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Parason: Revealing Subtask and Trial Parallelism in LLM Reasoning
Zhengyang Zhang, Zijian Zhang, Jiaxuan Gao, Shusheng Xu, Yi Wu, Song Han, Ligeng Zhu
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Abstract
Abstract:Scaling test-time reasoning has substantially improved the problem-solving ability of large language models (LLMs), but standard autoregressive decoding still executes long reasoning traces sequentially, creating severe latency for difficult tasks (up to days and weeks). Parallel reasoning offers a natural remedy. However, prior systems primarily focus on Subtask Parallelism, where the model learns to decompose a high-level task into smaller chunks that can be solved independently. This approach overlooks another pervasive form of parallelism: Trial Parallelism, where multiple speculative attempts explore, verify, and aggregate competing hypotheses in parallel. In this paper, we introduce Parason, which reveals and learns both forms of parallelism in LLM reasoning. Our analysis identifies Trial Parallelism as the majority of parallelizable reasoning computation (65.5% in DeepSeek-V4's reasoning steps in HLE), and it becomes increasingly dominant on hard problems. Guided by this taxonomy, Parason converts sequential reasoning traces into structured parallel trajectories with a context-free grammar, then trains models with Parallelism-Aware Group Relative Policy Optimization (PA-GRPO), whose reward jointly balances accuracy, latency, and the two parallelism ratios. At inference time, Parason executes the learned parallel structure through tool calls, translating theoretical savings to real-world wall-clock acceleration. Experiments on mathematical reasoning benchmarks including AIME24 and AIME25 show that Parason achieves an average acceleration about 1.7$\times$ while maintaining competitive accuracy.
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- Source: https://arxiv.org/abs/2608.24658v1
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Parason: Revealing Subtask- and Trial Parallelism in LLM Reasoning Zhengyang Zhang 1 Zijian Zhang 1 4 Jiaxuan Gao 1 Shusheng Xu 2 Yi Wu 1 Song Han 3 4 Ligeng Zhu 4â 1 Tsinghua University 2 Independent Researcher 3 Massachusetts Institute of Technology 4 NVIDIA Abstract Scaling test-time reasoning has substantially improved the problem-solving abil- ity of large language models (LLMs), but standard autoregressive decoding still executes long reasoning traces sequentially, creating severe latency for difficult tasks (up to days and weeks). Parallel reasoning offers a natural remedy. However, prior systems primarily focus on Subtask Parallelism, where the model learns to decompose a high-level task into smaller chunks that can be solved independently. This approach overlooks another pervasive form of parallelism: Trial Parallelism, where multiple speculative attempts explore, verify, and aggregate competing hypotheses in parallel. In this paper, we introduce Parason, which reveals and learns both forms of parallelism in LLM reasoning. Our analysis identifies Trial Parallelism as the majority of parallelizable reasoning computation (65.5% in DeepSeek-V4âs reasoning steps in HLE), and it becomes increasingly dominant on hard problems. Guided by this taxonomy, Parason converts sequential reasoning traces into structured parallel trajectories with a context-free grammar, then trains models with Parallelism-Aware Group Relative Policy Optimization (PA-GRPO), whose reward jointly balances accuracy, latency, and the two parallelism ratios. At inference time, Parason executes the learned parallel structure through tool calls, translating theoretical savings to real-world wall-clock acceleration. Experiments on mathematical reasoning benchmarks including AIME24 and AIME25 show that Parason achieves an average acceleration about 1.7Ăwhile maintaining competitive accuracy. Website| Code| Dataset 1 Introduction Recent advances in large language model (LLM) reasoning have made a simple recipe increasingly ef- fective: spend more test-time compute, and obtain better answers. Chain-of-Thought prompting [Wei et al., 2022] and reasoning-oriented systems such as OpenAI o1 [OpenAI et al., 2024] and DeepSeek- R1 [DeepSeek-AI et al., 2025] show that long, deliberate reasoning traces can substantially improve performance on mathematical and logical tasks. Yet this recipe has an immediate systems bottleneck. Standard autoregressive decoding serializes every token and every intermediate thought, so stronger reasoning often translates directly into longer waiting time. On difficult problems, reasoning traces can grow to hundreds of thousands or even millions of tokens [Hubert et al., 2025, Luong et al., 2025], making the usual âthink longerâ strategy impractical for interactive agents, coding assistants, and other latency-sensitive applications. For example, Googleâs AlphaProof [DeepMind, 2024] requires up to three days to solve challenging problems from the International Mathematical Olympiad (IMO) 2024, highlighting the extreme latency inherent in current sequential reasoning systems. â ligengz@nvidia.com arXiv:2608.24658v1 [cs.AI] 25 Aug 2026 Subtask ParallelismTrial Parallelism Everybody take a