Source-linked AI summary
PaCoRe: Learning to Scale Test-Time Compute with Parallel Coordinated Reasoning
Jingcheng Hu, Yinmin Zhang, Shijie Shang, Xiaobo Yang, Yue Peng, Zhewei Huang, Hebin Zhou, Xin Wu, Jie Cheng, Fanqi Wan, Xiangwen Kong, Chengyuan Yao, Kaiwen Yan, Ailin Huang, Hongyu Zhou, Qi Han, Zheng Ge, Daxin Jiang, Xiangyu Zhang, Heung-Yeung Shum
TL;DR
Contemporary language models face a fixed-context ceiling when scaling sequential test-time compute. PaCoRe coordinates parallel reasoning through iterative message passing and trains synthesis with outcome-based reinforcement learning. PaCoRe-8B reaches 94.5% on HMMT 2025 while scaling effective TTC to nearly two million tokens, with improvements across several domains.
Problem
Fixed context windows constrain how far contemporary language models can scale search-driven test-time compute through sequential reasoning.
Method
PaCoRe iteratively launches parallel reasoning trajectories, compacts their findings into messages, and trains synthesis with large-scale outcome-based reinforcement learning.
Results
94.5% on HMMT 2025 is achieved by PaCoRe-8B while scaling effective TTC to nearly two million tokens per problem, with gains reported across diverse domains.
Takeaways & Limitations
PaCoRe demonstrates that coordinated parallel exploration and message passing can support test-time scaling beyond sequential reasoning’s context-bound regime.
Takeaways & Limitations
The current approach scales primarily by compute volume, while the authors identify improving the utility of each compute unit as future work.
Abstract
from arXiv · showhide
We introduce Parallel Coordinated Reasoning (PaCoRe), a training-and-inference framework designed to overcome a central limitation of contemporary language models: their inability to scale test-time compute (TTC) far beyond sequential reasoning under a fixed context window. PaCoRe departs from the traditional sequential paradigm by driving TTC through massive parallel exploration coordinated via a message-passing architecture in multiple rounds. Each round launches many parallel reasoning trajectories, compacts their findings into context-bounded messages, and synthesizes these messages to guide the next round and ultimately produce the final answer. Trained end-to-end with large-scale, outcome-based reinforcement learning, the model masters the synthesis abilities required by PaCoRe and scales to multi-million-token effective TTC without exceeding context limits. The approach yields strong improvements across diverse domains, and notably pushes reasoning beyond frontier systems in mathematics: an 8B model reaches 94.5% on HMMT 2025, surpassing GPT-5's 93.2% by scaling effective TTC to roughly two million tokens. We open-source model checkpoints, training data, and the full inference pipeline to accelerate follow-up work.
1. Introduction
PaCoRe addresses the fixed-context ceiling on sequential test-time compute by coordinating parallel reasoning and compressing intermediate findings. Trained synthesis enables substantial scaling, including 94.5% on HMMT 2025 with nearly two million effective TTC tokens.
- Fixed context windows limit sequential reasoning because intermediate states accumulate in one expanding chain.
- PaCoRe coordinates parallel reasoning trajectories across rounds and compresses their insights into compact messages that guide subsequent exploration.
- Outcome-based reinforcement learning trains the model to synthesize and scrutinize parallel branches rather than ignore accumulated context.
- 94.5% on HMMT 2025 is achieved by PaCoRe-8B while scaling effective TTC to nearly two million tokens per problem.
- The work releases model checkpoints, training data, and the inference pipeline for evaluation and follow-up research.
2. Methods
PaCoRe uses repeated rounds of parallel exploration, message compaction, and synthesis to scale effective test-time compute under a fixed context window. Outcome-based reinforcement learning develops the synthesis capability needed to coordinate diverse trajectories.
- Inference Pipeline: Each round combines the problem with prior compact messages, generates parallel trajectories, and compresses them into messages for the next round.
- Inference Pipeline: Parallel generation drives effective TTC while each round’s input remains approximately constant by containing only the problem and prior compact messages.
