ). All evaluations were conducted with context lengths up to 128K tokens to maintain experimental consistency. 3.2. Analysis 1: Correlation Analysis We first analyze the Spearman correlation coefficients be- tween the performance on existing real-world and proposed atomic benchmarks. As shown in Figure 3, the results pro- vide strong statistical evidence (ρ-values), validating the effectiveness of our approach. High Predictive Validity.Our atomic probes demonstrate exceptional predictive power regarding the average perfor- mance on real-world benchmarks (Realmean). For instance, our NIAH and Anti-interfere probes achieve exceptional alignment with Realmean (ρ = 0.95andρ = 0.94, respec- tively). This superiority is particularly evident in challeng- ing benchmarks like Loong, where Multi-source reaches a correlation ofρ = 0.99. These consistently high cor- relations (all significant atp < 0.001) validate our tax- onomy: rather than being an arbitrary collection of tasks, these probes serve as accurate “proxies” that effectively de- compose the complexity of long-context understanding into measurable atomic units. Inadequacy of Generic Baselines. The results further show that generic baselines exhibit limited predictive power for real-world performance. The synthetic baseline OOlong- synth shows a negligible correlation with the average of real benchmarks (Realmean,ρ = 0.17). While GSM-infinite demonstrates a moderate correlation (ρ = 0.70), it consis- tently lags behind Calc-reason (ρ = 0.94). 3.3. Analysis 2: Diagnosing the Capability Gap By cross-referencing the correlation data (Figure 3) with the absolute performance scores (Table 1), we further identify critical structural flaws in current models. The “Importance-Proficiency” Mismatch.Our analysis reveals a specific pattern of High Correlation, Low Per- formance. For example, Anti-interfere and Multi-source are strong predictors of real-world success (ρ = 0.94and ρ = 0.91, respectively). However, most models struggle on these tasks: whileQwen2.5-32b-instructachieves 37.00% on basic NIAH, it drops to 22.13% on Anti-interfere and 23.88% on Multi-source. Similarly, Logic proves to be the most difficult task (e.g., 13.00% for the same model), though its correlation with real-world performance is mod- erate (ρ = 0.77). Moreover, there exists a Retrieval Ceiling, that is, most models perform relatively well on clean NIAH tasks. However, since NIAH is merely a prerequisite, im- proving it further yields diminishing returns for complex real-world tasks. The Robustness Bottleneck. The perform difference be- tween NIAH and Anti-Interference (e.g., 37.00% v.s. 22.13% forQwen2.5-32b-instruct) highlights that models lack discrimination capabilities. They can retrieve informa- tion but tend to be easily distracted by “lure” noise. Since Anti-Interference correlates highly with real-world bench- marks (ρ = 0.94), this fragility can be an important factor for general performance. 4. RL-Based Enhancement 4.1. Setup Training Setup To enhance atomic skills, we employ the Group Relative Policy Optimization (GRPO) algo- 4 Submission and Formatting Instructions for ICML 2026 Table 1. Performance comparison on atomic skills. ModelNIAHAnti-interfereMultisourceLogicCalcreason QwenLong-L1-32B66.50%33.83%38.81%28.50%47.37% Qwen2.5-32b-instruct37.00%22.13%23.88%13.00%36.59% DeepSeek-R1-Distill-Qwen-32B58.25%25.96%32.54%17.50%42.11% Qwen3-32B23.00%12.55%23.28%19.00%19.80% Qwen3-32B69.50%29.15%37.01%27.25%52.13% Qwen3-30B-A3B-thinking-250774.25%41.70%47.46%31.50%60.15% Qwen3-14B46.50%21.06%29.25%19.50%37.09% Deepseek-R1-Distill-Qwen-14B37.50%13.40%19.10%9.00%24.31% Qwen2.5-14b-instruct27.75%14.47%19.70%14.25%31.58% Qwen3-8B42.00%17.66%25.37%15.00%37.09% Qwen2.5-7b-instruct16.50%8.30%11.64%9.25%19.30% Deepseek-R1-Distill-Qwen-7B5.25%2.13%3.28%3.75%4.51% rithm (Shao et al., 2024). To mitigate reward homogeniza- tion and accelerate convergence, we incorporate Dynamic Sampling (Yu et al., 2025) to prune redundant trajecto- ries. The reward signal is derived from an LLM-as-a-Judge framework usinggpt-oss-120B(Agarwal et al., 2025), which assigns binary correctness rewards. Specifically for instruction-tuned models, we introduce a Chain-of-Thought (CoT) system prompt and a format-compliance reward to in- duce deliberate reasoning, whereas models with CoT follow