chunk! Everybody try an idea! Big Problem Compute the sum of 1â800 Open Lock Problem What's the correct key? Task A 1â200 Task B 202â400 Task C 402â600 Task D 602â800 Idea 1 Key 21415 Idea 2 Key 27182 Idea 3 Key 16180 Idea 4 Key 42424 Idea 5 Key 12345 AND OR All results must be collected One good result is enough Final Answer The sum of 1â800 is 320,400 Success! Correct key is 12345 Known plan Different sub-goals Need ALL branches (AND) Unknown path Alternative attempts Need ONE good branch (OR) Figure 1: Overview of two types of parallelism. The figure contrasts Subtask Parallelism, where all decomposed branches are needed for the final answer, with Trial Parallelism, where multiple uncertain paths are explored as alternative (OR) branches. Despite this OR relation, the outputs of all Trial branches are concatenated into the subsequent context, making every branchâs content available for final synthesis. While previous work mainly focuses on Subtask Parallelism, our analysis shows that Trial Parallelism accounts for the majority of parallelizable reasoning on HLE for every model we study, and exceeds 58% for DeepSeek-R1 and DeepSeek-V4 across both datasets. A natural response is to make reasoning parallel: let multiple reasoning branches proceed con- currently instead of decoding every thought in sequence. Existing methods explore this direction through independent sampling, such as self-consistency and Best-of-N [Wang et al., 2022, Hu et al., 2026], or adaptive branching frameworks [Yang et al., 2025b, Jin et al., 2025, Zheng et al., 2025, Lian et al., 2025, Wang et al., 2025]. However, methods such as Multiverse [Yang et al., 2025b], ThreadWeaver [Lian et al., 2025], and APR [Pan et al., 2025] mainly exploit subtask-style parallelism: splitting a high-level task into smaller chunks and merging their results. Trial-style exploration, which tries uncertain paths and incorporates diverse trajectories, is less discussed. In this work, we argue that the key missing piece is a semantic taxonomy of parallel reasoning. As illustrated in Figure 1, we identify two complementary forms of parallelism. Subtask Parallelism applies when a problem can be decomposed into independent steps: each branch solves a distinct sub-goal, and the final answer combines all branch results. This is the form emphasized by most prior adaptive parallel systems. Trial Parallelism applies when the model is uncertain about which path will work: multiple branches test competing hypotheses, and the final trajectory keeps the useful results. These modes have different execution semantics. Subtask branches are usually all necessary, while trial branches are speculative and most useful when the reasoning path is uncertain. Our empirical analysis shows that this distinction is practical, not merely conceptual. Trial Parallelism accounts for the majority of analyzed parallelizable steps on Humanityâs Last Exam for every model we study, including73.8%and65.5%forDeepSeek-R1andDeepSeek-V4, respectively. On OpenMath, it remains the majority for most models and reaches 68.5% and 58.1% for the same two open-source models. This suggests that hard reasoning is not only decomposition, but also trying and refining uncertain solution paths. Systems that focus solely on subtask decomposition therefore miss much of the computation in hard cases. Guided by this observation, we introduce Parason, a training-and-inference codesign framework for revealing and exploiting both Subtask Parallelism and Trial Parallelism. Parason converts sequential reasoning traces into structured parallel trajectories without changing their final semantics, and uses a context-free grammar to mark parallel regions, individual branches, and summaries in an engine-parseable format. We then train the model with Parallelism-Aware Group Relative Policy Optimization (PA-GRPO), which augments outcome-based reinforcement learning with rewards for lower latency along the longest token path and balanced use of the two parallelism types. At inference time, the generated structure is executed through tool calls, allowing Parason to dispatch independent workers with subtasks and competing trial branches. Across mathematical reasoning benchmarks including AIME24 and AIME25, Parason preserves competitive accuracy while reducing effective reasoning latency. Our contributions are summarized as follows: 2 Sequential Reasoning is Naturally Parallelizable â A Case of 24 Puzzle Solving Prompt: Calculate 24 using 6 9 9 10 <think> We are given the numbers 6, 9, 9, 10 and we need to make 24 using basic arithmetic operations (+, -, *, /) and possibly parentheses. We need to find an expression that equals 24. Let's try different combinations: We have two 9's, one 6, and one 10. Goal: 24. Some common approaches: 24 = 4*6, 24=30-6, 24=2.4*10, etc. Since we have a 6, maybe we can get 4 from 9,9,10 to multiply by 6? 4*6=24. How to get 4 from 9,9,10? 10 - 9 = 1, then 9 - 1 = 8, not 4. Or (9+9)/10? =18/10=1.8, not 4. Maybe 24 = 30 - 6. So if we can make 30 from 9,9,10 and then subtract 6? But we have to use all numbers. So maybe (9+9+10) = 28, then 28 - 4? But we have 6. Alternatively, (9*10)/? Not sure. Or 24 = (10-6)*6, but we only have one 6. Maybe using fractions: 24 = 9/(something) etc. Let's try other combinations systematically: We can think of possible expressions: One idea: 10 * (9 - 6) = 10*3=30, then 30 - 9 = 21, not 24. 