- Inference Pipeline: Trajectorywise compaction retains final conclusions while discarding intermediate steps, keeping synthesis input within the context window as aggregate TTC grows.
- Inference Pipeline: The final round uses one trajectory, whose compact message becomes the inference pipeline’s output.
- Training Procedure: Outcome-based reinforcement learning trains synthesis by evaluating extracted messages and filtering out message sets whose average accuracy is too high for naive selection.
- Training Procedure: PaCoRe operates in an implicitly multi-agent environment because its input messages are generated by other model trajectories.
- Ablations: Message passing is essential: without compaction, performance degrades as test-time compute scales and remains limited by context length.
3. Experiments
Experiments show that PaCoRe learns effective synthesis and parallel test-time scaling, improving performance across mathematics, coding, and other domains. Gains persist across ablations and include strong results against Self-Consistency and larger models.
- Training Results: Training reward, response length, HMMT 2025 performance, and LiveCodeBench performance all increase during training, indicating stable and effective learning.The training evaluation uses cached RLVR-8B responses to seed subsequent rounds for efficiency.
- Evaluation Results: 88.1% on HMMT2025 and 75.8% on LiveCodeBench are achieved in the Low setting, outperforming the RLVR-8B baseline and some much larger models.PaCoRe-8B consistently outperforms its starting checkpoint across all reported test-time effort settings.
- Ablation of Core Design Principles: Parallel coordinated reasoning uses TTC more effectively than sequential scaling, while message passing enables robust scaling without the same observed bound.The ablation compares approaches under the same total number of generated trajectories and separately removes message passing.
- Evolution of Synthesis Capabilities: The Emergent Correctness Rate rises during training, showing recovery of valid solutions from input messages that are all incorrect rather than simple majority voting.PaCoRe’s robust scaling contrasts with rapid saturation from the voting-based Self-Consistency baseline.
- Generalization Across Domains: 34.0% resolve rate on SWE-Verified and 48.0% on MultiChallenge demonstrate transfer to software engineering and multi-turn conversation tasks.The SWE-Verified comparison uses a low-compute variant without task-specific tuning of the starting checkpoint.
- General Effectiveness of PaCoRe Data: PaCoRe-curated data produces substantial benchmark gains when used for standard RLVR under a minimal compute budget.The result supports the dataset’s broader usefulness beyond training the PaCoRe framework itself.
- Ablation on Message Sampling Strategy in Training: Training on diverse, relatively large message sets sampled with |M| ∼ U(8, 16) yields the best performance under a fixed inference configuration.Randomized message-set sizes familiarize the model with varying coordination settings and improve test-time scaling.
4. Related Work
Prior approaches scale reasoning sequentially or coordinate parallel search with task-specific rules, but context limits and limited generality remain central challenges. PaCoRe is positioned as a general, open framework with message passing and targeted synthesis-oriented data curation.
- Sequential Test-Time Scaling: Sequential CoT-style scaling packs intermediate steps into one expanding chain and inevitably saturates the context window.Large-scale reinforcement learning does not remove this context ceiling.
- Parallel Search: Early parallel-search methods achieve strong domain-specific performance but often depend on task-specific scaffolds or priors.This dependence limits their general applicability.
- Coordination and Context Management: Several coordination methods synthesize parallel outputs without message passing or context management, while compression-based alternatives remain sequential.Both classes therefore retain limitations on test-time compute scaling.
- Concurrent Work: PaCoRe differs from concurrent PDR by targeting test-time compute far beyond context limits and curating data for complex synthesis rather than refinement.The paper presents this design as encouraging behavior beyond naive aggregation.
- Frontier Proprietary Systems: PaCoRe provides an open-sourced parallel coordinated reasoning framework in contrast to proprietary systems whose technical details are undisclosed.The release is intended to support broader research in parallel test-time scaling.
5. Conclusion and Future Work
PaCoRe combines coordinated parallel exploration, context-bounded message passing, and outcome-based reinforcement learning to scale test-time compute beyond sequential limits. The paper reports broad improvements and a 94.5% HMMT 2025 result from an 8B model using roughly two million effective tokens.