standard procedures. More training details are showned in Appendix B. Weconductourmainexperimentsusingthree backbonemodels:Qwen2.5-14B-Instruct, Qwen2.5-32B-Instruct(Alibaba,2024),and DeepSeek-R1-Distill-32B(DeepSeek, 2025a), with ablation studies and in-depth analyses performed on the latter. All models are trained from scratch (cold-started) without prior fine-tuned policies. We construct the training dataset by sampling DeepSeek V3.1, filtering for queries with a pass rate between 0.3 and 0.6 to ensure appropriate difficulty. The final dataset mixture adheres to the ratio of Anti-interfere : Multi-hop : Multi-source : Logic : Calc-reason : NIAH =5 : 3 : 2 : 2 : 2 : 1. During the rollout phase, we set sampling hyperparameters to topp = 0.6andtopk = 20. The maximum sequence lengths for input and output are restricted to 24k and 8k tokens, respectively. All models are trained on 64 H20 GPUs. Evaluation Our evaluation framework incorporates both standard open-source benchmarks and a custom atomic ca- pability dataset. For open-source benchmarks, we select LongBench-v2(Bai et al., 2025),Loong(Wang et al., 2024),MRCR(OpenAI, 2025c),BrowsCompLong(Ope- nAI, 2025a), theqa2subset fromRuler(Hsieh et al., 2024), and the real-prompt subset ofLoogle(Li et al., 2024b). To ensure consistency, we filter these datasets to include only samples with context lengths less than or equal to 128k tokens. The evaluation metrics for these open- source benchmarks align strictly with the protocols defined in their respective original papers. Additionally, we assess atomic capabilities using a dataset constructed via our pro- posed methodology, employinggpt-oss-120B(OpenAI, 2025b) to conduct consistency-based evaluation. Baselines Wecompareourapproachagainst some general baselines including the closed-source (Gemini-3-Pro)aswellasopen-sourcebase- lines includingKimi-K2-Thinking(Team et al., 2025),DeepSeek-V3.1(DeepSeek,2025b), QwenLong-L1-32B(Wanetal.,2025),and Qwen3-235B(Yang et al., 2025a).In addition, to further show the superiority of our approach, we compare it with some direct baselines, which are obtained by training DeepSeek-R1-distill-32B on the synthetic long-context reasoning datasets named LongReason (Ling et al., 2025), QwenDocqa (Wan et al., 2025), LoonngRl (Wang et al., 2025). In details, we utilize the officially released datasets for LongReason and QwenDocQA. Additionally, we reproduce the data construction pipeline of Loonngrl to generate a dataset of4, 000samples for comparison. To accommodate the long-context requirements of our evaluation, for any baseline model with a native context window smaller than 128k, we apply YaRN for length extrapolation. 4.2. Main Results Overall Performance on Long Context BenchmarksTa- ble 2 presents the comprehensive evaluation results across six challenging long-context benchmarks. We can see that our approach yields an absolute gain of 7.7% in av- erage over the backboneDeepSeek-R1-distill-32B 5 Submission and Formatting Instructions for ICML 2026 Table 2. Performance comparison on Open Long Context Benchmarks. The top block shows general baselines and the bottom block illustrates the direct baselines with the same backbone. The best result in each column within its block is in bold. ModelLoogleLongbench-v2LoongBrowscomplongRuler-qa2MRCRAverage Gemini-3-pro52.86%69.38%65.43%88.07%83.01%75.30%72.34% Kimi-K2-Thinking51.50%49.30%58.01%58.10%49.98%51.77%53.11% DeepSeek-V3.155.77%52.88%50.55%56.27%42.97%46.62%50.84% Qwen3-235B-A22B-thinking-250752.77%49.30%53.70%50.76%46.81%44.61%49.66% QwenLong-L1-32B49.32%43.74%44.68%69.93%47.70%27.70%47.18% DeepSeek-R1-distill-32B42.31%43.94%38.17%64.22%57.23%31.94%46.30% DeepSeek-R1-distill-32B+LongReason43.23%44.14%38.57%57.90%58.36%32.85%45.84% DeepSeek-R1-distill-32B+QwenDocqa47.96%46.32%39.98%71.56%67.45%34.59%51.31% DeepSeek-R1-distill-32B+LoongRL48.41%45.73%40.29%70.74%61.84%37.23%50.71% DeepSeek-R1-distill-32B+Ours50.59%49.70%44.68%73.09%69.38%36.74%54.03% DeepSeek-R1-distill-32B+Ours+LoongRL55.59%51.29%44.45%72.27%67.01%36.12%54.46% and it consistently outperforms all three direct baselines including LongReason, QwenDocqa, LoogRL. Moreover, Our approach achieves superior performance over the re- markableKimi-K2-Thinkingmodel, outperforming DeepSeek-V3.1 and Qwen3-235B by a large margin. Performance Superiority.As