10 * (9 - 6) - 9 = 30-9=21. 9 * (10 - 6) = 9*4=36, then 36 - 9 = 27, not 24. (9+9)* (10-6)? =18*4=72 too big. (9+9-10)*6 = (8)*6=48, too big. Maybe divide: (9*10)/ (something) = 90/ something. 90/4 = 22.5, not 24. Or (9*10*9)/ something. 810/33.75 = 24? Not likely. Maybe using subtraction and division: 24 = (10*9)/(something) - something. Let's try: 9*10 = 90, 90/6=15, then 15+9=24! That works: 9*10/6+9 = 90/6+9=15+9=24. But we have to use two 9's and one 10 and one 6. In that expression we used one 9, one 10, one 6, and then added the other 9. So it's 9*10/6+9. But check order of operations: multiplication and division first: 9*10=90, 90/6=15, 15+9=24. Yes. So the expression is: 9 Ă 10 á 6 + 9 = 24. we found a solution. But let's check if there are other ways: maybe (9 - 6) Ă (10 - â 9) but we cannot use square root unless specified. So basic operations only. Another: (10 - 9/9)*? (10-1)=9, 9*? Not 24. (9+9+10-6)? =22, not 24.(9*9-10)/6? (81-10)/6=71/6â11.83, no. So the one we found seems simplest. Thus, the answer is: 9 Ă 10 á 6 + 9 = 24. </think> One solution is: 9Ă 10 á 6 + 9 = 24 Figure 2: Visualization of Trial and Subtask Parallelism. The 24 Puzzle trace generated by DeepSeek-R1 [DeepSeek-AI et al., 2025] highlights Subtask Parallelism in blue and Trial Parallelism in green. Subtask branches implement divide-and-conquer execution, while Trial branches explore and verify competing hypotheses; Trial steps occupy the majority of reasoning tokens. â˘A taxonomy of parallel reasoning. We distinguish Subtask Parallelism and Trial Par- allelism, identifying Trial Parallelism as the missing component. Based on this taxonomy, we introduce Parason, which converts sequential reasoning data into grammar-constrained parallel trajectories that can be parsed and executed by inference engines. â˘Parallelism-aware reinforcement learning. We propose PA-GRPO, a multi-objective RL objective that jointly optimizes answer accuracy, latency along the longest token path, and the modelâs use of the two parallelism modes. ⢠Empirical speedups with competitive accuracy. Experiments across challenging math benchmarks demonstrate that Parason improves the latencyâaccuracy Pareto frontier, achiev- ing an average acceleration about1.7Ăwhile maintaining competitive accuracy. Under latency-constrained settings, Parason matches the performance of an 8k-token latency budget using only 25% of the budget. â˘Seamless inference engine support. We define a CFG that marks parallel regions as tool calls and integrate Parason into SGLang [Zheng et al., 2023]. This makes parallel reasoning directly executable in a real inference engine, while prior work either reports only theoretical speedups that are hard to translate into actual latency reduction, or introduces complicated designs that require deep modifications to modern inference engines. 2 Related Work Test-time scaling for LLM reasoning. Scaling inference-time computation has become a cen- tral recipe for improving LLM reasoning. CoT prompting [Wei et al., 2022] elicits intermediate derivations, while recent reasoning models such as OpenAI o1 [OpenAI et al., 2024] and DeepSeek- R1 [DeepSeek-AI et al., 2025] further improve performance by producing longer and more deliberate reasoning traces. This sequential scaling is powerful but expensive: autoregressive decoding generates every token one after another, so longer reasoning directly increases latency. Parallel reasoning is an attractive direction for preserving test-time compute while shortening the longest token path. Independent parallel sampling and majority voting. A simple form of parallel reasoning is to sample multiple complete solutions and aggregate their answers. Self-consistency [Wang et al., 3 Model Dataset: OpenMathDataset: HLE Subtask (%)Trial (%)Subtask (%)Trial (%) Open Source Models DeepSeek-R1 [DeepSeek-AI et al., 2025]31.568.5 +37.00 26.273.8 +47.60 Qwen3-30B-A3B [Yang et al., 2025a]43.656.3 +12.70 38.861.2 +22.40 MiniMax 2.7 [MiniMax AI, 2025]47.752.3 +4.60 38.261.8 +23.60 Kimi-2.6 [Moonshot AI, 2025]43.057.0 +14.00 42.157.9 +15.80 DeepSeek-V4 [DeepSeek-AI, 2026]41.958.1 +16.20 34.565.5 +31.00 Commercial Models Gemini-2.5-Pro [Google, 2025]62.937.1 â25.80 49.450.6 +1.20 Claude-Opus-4.5 [Anthropic, 2025b]44.955.1 +10.20 29.970.1 +40.20 Gemini-3-Pro [Google DeepMind, 2025]57.442.6 â14.80 46.953.1 +6.20 GPT-5.5 [OpenAI, 2026]34.465.6 +31.20 23.976.1 +52.20 Table 1: Trial Parallelism dominates on harder reasoning datasets. We report Subtask and Trial ratios in reasoning traces from OpenMathReasoning [Moshkov et al., 2025] and Humanityâs Last Exam (HLE) [Phan et al., 2025]. Ratios are computed on the first 100 problems of each dataset, and annotation details are provided in Appendix A. For closed-source models, the original thinking trace is hidden, thus we counted summary statistics instead. 