presented in Table 2, while existing strategies like QwenDocQA and LoongRL ef- fectively improve the baseline (raising the average score from46.30%to51.31%and50.71%, respectively), our method demonstrates superior efficacy. Without relying on external data,DeepSeek-R1-distill-32B+Ours achieves an average score of54.03%, outperforming the robust LoongRL baseline by3.32%and the original base model by7.73%. This significant margin indicates that our construction strategy captures critical long-context depen- dencies more effectively than previous approaches. Effectiveness on More Backbone Models To broadly evaluate the effectiveness of our approach, we implement it on top of theQwen2.5family and the results are shown in Table 3. ForQwen2.5-14B-instruct, our approach achieves a remarkable performance boost, increasing the average score from35.59%to45.83%(an absolute gain of+10.24%). Notably, on the Rulerqa2 and Browscomp- long datasets, our method yields absolute gains of over20% (40.28%→ 63.21%and47.30%→ 69.72%, respectively). Similarly, for the largerQwen2.5-32B-instruct, our method improves the average performance from41.54%to 45.50%, demonstrating robustness across different parame- ter scales. Synergistic Effect. We hypothesize that our method and Loongrl data address different aspects of long-context ca- pabilities. Experimental results support this hypothesis: combining our method with1, 000LoongRL data yields the highest overall performance of54.46%. This “stacking” effect suggests that our method is not merely a replacement but a complementary enhancement that can be integrated Figure 4. Performance Gain over Base Model. The radar chart compares the performance improvements of our full method (red, with stars) against various ablation variants across six real-world long-context benchmarks. with LoongRL data construction pipelines to push the bound- aries of long-context understanding. 4.3. In-depth Analyses 4.3.1. IMPACT OF ATOMIC CAPABILITIES To verify the contribution of each atomic capability, we con- ducted an ablation study by removing specific components from our training data. Figure 4 illustrates the performance gains over the Base model (represented by the grey dashed hexagon at 0). Synergy of Atomic Capabilities.The Full Method (red line) consistently yields the highest improvements, com- pletely enveloping all other ablated variants in Figure 4. It achieves remarkable gains across diverse benchmarks, such as +13.3 on Loogle and +9.8 on Ruler-qa2. This comprehen- sive superiority demonstrates that the synergy of all atomic capabilities is essential for maximizing robust long-context performance. 6 Submission and Formatting Instructions for ICML 2026 Table 3. Performance of our approach applied to more backbone models. The best result in each column with its block is highlighted in bold. ModelLoogleLongbench-v2LoongBrowscomplongRuler-qa2MRCRAverage Qwen2.5-14B-instruct33.06%36.38%24.65%47.30%40.28%31.87%35.59% Qwen2.5-14B-instruct+Ours40.51%41.15%28.63%69.72%63.21%31.73%45.83% Qwen2.5-32B-instruct35.97%39.76%34.27%60.65%45.25%33.33%41.54% Qwen2.5-32B-instruct+Ours45.78%43.94%38.34%60.86%47.74%36.33%45.50% Criticality of Multi-source Integration. Removing Multi-source data (blue line) reveals a critical phenomenon: performance on general benchmarks like Loong and LongBench-v2 drops below the Base model, despite remain- ing positive on MRCR. This suggests that Multi-source data acts as a foundational stabilizer, without which the model develops a skill imbalance that degrades its fundamental ability to process general long contexts. Impact of Logical Reasoning. The removal of Logic (green line) leads to substantial performance degradation on Browscomplong and Rulerqa2. The wide gap between the green and red lines on these axes suggests that tasks involving long-document browsing or complex QA rules rely heavily on the model’s logical structure and reasoning chain, rather than simple retrieval. Generalization via Calculation. The Calcreason ca- pability (purple line) proves to be a global performance enhancer, not limited to the numerical tasks in Loogle. The consistent drops across general benchmarks like Rulerqa2 and Loong indicate that training on calculation data instills a rigorous reasoning mindset, improving the model’s gener- alized ability to track complex dependencies and maintain precision over long contexts. 4.3.2. NON-ORTHOGONALITY AND HIERARCHICAL DEPENDENCIES To validate our hypothesis that long-context capability is a hierarchical spectrum rather than a monolithic skill, we analyzed the performance drops on atomic probes when individual training components were ablated (Figure 5). Diagonal Dominance (Distinctness). The heatmap ex- hibits a strong diagonal pattern, particularly for Logic (-29) and Anti-interfere (-21.1). This confirms that ”Logical Structuring” and ”Robust Discrimination” are specialized skills requiring dedicated training, as they cannot be implic- itly learned solely through simple retrieval tasks. Hierarchical Dependencies. The off-diagonal values re- veal a clear cognitive hierarchy. We observe an asymmetric dependency where removing Logic significantly impairs Figure 5. Non-Orthogonality Analysis: Performance Drop by Module Removal. The heatmap illustrates the performance degradation across different atomic capability probes when specific training modules are ablated. Calcreason (-12.3), whereas removing Calcreason has a much smaller impact on Logic (-6.0). This supports the hypothesis that dynamic state manipulation relies on underlying logical structuring. Furthermore, the removal of Multisource causes consistent degradation across all atomic capabilities (e.g., -10.6 on Anti-interfere, -10.5 on Calcreason). This corroborates the ”skill imbalance” ob- served in 4.3.1, confirming that Global Integration acts as a foundational stabilizer—essential for maintaining the gen- eral distribution alignment required to support specialized cognitive skills. 4.3.3. ANALYSIS OF ATOMIC CAPABILITY ENHANCEMENT To evaluate specific capability enhancements, we compared our method against the Base model and the LoongRL base- line (Figure 6). Transformative Gains in Complex Reasoning.Our method yields substantial improvements over the Base model across all dimensions, particularly in tasks requir- ing deep cognitive processing. Notably, Logic surges from ∼ 18%to 68.8%, and Calcreason nearly doubles to 80.7%. These results confirm that our approach effectively activates the model’s ability to handle complex numerical and logical reasoning within long contexts. Surpassing the Retrieval Ceiling. A comparative anal- 7 Submission and Formatting Instructions for ICML 2026 Figure 6. Performance comparison on Atomic Capability Probes. We compare the DeepSeek-R1-distill-32B base model (Grey), the model trained with 4k LoongRL (Blue), and our proposed method (Orange). Figure 7. Performance Comparison across Context Length Intervals on LongBench-v2. The Pass@1 accuracy of baseline models (dashed lines) versus our method (solid lines) across dif- ferent length buckets. ysis reveals the limitations of standard data construction. While LoongRL matches our performance on simple re- trieval (NIAH:∼ 78%vs. 79.8%), it fails to generalize to higher-order tasks. Our method significantly outperforms LoongRL on Anti-interfere (+26.7%) and Logic (+41.8%). This demonstrates that while standard long-context data im- proves window utilization, our synthesized data is essential for bridging the gap between simple retrieval and complex problem-solving. 4.3.4. PERFORMANCE ANALYSIS ACROSS CONTEXT LENGTH INTERVALS To investigate the robustness of our method under varying input lengths, we analyze performance on LongBench-v2 across four distinct intervals ranging from 8k to 128k. As illustrated in Figure 7, our method consistently shifts the per- formance curve upward, maintaining superiority regardless of context length. Length-Invariant Robustness The results confirm that our approach effectively mitigates the performance degra- dation typically observed in extended contexts. Specifi- cally, for theDeepSeek-R1-distill-32Bmodel, we achieve a substantial gain in the 32k-64k interval, boosting accuracy from 48.48% to 59.09%. Crucially, this advantage persists even in the challenging 64k-128k bucket, demon- strating that our method sustains high-quality reasoning capabilities across the entire long-context spectrum without suffering from significant information loss. 5. Related Works Enhancing the long-context reasoning of LLMs is a crucial yet challenging research problem, attracting extensive ef- forts (Chen et al., 2023; Li et al., 2024d; Bai et