2022], verifier-guided Best-of-N sampling [Cobbe et al., 2021], and confidence-based variants such as DeepConf [Fu et al., 2025] improve robustness by exploring several candidate trajectories. These methods implicitly use trial-style computation, since different samples may try different solution paths. However, these samples are independent full traces. They do not share intermediate work, expose branch structure inside a trace, or tell an inference engine where parallel execution should begin and end. As a result, they improve accuracy at the cost of redundant computation with little control over latency. Structured and adaptive parallel reasoning. Another line of work introduces explicit structures for parallel reasoning. Tree-of-Thoughts [Yao et al., 2023], Graph-of-Thoughts [Besta et al., 2023], Skeleton-of-Thought [Ning et al., 2023], and agentic decomposition methods split reasoning into trees, graphs, outlines, or sub-agents. More recent adaptive systems, including PASTA [Jin et al., 2025], Multiverse [Yang et al., 2025b], Parallel-R1 [Zheng et al., 2025], APR [Pan et al., 2025], ThreadWeaver [Lian et al., 2025], and PaCoRe [Hu et al., 2026], train or prompt models to create parallel branches and merge their outputs. PaCoRe further scales test-time compute with multiple rounds of coordinated parallel exploration and message passing. Figure 2 visualizes the same broader opportunity: LLM reasoning can be parallelized. Yet their main mechanism is still subtask-centric: the model decomposes a high-level task into smaller chunks, runs the chunks in parallel, and merges the results. This is effective when the problem admits a clean divide-and-conquer structure, but it misses a common behavior in difficult reasoning: trying uncertain paths, rejecting failed attempts, and keeping the path that works. Our analysis shows that this missing Trial Parallelism is not rare; it accounts for most parallelizable reasoning steps in hard cases. Parason therefore separates Subtask Parallelism from Trial Parallelism and trains the model to exploit both forms explicitly. 3 Methodology Parason turns long sequential reasoning traces into executable parallel programs, which is critical for long-horizon tasks such as Googleâs AlphaProof [DeepMind, 2024], OpenAIâs IMO reasoning efforts [Luong et al., 2025], and recent agentic coding workflows such as Claude Code [Anthropic, 2025a] and OpenAI Codex [OpenAI, 2025]. The framework has three parts. First, we define two semantic forms of parallel reasoning: Subtask Parallelism decomposes a problem into independent required parts, while Trial Parallelism explores competing uncertain attempts and incorporates the diverse exploration into the final reasoning path. Second, we define a context-free grammar (CFG) that gives Parason a formal syntax, helps data generation, processing, and rollouts avoid syntax errors, and makes later system integration simple. Third, we propose Parallelism-Aware GRPO (PA-GRPO), 4 Parallel Reasoning in Parason â A Case of 24 Puzzle Solving Prompt: Calculate 24 using 6, 9, 9, 10. <think> We are given the numbers 6, 9, 9, 10 and need to make 24 using basic arithmetic operations (+, -, *, /). Goal: 24. <Parallel> <Outlines> <Subtask> 1. Try to use 6 as a multiplier and derive 4 from 9, 9, 10. </Subtask> <Subtask> 2. Try division with 9*10 and use the remaining 6 and 9. </Subtask> <Subtask> 3. Verify whether there are simpler alternatives. </Subtask> <Thread> 1. <Parallel> <Outlines> <Trial> 1. Try use 9, 9, 10 to make 4. 10-9=1, then 9-1=8, not 4. This route does not find 4. </Trial> <Trial> 2. Try 10*(9-6)-9. This gives 21, not 24. This route does not find 24. </Trial> <Trial> 3. Try 9*(10-6)-9. This gives 27, not 24. </Trial> <Trial> 4. Try (9+9)*(10-6). This gives 72, not 24. </Trial> </Outlines> </Parallel> </Thread> <Thread> 2. <Parallel> <Outlines> <Trial> 1. Try 9*10/6+9. 90/6=15, 15+9=24. This works. </Trial> </Outlines> </Parallel> </Thread> <Thread> 3. <Parallel> <Outlines> <Trial> 1. Try (9-6)*(10-sqrt(9)). Square root is not allowed. </Trial> <Trial> 2. Try 9+9+10-6. Result is 22, not 24. </Trial> <Trial> 3. Try (9*9-10)/6. Result is 11.83, not 24. </Trial> </Outlines> </Parallel> </Thread> </Outlines> </Outlines> </Parallel> Thus, the answer is 9 Ă 10 á 6 + 9 = 24. </think> Figure 3: Solving the 24 Puzzle in Parason format. This example is adapted from a real 24 Puzzle reasoning trace. The blue region gives the Subtask plan, splitting the problem into three independent subtasks. The green regions show Trial Parallelism, where each subtask explores candidate routes in parallel. The correct solution appears in the first Trial branch of the second subtask. a training algorithm that teaches the model to use parallelism effectively while preserving final-answer correctness. 