al., 2024). Conventional paradigms for enhancing long-context rea- soning typically curate task-specific datasets (Chen et al., 2023; Bai et al., 2024) and then optimize LLMs via fine- tuning (Li et al., 2024a; Zhang et al., 2025) or reinforcement learning (Wan et al., 2025; Shen et al., 2025; Wang et al., 2025). Nevertheless, long-context reasoning is an inher- ently complex and monolithic task, making the construction of high-quality training data for this task fraught with in- tractable challenges (Yang et al., 2025b), including the misinformation risk caused by inadequate verification proto- cols in data curation (Li et al., 2024c) and latent knowledge conflicts existing in the manually or automatically curated datasets (Xu et al., 2024). In response to these limitations, we embrace a decomposition perspective and propose AbR framework that breaks down long-context reasoning into atomic skills. This approach enables the automatic cura- tion of verifiable training data, effectively mitigating the data quality and scalability bottlenecks inherent in conven- tional monolithic paradigms. In parallel, we also examine the impact of table-style tasks on long-context reasoning in another work. 6. Conclusions This paper presents a decomposition perspective to long- context reasoning for LLMs and decomposes the long- context reasoning capability into five atomic skills. Then it designs an automatic pipeline to curate training data for each of these skills. Empirical experiments demonstrate that these atomic skills correlate well with standard long-context reasoning benchmarks. Based on this finding, it proposes an effective approach based on reinforcement learning to train LLMs on the curated atomic dataset, in the hope of enhancing the long-context reasoning capability. Intensive experiments on six standard long-context reasoning bench- marks indeed show that the proposed approach yields a 8 Submission and Formatting Instructions for ICML 2026 substantial gain over the strong backbone LLMs and outper- forms several baselines on long-context reasoning. Impact Statement This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here. References Agarwal, S., Ahmad, L., Ai, J., Altman, S., Applebaum, A., Arbus, E., Arora, R. K., Bai, Y., Baker, B., Bao, H., et al. gpt-oss-120b & gpt-oss-20b model card. arXiv preprint arXiv:2508.10925, 2025. Alibaba. Qwen 2.5 technical report.https://arxiv. org/abs/2409.13586, 2024. Bai, Y., Lv, X., Zhang, J., He, Y., Qi, J., Hou, L., Tang, J., Dong, Y., and Li, J. Longalign: A recipe for long con- text alignment of large language models. arXiv preprint arXiv:2401.18058, 2024. 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Li, J., Wang, M., Zheng, Z., and Zhang, M. Loogle: Can long-context language models understand long contexts? In Proceedings of the 62nd Annual Meeting of the Asso- ciation for Computational Linguistics (Volume 1: Long Papers), p. 16304–16333, 2024b. Li, S., Yang, C., Cheng, Z., Liu, L., Yu, M., Yang, Y., and Lam, W. Large language models can self-improve in long-context reasoning. arXiv preprint arXiv:2411.08147, 2024c. Li, Y., Liang, S., Lyu, M., and Wang, L. Making long- context language models better multi-hop reasoners. In Proceedings of the 62nd Annual Meeting of the Associ- ation for Computational Linguistics (Volume 1: Long Papers), p. 2462–2475, 2024d. Ling, Z., Liu, K., Yan, K., Yang, Y., Lin, W., Fan, T.-H., Shen, L., Du, Z., and Chen, J. Longreason: A synthetic long-context reasoning benchmark via context expansion. arXiv preprint arXiv:2501.15089, 2025. Liu, A., Mei, A., Lin, B., Xue, B., Wang, B., Xu, B., Wu, B., Zhang, B., Lin, C., Dong, C., et al. Deepseek-v3. 2: Pushing the frontier of open large language models. arXiv preprint arXiv:2512.02556, 2025. Meyur, R., Phan, H. D., Hayashi, K. B., Stewart, I., Sharma, S., Chaturvedi, S., Parker, M., Nally, D. M., Montgomery, S. A., Pazdernik, K., et al. Benchmarking llms for en- vironmental review and permitting. In Large Language Models for Scientific and Societal Advances, 2025. OpenAI.Browscomp long hugging face dataset. https://huggingface.co/datasets/ openai/BrowseCompLongContext, 2025a. OpenAI.Gpt-ossmodelcard:Open- weightreasoningmodels(120bparame- ters).https://cdn.openai.com/pdf/ 419b6906-9da6-406c-a19d-1b078ac7637/ oai_gpt-oss_model_card.pdf, 2025b. 9 Submission and Formatting Instructions for ICML 2026 OpenAI. Openai mrcr: Long context multiple needle in a haystack benchmark.https://huggingface.co/ datasets/openai/mrcr, 2025c. Paulsen, N. Context is what you need: The maximum effective context window for real world limits of llms. arXiv preprint arXiv:2509.21361, 2025. Reddy, V., Koncel-Kedziorski, R., Lai, V. D., Krumdick, M., Lovering, C., and Tanner, C. Docfinqa: A long- context financial reasoning dataset.arXiv preprint arXiv:2401.06915, 2024. Shao, Z., Wang, P., Zhu, Q., Xu, R., Song, J., Bi, X., Zhang, H., Zhang, M., Li, Y., Wu, Y., et al. Deepseekmath: Push- ing the limits of mathematical reasoning in open language models. arXiv preprint arXiv:2402.03300, 2024. Shen, W., Yang, Z., Li, C., Lu, Z., Peng, M., Sun, H., Shi, Y., Liao, S., Lai, S., Zhang, B., et al. Qwenlong-l1. 5: Post- training recipe for long-context reasoning and memory management. arXiv preprint arXiv:2512.12967, 2025. Team, G., Georgiev, P., Lei, V. I., Burnell, R., Bai, L., Gulati, A., Tanzer, G., Vincent, D., et al. Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context, 2024. URL https://arxiv. org/abs/2403.05530, 2024. Team, K., Bai, Y., Bao, Y., Chen, G., Chen, J., Chen, N., Chen, R., Chen, Y., Chen, Y., Chen, Y., et al. Kimi k2: Open agentic intelligence. arXiv preprint arXiv:2507.20534, 2025. Wan, F., Shen, W., Liao, S., Shi, Y., Li, C., Yang, Z., Zhang, J., Huang, F., Zhou, J., and Yan, M. Qwenlong-l1: To- wards long-context large reasoning models with reinforce- ment learning. arXiv preprint arXiv:2505.17667, 2025. Wang, M., Chen, L., Cheng, F., Liao, S., Zhang, X., Wu, B., Yu, H., Xu, N., Zhang, L., Luo, R., et al. Leave no document behind: Benchmarking long-context llms with extended multi-doc qa. In Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing, p. 5627–5646, 2024. Wang, S., Zhang, G., Zhang, L. L., Shang, N., Yang, F., Chen, D., and Yang, M. Loongrl: Reinforcement learning for advanced reasoning over long contexts. arXiv preprint arXiv:2510.19363, 2025. Xu, R., Qi, Z., Guo, Z., Wang, C., Wang, H., Zhang, Y., and Xu, W. Knowledge conflicts for llms: A survey. arXiv preprint arXiv:2403.08319, 2024. Yang, A., Li, A., Yang, B., Zhang, B., Hui, B., Zheng, B., Yu, B., Gao, C., Huang, C., Lv, C., et al. Qwen3 technical report. arXiv preprint arXiv:2505.09388, 2025a. Yang, C., Lin, X., Xu, C., Jiang, X., Ma, S., Liu, A., Xiong, H., and Guo, J. Longfaith: Enhancing long-context rea- soning in llms with faithful synthetic data. arXiv preprint arXiv:2502.12583, 2025b. Yu, Q., Zhang, Z., Zhu, R., Yuan, Y., Zuo, X., Yue, Y., Dai, W., Fan, T., Liu, G., Liu, L., et al. Dapo: An open-source llm reinforcement learning system at scale. arXiv preprint arXiv:2503.14476, 2025. Zhang, J., Hou, Z., Lv, X., Cao, S., Hou, Z., Niu, Y., Hou, L., Dong, Y., Feng, L., and Li, J. Longreward: Improving long-context large language models with ai feedback. In Proceedings of the 63rd Annual Meeting of the Associ- ation for Computational Linguistics (Volume 1: Long Papers), p. 3718–3739, 2025. 10 Submission and Formatting Instructions for ICML 2026 A. Showcases for 5 Atomic Skills A.1. Foundational Retrieval: NIAH Multiple specific anchor-question pairs are distributed across a long context. The model is tested on its ability to precisely locate a specific anchor and other similar anchors, and answer associated objective questions. Case ID: Distributed-Retrieval-NIAH Category: NIAH Key Mechanism: Distributed Anchors Context Overview: • The Haystack (Background Context): A long sequence of unrelated text segments (e.g., financial reports, historical essays, or technical logs) serving as noise. •Inserted Needles (Distributed Pairs): Specific Anchor-Question pairs are inserted at random intervals through- out the context. [Segment 0-10%] ... The industrial revolution marked a turning point ... [ID: A-105]→Question 1 ... [Segment 40-50%] ... regarding the molecular structure of polymers ... [ID: B-292]→Question 2 ... [Segment 80-90%] ... market volatility observed in the last quarter ... [ID: C-345]→Question 3 ... • Target Needle: The specific pair required by the instruction (e.g., the pair located at the 50% depth). Instruction: Please answer the question following the anchor [ID: B-292] in the text above. Target Answer: 3398(The model must retrieve the exact objective question associated with the specific key, and answer the question correctly. A.2. Robustness to Noise: Anti-Interference The anchor string 1760536321726-5em0 appears in Doc 1 (twice) and Doc 3 (once). The prompt explicitly requests the content from Doc 3. Tests if the model respects document boundaries despite conflicted retrieval anchors. Case ID: Anchor-Conflict Category: Anti-interfere Key Mechanism: Anchor Duplication & Document Scope Constraint Context Overview: •Document 1 (Distractor): Contains the anchor string twice, associated with a Geometry problem and a Matrix Trace problem. ... [Noise] ... 