3.1 Parallelism in Reasoning A reasoning trace is not uniformly sequential, as shown by the visualization of Trial and Subtask Parallelism in Figure 2. Some steps derive independent facts that will all be used later; other steps try uncertain ideas, explore multiple paths, and aggregate their findings. Following the overview and examples in Figures 1, 2, and 3, Parason treats these behaviors as two semantic forms of parallelism with different merge rules. Subtask Parallelism is an AND-branch form of parallelism. A problem is split into independent sub-goalsg 1 ,...,g k , each branch computes a necessary resultr i , and the main trajectory aggregates all resultsr i k i=1 to continue the derivation. These branches are parallel because they do not depend on one another, but all of them are mandatory: dropping one branch would remove the information required for generating the final answer. For example, a geometry solution may compute two distances independently before combining them in a final formula. This is the dominant form assumed by prior adaptive parallel systems [Yang et al., 2025b, Lian et al., 2025, Pan et al., 2025, Hu et al., 2026]. Trial Parallelism is an OR-branch form of parallelism. Given an uncertain state, the model launches competing attemptsa 1 ,...,a k that test different hypotheses, heuristics, or solution routes. The merge step concatenates the branches to incorporate the exploratory trajectories into the reasoning history, rather than selecting a single branch. Thus, Trial Parallelism is parallel search inside a single reasoning trace, rather than decomposition into mandatory parts. This mirrors how strong reasoning models often behave on hard problems: they try a path, detect a dead end, and revise. Our empirical analysis in Table 1 shows that Trial Parallelism accounts for more than 50% of parallelizable steps for every model on HLE [Phan et al., 2025] and for most models on OpenMath, with higher Trial shares on HLE across all listed models. 5 Context-Free Grammar (CFG) for Parason LetG=(V, ÎŁ,R,S)bethecontext-freegrammarforstructuredparallelreasoning. Terminology ⢠Terminals(ÎŁ):<think>, <Parallel>,<Outlines>, <Subtask>,<Trial>,<Thread>, their matching closing tags, Text ⢠Non-terminals (V ): â S: start of reasoning â B: reasoning body â P : parallel region â O: outlines block â G: list of outline entries â E: one Subtask or Trial entry â H : list of thread bodies â W : one Thread body â T : free-form reasoning text ⢠Start symbol: S ⢠Rules:Rdefines valid tag nesting and branch structure. Production Rules R Sâ <think> B </think> Bâ T B| P B| Îľ Pâ <Parallel> O H </Parallel> Oâ <Outlines> G </Outlines> Gâ E G| E Eâ <Subtask> T </Subtask> | <Trial> T </Trial> Hâ W H| W Wâ <Thread> B </Thread> Tâ nonempty free-form text excluding reserved tags Figure 4: Context-Free Grammar for Parason. Each parallel region contains an Outlines block with one or more correctly matched Subtask or Trial entries, followed by one or more Thread bodies. As in Figure 3, each Thread may contain free-form reasoning or a nested parallel region. 3.2 Parallel Tracjectory Format To make these two modes executable, Parason represents reasoning traces with a grammar-constrained format. We extend ordinary<think>traces with parallel tags:<Parallel>marks a parallel region, <Outlines>describes the purpose of the region,<Subtask>and<Trial>mark branch type, <Thread>stores branch outcome. The full CFG is shown in Figure 4. While real-world reasoning often exhibits mixed dependencies (e.g., a subtask internally spawning trial branches), our training data keeps a strict separation for simplicity. However, we observe that the model can generalize to these complex compositions during evaluation. The format is designed around two requirements. First, it is semantic: the tags indicate whether a branch is a necessary subtask or a speculative trial branch, not merely that it can run in parallel. This matters because prior parallel-reasoning methods often mix the two forms under a single branching interface, making it hard to decide whether branches should be all merged or aggregated as exploration history. Second, it is engine-parseable: each branch has explicit start and stop tags, so an inference runtime can dispatch workers without modifying the model architecture. Compared with free-form summaries or prompt-only, the CFG gives the training and inference infra a shared contract. 3.3 Parallelism-Aware Reinforcement Learning Supervised conversion teaches the model to imitate parallel traces, but it does not directly opti- mize latency or decide when and what parallelism is worth using. We therefore RL fine-tune with Parallelism-Aware Group Relative Policy Optimization (PA-GRPO). The reward keeps correct- ness as the primary objective, while shaping the model toward useful parallel branches. For a sampled trajectoryi, letT i denote its token-level latency, and letR i subtask andR i trial be the ratios of tokens placed in Subtask and Trial branches. We define: 6 Definition 3.1. Parallel RL Reward R i =â1 + 2Ă 1(correct i ) Ă 1â Îąf T i â Îź T Ď T + β subtask f R i subtask â Îź s Ď s + β trial f R i trial â Îź r Ď r + min(Ď¡ Ρ(s), Ď clip ) ! . The symbols in Eq. 3.1 are defined as follows: ⢠R i : final reward for sampled trajectory i. ⢠1(correct i ) : correctness indicator; incorrect an- swers receive the base negative reward. ⢠T i : token-level latency of trajectoryi, measured by its critical-path token count. ⢠ι: coefficient controlling the normalized latency penalty. ⢠R i subtask : Number of tokens placed in Subtask Parallelism branches/Total generated tokens ⢠Ρ(s):Ρ(s) = 1â L latency L total , whereL latency and L total denote the number of latency tokens and the total number of tokens, respectively. ⢠Ď,Ď clip : Parameters for controlling acceleration reward. ⢠R i trial : Number of tokens placed in Trial Paral- lelism branches/Total generated tokens ⢠β subtask andβ trial : incentives for Subtask and Trial Parallelism. ⢠f : shaping function applied to normalized reward