1760536321726-5em0: Given a set of pointsP =P 1 , . . .on a plane... [Noise] ... 1760536321726- 5em0: Calculate the trace of the following matrix... • Document 2 (Noise): Irrelevant content (Programming Q&A). • Document 3 (Target): Contains the anchor string once, associated with a Complex Analysis problem. ... [Noise] ... 1760536321726-5em0: Evaluate the integral R C exp(z 2 ) z 2 (z−1−i) dz, where C consists of the contour... Instruction: Please answer the question following ‘1760536321726-5em0’ in document 3. Target Answer: πe 2i (The model must ignore the questions in Document 1 and solve the integral in Document 3). 11 Submission and Formatting Instructions for ICML 2026 A.3. Global Integration: Multi-Source Information Processing A single mathematical problem is split into three parts (Setup, Question 1, Question 2) across three different documents. The model must perform cross-document retrieval to reconstruct the full problem context before solving it. Case ID: Global-Integration Category: Global Integration Key Mechanism: Fragmented Information Aggregation Context Overview: •Document 1 (Problem Setup): Contains the initial conditions of the geometry problem embedded within medical text. ... [Medical Q&A Noise] ... h6qKmUOmz2m: Given circleC : x 2 + y 2 + 2x− 2y− 6 = 0, linelpasses through point P(1, 2) and intersects circle C at points A and B. ... [Noise] ... •Document 2 (Sub-question 1): Contains the first part of the specific question embedded within different medical/pharmaceutical text. ... [Medical Q&A Noise] ... h6qKmUOmz2m: (1) If△ABCis an isosceles right-angled triangle, find the equation of line l; ... [Noise] ... •Document 3 (Sub-question 2): Contains the second part of the question embedded within a financial project report. ... [Financial Report Noise] ... h6qKmUOmz2m: (2) WhenP C ⊥ l, find the equation of the circumcircle of △ABC. ... [Noise] ... Instruction: Please assemble the question corresponding to ‘h6qKmUOmz2m’ and answer it. Target Answer: (1) x = 1 or 3x + 4y− 11 = 0 (2) 5x 2 + 5y 2 − 6x− 18y + 2 = 0 (The model must retrieve the setup from Doc 1, combine it with conditions from Doc 2 and Doc 3, and solve the aggregated geometry problem). A.4. Relational Reasoning: Structure Understanding and Logic The model must perform a global scan to determine anchor uniqueness frequencies, select the correct document based on key density, and apply strict positional logic to locate the target question, filtering out ”trap” anchors (duplicates) during the process. 12 Submission and Formatting Instructions for ICML 2026 Case ID: Logic-Constrained Category: Relational Reasoning Key Mechanism: Global Frequency Analysis & Relative Positional Logic Context Overview: • Document 1 (E-Commerce Report): Contains multiple unique keys associated with Math and Logic problems. ... Consumer Expectations in 2018 ... OSXVANVP: Sequence problema n+1 = a n + 2 n ... BEKAHJXW: Statistics problem ... • Document 2 (Environmental Report): Plain text with no embedded keys (Distractor). • Document 3 (Biography): Contains a mix of unique keys and a duplicated key. ... General Walker commanded the Eighth Army ... KNGUKM: Tennis tournament logic ... ABNKRKRH: Inequality problem ln a e a = . . . ... GIEDWE: Physics wave calculation ... RJTGAYG: House logic puzzle ... • Document 4 (Linear Algebra): Contains the duplicated key found in Document 3. ... Problem 5: Decide if range of map ... GIEDWE: Geometry point set problem ... Instruction: First, identify anchors that appear only once across all documents. Find the document with the highest total count of anchors. In that document, locate the last unique anchor and answer the question associated with the unique anchor immediately preceding it. Target Answer (for ABNKRKRH): C (Based on the analysis of the inequality lna e a = lnb b =− lnc c < 0, implying a < b < c). A.5. Dynamic State Tracking: Long-Range Computational Reasoning The model cannot simply retrieve a value; it must first determine the state of the context (counting specific key occurrences), evaluate a logical condition based on that state, and then perform a specific sequence of mathematical operations on values retrieved from distributed anchors. 