signals; here we use the linear function y = x. ⢠Ο T ,Îź s ,Îź r andĎ T ,Ď s ,Ď r : means and standard deviations used to normalize latency, Subtask ra- tio, and Trial ratio, respectively. The first term makes correctness the primary signal by assigning a negative base reward to incorrect answers and a positive base reward to correct answers. The latency term, weighted byÎą, penalizes trajectories with high normalized critical-path latency. The Subtask and Trial incentives, weighted by β subtask andβ trial , encourage useful parallel structure, while the clipped acceleration reward directly favors reductions in the critical path relative to total generation length. It is important to note thatβ subtask andβ trial target fundamentally different optimization goals: Trial Parallelism improves accuracy by trading total tokens for search width, while Subtask Parallelism reduces latency by compressing the longest token path. In practice, this reward lets us separately tune these two dimensions, as detailed in Section 4.2. 3.4 Integration into Modern Inference Engine Parason integrates with modern inference engines by treating parallel branches as tool calls rather than requiring deep runtime changes. Following the CFG in Figure 4, the runtime decodes normally until a<Parallel>region appears, parses the<Outlines>, dispatches each<Subtask>or<Trial>as an independent worker, and returns the resulting<Thread>outputs to the main trajectory; Figure 3 shows this format on the 24 Puzzle. XGrammar [Dong et al., 2024] enforces valid tags, and we implement this tool-call execution in SGLang [Zheng et al., 2023]. 4 Experiments We provide details on training data curation, training framework, and evaluation below, and will open-source our implementation to facilitate reproducibility. Training Data Curation.We build parallel training data from the 964 annotated Qwen3-8B traces released by ThreadWeaver [Lian et al., 2025]. Gemini-3-Flash labels each parallel stage as Subtask or Trial; for Trial stages, Qwen3-8B samples extra branches and Gemini-3-Flash generates their <Trial>goals. For reinforcement learning (RL), we use Polaris-53k [An et al., 2025], a collection of about 53,000 complex reasoning problems. Training Framework.We use a two-stage post-training pipeline. First, we fine-tune the model with TRL [von Werra et al., 2020] on the curated parallel trajectories. Second, we train with VeRL [Sheng 7 MethodAIME24AIME25Math500AMCAvg Avg. Latency #Tokens Parallel-R1 (4B)19.419.2---- ShorterBetter (7B)53.3----- ThinkPrune (32B)72.5-93.895.9-- DYNASOR-COT (32B)78.0 -93.094.0-- Dynamic Early Exit (32B)70.0-94.895.0-- AdaptThink (7B)55.6-92.0--- Multiverse (32B)53.845.891.8--- ThreadWeaver (8B)79.960.592.391.481.014.8k Parason-8B (w/vanilla SFT)73.567.993.493.982.213.2k + PA-GRPO (β subtask = 0.025)75.169.793.896.683.813.8k + PA-GRPO (β subtask = 0.050)76.370.094.695.084.015.6k + PA-GRPO (β subtask = 0.100)77.368.594.696.384.214.1k + PA-GRPO (β trial = 0.025)75.569.994.496.384.014.2k + PA-GRPO (β trial = 0.050)76.570.694.096.984.514.5k + PA-GRPO (β trial = 0.100)78.268.994.297.584.714.5k Additional runs with Îą = 0.1 + PA-GRPO (β subtask = 0.025)75.767.693.695.983.212.2k + PA-GRPO (β subtask = 0.050)74.266.193.895.982.512.2k + PA-GRPO (β subtask = 0.100)75.565.992.697.582.913.2k + PA-GRPO (β trial = 0.025)76.966.694.697.283.812.1k + PA-GRPO (β trial = 0.050)77.367.393.496.683.712.5k + PA-GRPO (β trial = 0.100)78.269.293.495.684.113.4k Table 2: Trial rewards improve accuracy, while Subtask rewards reduce latency. We compare Parason with prior systems and ablateβ subtask andβ trial . Avg and Token Latency average AIME24, AIME25, Math500, and AMC for each PA-GRPO row. Bold and underlined values mark the highest and second-highest PA-GRPO results, except Token Latency, where lower is better. et al., 2024] using Parallelism-Aware GRPO (PA-GRPO). Unless otherwise noted, RL uses learning rate1eâ6, batch size 128, 8 rollouts, lower clip ratio 0.2, and upper clip ratio 0.28; SFT uses learning rate 1eâ5, batch size 16, 8 epochs, and a cosine learning-rate scheduler. Evaluation. We evaluate on AIME 2024 [Mathematical Association of America, 2024], AIME 2025 [Mathematical Association of America, 2025], AMC [Mathematical Association of America, 2023], Math500 [Hendrycks et al., 2021], and Minerva Math [Lewkowycz et al., 2022], and compare against sequential baselines trained from the same base model and data source as well as external parallel and efficient-reasoning systems. We report final-answer accuracy and executable latency. For Parason, model latency is the token length of the longest generation path: sequential tokens are counted normally, while each<Parallel>block contributes the maximum branch length rather than the sum of all branches. This metric captures the wall-clock benefit available to an inference engine that runs branches concurrently. 4.1 Main Results Parason improves accuracy over prior parallel reasoning systems. Table 2 compares Parason with existing parallel and efficient-reasoning methods. Parason gives the best reported AIME25 and AMC results among the listed systems, reaches the best Parason four-benchmark average accuracy of 84.7%, and stays close to ThreadWeaver on AIME24. Across the original settings and the additional Îą = 0.1runs, PA-GRPO reaches 70.6% on AIME25, 97.5% on AMC, and 94.6% on Math500. These gains show that Parason improves both accuracy and average benchmark coverage over prior parallel work, even though it uses an 8B model rather than several 32B baselines. Parason gives a better token-latencyâaccuracy trade-off under constraints. Table 3 shows that Parason is most useful when the model has a small thinking budget on the longest token path. At 2048 tokens, the best Subtask-aware PA-GRPO model reaches 34.7% AIME24 accuracy, compared with 16.8% for SFT only. At 8192 tokens, it reaches 60.3%, compared with 41.8% for SFT only 8 AIME24 Accuracy (%) ModelB = 2,048 B = 8,192 B = 16,384 B = 24,576 SFT only16.841.866.870.2 PA-GRPO (β subtask = 0.025)16.7 â0.10 45.2 +3.40 68.0 +1.20 73.2 +3.00 PA-GRPO (β subtask = 0.050)26.8 +10.00 60.0 +18.20 72.2 +5.40 74.8 +4.60 PA-GRPO (β subtask = 0.100)34.7 +17.90 60.3 +18.50 74.4 +7.60 75.7 +5.50 Table 3: Accuracy under token-latency budgets. Each column reports AIME24 accuracy for a fixed thinking budgetBon the longest token path. Subscripts show absolute accuracy-point gains relative to SFT only under the same budget; red indicates a decrease. Subtask-aware PA-GRPO provides the largest gains in low-budget regimes: atB = 2,048,β subtask = 0.100reaches 34.7% accuracy, compared with 16.8% for SFT only. MethodTrigger RatioToken LatencyAcceleration RatioAvg. Math Acc. ThreadWeaver (8B)83.713.3k1.18x77.6 Multiverse (32B)65.610.3k1.16x63.8 Parason-8B (w/ SFT only)69.314.1k1.27x78.3 Original runs with Îą = 0.000 + PA-GRPO (β trial = 0.025, Îą = 0.000)77.315.2k1.46x 79.9 + PA-GRPO (β trial = 0.050, Îą = 0.000)84.015.8k1.61x80.4 + PA-GRPO (β trial = 0.100, Îą = 0.000)98.815.7k1.71x80.4 + PA-GRPO (β subtask = 0.025, Îą = 0.000)70.114.9k1.48x79.5 + PA-GRPO (β subtask = 0.050, Îą = 0.000)79.316.6k1.75x80.3 + PA-GRPO (β subtask = 0.100, Îą = 0.000)89.615.4k1.73x80.1 Additional runs with Îą = 0.100 + PA-GRPO (β trial = 0.025, Îą = 0.100)62.313.2k1.46x79.4 + PA-GRPO (β trial = 0.050, Îą = 0.100)79.713.6k1.50x79.3 + PA-GRPO (β trial = 0.100, Îą = 0.100)95.314.5k1.72x80.3 + PA-GRPO (β subtask = 0.025, Îą = 0.100)53.713.4k1.34x79.0 + PA-GRPO (β subtask = 0.050, Îą = 0.100)81.313.2k1.60x78.0 + PA-GRPO (β subtask = 0.100, Îą = 0.100)96.514.3k1.74x78.0 Table 4: PA-GRPO produces usable parallelism across latency-penalty settings. For PA-GRPO, Trigger Ratio and Avg. Math Acc. are averaged over AIME24, AIME25, and Math500. Acceleration ratio is total tokens / longest-path tokens, and trigger ratio is the fraction of samples containing at least one <Parallel> block. Bold and underlined values mark the best and second-best PA-GRPO results among available measurements. at the same budget. Thus, Parason does not simply spend more tokens; it moves useful work into parallel branches and keeps the longest path short. 4.2 Insights and Findings Trial rewards give the clearest accuracy gains, while the latency penalty shortens the critical path. Table 2 compares PA-GRPO with ThreadWeaver, which obtains 81.0% average accuracy with a four-benchmark token latency of 14.8k. The originalβ trial = 0.100setting gives the best average accuracy (84.7%), whileβ trial = 0.050gives the best AIME25 result (70.6%). The best AIME24 result (78.2%) is shared by the original and additionalβ trial = 0.100settings, and the best AMC result (97.5%) is shared by the originalβ trial = 0.100model and the additionalÎą = 0.1,β subtask = 0.100 model. Among the additional runs,β trial = 0.025gives the lowest four-benchmark token latency at 12.1k. The additional sweep spans 12.1â13.4k, below ThreadWeaverâs 14.8k average latency. PA-GRPO turns more parallel structure into executable acceleration. Table 4 shows that the learned parallel regions are usable by the runtime. SFT alone already triggers parallel execution on 69.3% of samples and yields 1.27Ătoken-level acceleration. Under the originalÎą = 0.000 setting, the Trial sweep raises the trigger ratio from 77.3% to 98.8% and the acceleration ratio from 1.46Ăto 1.71Ă, while maintaining 79.9â80.4% average math accuracy. Subtask incentives 9 provide another route to high acceleration, withβ subtask = 0.050reaching the best acceleration ratio of 1.75Ăand 80.3% average accuracy. In the additionalÎą = 0.100runs, acceleration rises with the parallelism coefficient:β subtask = 0.100reaches 1.74Ăandβ trial = 0.100reaches 1.72Ă. The lowest three-benchmark token latency is 13.2k, reached byβ trial = 0.025andβ subtask = 0.050after rounding. Token-Level MetricsWall-Clock Metrics Difficulty #Problems Generated #Tokens Latency #Tokens Acceleration Ratio Saved #Tokens Parallel (s) Sequential (s) Easy1321.3k12.5k1.70Ă8.8k188.3304.2 Medium1136.8k21.2k1.74Ă15.6k336.2464.7 Hard650.3k29.0k1.73Ă21.3k487.3716.3 Table 5: Harder questions save more tokens, while parallel execution reduces wall-clock latency across all difficulty levels. We break down AIME24 thinking tokens and measured wall-clock time by difficulty. Latency #Tokens denotes the length of the longest token path, Acceleration Ratio is generated tokens divided by latency tokens, and Saved #Tokens is generated tokens minus latency tokens. The experiment is executed on A800 GPUs. Harder questions create more parallelizable