13 Submission and Formatting Instructions for ICML 2026 Case ID: Dynamic-State-Tracking-Math Category: Dynamic State Tracking / Computational Reasoning Key Mechanism: Conditional Logic & Multi-Stage Aggregation Context Overview: • Document 1 (Survey Analysis): Contains a key embedded in statistical text. ... excluding incomplete questionnaires ... LTUCRHGAXK: 82× 67 ... • Document 2 (Game Design Manual): Contains a key embedded in UI/UX instructions. ... visual balance lines ... NNQABR: 6− (8− 4) + 16 ... • Document 3 (Stock Market Report): Contains the target keys for the ”False” branch. ... A-share defense battle ... ROXBXXYMYU:2− 14.9/6 + 7... market leverage ... MPEOEZHO:19× 19.7 + 20/2 ... • Document 4 (Electricity Report): Contains the target keys for the ”True” branch (Distractors). ... 16-candle lamps installed ... TBWYKIE:(20× 4)× (3− 16)... KYPNFYC:sin(135 ◦ )× cos(135 ◦ ) + 3... Instruction: If the number of documents containingLTUCRHGAXKis greater than the number of documents containingNNQABR, calculate the sum of the answers forTBWYKIEandKYPNFYC. Otherwise, calculate the product of the answers for ROXBXXYMYU and MPEOEZHO. (Round intermediate steps to 2 decimal places). Target Answer: 2505.64 B. Training Details This section details the reinforcement learning algorithms and techniques utilized for enhancing atomic skills, including the optimization objective, sampling strategies, and reward mechanisms. B.1. Group Relative Policy Optimization (GRPO) Group Relative Policy Optimization (GRPO) (Shao et al., 2024) is designed to reduce the computational overhead in large-scale model training by eschewing a trained value function. The core innovation lies in its advantage estimation mechanism. Instead of relying on a critic network to provide a value baseline, GRPO computes the advantage for each sample relative to the average reward of a group of samples generated from the same prompt. For a given prompt, a group ofGoutputs o 1 ,o 2 ,...,o G is sampled from the policyπ old . Upon obtaining a rewardr i for each outputo i , the advantageA i is calculated as: A i = r i − 1 |G| |G| X j=1 r j (1) This formulation utilizes the group mean reward as a dynamic baseline. The policy is updated using a clipped surrogate objective augmented with a KL-divergence penalty. Formally, the objective is defined as follows. E min π θ (a|s) π old (a|s) A i , clip π θ (a|s) π old (a|s) , 1− ε, 1 + ε A i − β· D KL (π θ ∥π old )(2) where θ represents the parameters, ε is the clipping hyperparameter, and β controls the strength of the KL regularization. B.2. Dynamic Sampling To address the issue of reward homogenization—where similar rewards within a group lead to near-zero advantages and vanishing gradients—Dynamic Sampling (Yu et al., 2025) is employed. This strategy dynamically prunes samples with 14 Submission and Formatting Instructions for ICML 2026 redundant rewards during training. By ensuring that training batches are composed of diverse and informative trajectories, this method strengthens the gradient signal and accelerates convergence. B.3. Reward Modeling and Reasoning Induction The reward signal is typically derived from an LLM-as-a-Judge paradigm, where a larger model evaluates the correctness of generated outputs. A binary reward (1 for a match, 0 otherwise) is assigned based on whether the output matches the reference answer. Different strategies are applied depending on the model type: •Instruct Models: To guide standard instruction-tuned models toward a deliberate reasoning mode, a specialized “chain-of-thought” system prompt is introduced alongside a format-compliance reward signal. •Models with CoT: For models that inherently incorporate a reasoning process, standard training procedures are followed without additional reasoning-inducing prompts. 15

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