work, not less acceleration. Table 5 breaks down the step-200 AIME24 run by difficulty. Generated tokens grow sharply with difficulty, from 21.3k on easy problems to 36.8k on medium problems and 50.3k on hard problems. The longest token path also grows, but much more slowly: 12.5k, 21.2k, and 29.0k tokens, respectively. As a result, Parason keeps a stable 1.70â1.74Ătoken-level acceleration ratio across all three difficulty groups. This translates into measured wall-clock speedups of 1.62Ăon easy, 1.38Ăon medium, and 1.47Ă on hard problems. The absolute number of saved tokens increases from 8.8k on easy problems to 21.3k on hard problems, showing that harder questions expose more branch-level work that can be moved off the critical path. This supports the central motivation of Parason: difficult reasoning still requires long and diverse computation, but much of that computation does not need to remain serial. 5 Conclusion In this work, we introduced Parason, an algorithm-system co-design framework that brings parallel processing to sequential LLM reasoning. Parason distinguishes deterministic Subtask Parallelism from speculative Trial Parallelism, and provides a stable pipeline for data curation, CFG-based structure, PA-GRPO training, and inference-engine execution. This design enables efficient parallel reasoning and improves the responsiveness of interactive agents, coding assistants, and scientific problem-solving tools. 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This setting provides a controlled testbed for studying parallel reasoning, but it does not fully show how Parason behaves across model families and sizes. In future work, we will scale Parason to more backbones and larger models to study whether the same parallelism patterns and latency gains hold at broader scales. B Prompts Used for Data Curation We use the following prompts to identify Trial and Subtask steps in LLM reasoning trajectories. For open-source models, we first split each reasoning trajectory by . The first prompt reconstructs logical steps by deciding whether each segment starts a new subproblem or continues a previous one. The second prompt then classifies each logical step as either a Trial step or a Subtask step. For commercial models, the released reasoning summaries already mark steps with â***Step i***â. We therefore apply the second prompt directly to classify each marked step as Trial or Subtask. Reconstruction by Logical Steps SYSTEM: You are a helpful assistant that analyzes chain-of-thought traces from reasoning models.,â The chain of thought has been split into multiple steps. For each step, decide whether it starts a new subproblem or continues the previous one.,â Use the content of each step to make the decision. If a step introduces a new concept, question, or task that is distinct from previous steps, it likely starts a new subproblem. If it builds on previous steps by adding details, explanations, reflections, or calculations about the same concept, it likely continues the previous subproblem. ,â ,â ,â ,â More specifically, steps that start with "Alternatively", "Wait", or "But" are likely to start a new subproblem, while steps that start with "Therefore", "Thus", or "Consequently" are likely to continue the previous subproblem. ,â ,â Your output should be in the following format: Step i: [New Subproblem|Continue Previous Subproblem] If a step continues a previous subproblem, report where that subproblem starts. For example, if Step 5 continues the subproblem that started at Step 3, output: ,â ,â Step 5: Continue Previous Subproblem (started at Step 3) IMPORTANT: Output the analysis in the specified format. Use one line per step. Do not include additional explanations or text.,â Example: Step 1: New Subproblem Step 2: Continue Previous Subproblem (started at Step 1) Step 3: New Subproblem Step 4: Continue Previous Subproblem (started at Step 3) Step 5: Continue Previous Subproblem (started at Step 3) 17 Parallel Stage Identification SYSTEM: You are given a series of mathematical reasoning steps. Classify each step into one of the following categories:,â 1. Trial Step: A step that introduces a new idea, approach, or line of thought whose success is uncertain but worth exploring.,â 2. Subtask Step: A step that belongs to a known solution path and directly contributes to the final solution.,â Your output should be in the following format: Step i: [Trial Step|Subtask Step] [Reason] The number of output steps should match the number of input steps. Each step has its own number and is separated by "================================= â ===============================================". Ignore the content under "Content after </think> tag: ,â ,â ,â " Give the reason for each classification after the step type. C AIME 2024 Problem Indices Table 6 lists the AIME 2024 validation problems used for the difficulty-based analysis in Table 5. We group problems into Easy, Mid, and Hard subsets according to their difficulty labels, and report the corresponding zero-based problem indices for reproducibility. DifficultyProblem Indices Hard2, 3, 13, 21, 28, 29 Mid1, 4, 5, 10, 16, 17, 18, 20, 25, 26, 27 Easy0, 6, 7, 8, 9, 11, 12, 14, 15, 19, 22, 23, 24 Table 6: AIME 2024 Problem Classification by Difficulty. 18