- Conclusion: PaCoRe launches parallel reasoning trajectories, compacts their findings into messages, and synthesizes those messages across rounds within the context window.This message-passing architecture shifts inference toward coordinated parallel breadth.
- Conclusion: Large-scale, outcome-based reinforcement learning trains the synthesis capabilities required for effective coordination.The framework includes both training and inference pipelines.
- Conclusion: 94.5% on HMMT 2025 is achieved by PaCoRe-8B while scaling effective TTC to roughly two million tokens within a standard context window.The paper reports significant improvements across diverse domains alongside this mathematics result.
- Future Work: Future work targets larger models, more domains, greater parallel breadth and coordination depth, higher token intelligence density, and emergent multi-agent intelligence.The proposed extensions include agentic tasks, multimodal understanding, and joint training of synthesis and message-passing mechanisms.
A. Initial Checkpoint Derivation
The initial checkpoint is built through supervised fine-tuning and verifiable-reward reinforcement learning on broad, filtered reasoning data. The pipeline also defines how problems and compact message sets are serialized for synthesis.
- Training Pipeline: Qwen3-8B-Base is post-trained with supervised fine-tuning and Reinforcement Learning with Verifiable Rewards.The pipeline is explicitly designed to facilitate effective test-time scaling.
- Reasoning-Oriented SFT: 10.4M verified SFT samples totaling 61.1B tokens span mathematics, coding, science, software engineering, tool use, logic, and creative writing.The data are distilled from multiple frontier models and undergo correctness verification.
- Data Filtering: Rule-based filtering removes repetition, harmful content, and personal information, while exact and 64-gram matching supports benchmark decontamination.The two filtering pipes target data quality, integrity, and leakage prevention.
- SFT Configuration: The SFT stage uses a 64k maximum sequence length and trains the model for approximately 165B tokens.The learning rate uses warmup and cosine annealing, with domain-specific sampling weights.
- Reasoning-Oriented RLVR: The RLVR stage uses approximately 500k grounded prompts across mathematics, coding, science, logic, and instruction following, generating 16 responses per prompt.Verification combines an LLM judge for non-coding tasks with sandbox execution for coding tasks.
- Input Serialization: The serialization template embeds the original problem x and compact message set M into context, bypassing the template when M = ∅.The table names these fields original_prompt and ref_responses.
B. PaCoRe Synthesis Prompt Template
PaCoRe serializes the problem and compact messages into a structured prompt, presenting prior findings as reference responses for critical synthesis. The template can also support interactive settings by incorporating the latest observation and preceding interaction history.
- B. PaCoRe Synthesis Prompt Template: PaCoRe maps the problem instance x and compact messages M into structured natural-language input through P(x, M).The exact serialization template is provided in Table 6.
- B. PaCoRe Synthesis Prompt Template: Labeling compact messages as “Reference Responses” prompts the model to critically evaluate and synthesize prior parallel perspectives.
- B. PaCoRe Synthesis Prompt Template: In interactive environments, the pipeline uses the latest observation or user message as the Original Problem while retaining preceding interaction history.The framework is described as extensible to dialogues and agentic tool-use loops.
C.1. Math Data
The math data combine open-source datasets and competition archives with synthetic arithmetic problems. Rule-based filtering and expert spot-checking are used to improve well-posedness and rule-checkability.
- C.1. Math Data: Math problems are aggregated from open-source datasets and historical archives spanning AIME, HMMT, SMT, CMIMC, and other competitions.Official solutions are included where available.
- C.1. Math Data: 13k synthetic large-integer arithmetic problems augment the data to strengthen a basic skill underlying many competition-style solutions.
- C.1. Math Data: Synthetic arithmetic instances sample integers A and B uniformly between 10^11 and 10^13 and use addition, subtraction, multiplication, or modular exponentiation.Exact integer answers are computed and recorded as ground-truth labels.
- C.1. Math Data: Deterministic filters remove image-dependent, multi-answer, and vague open-ended problems before expert spot-checking.The quality-control process targets well-posed and rule-checkable math data.
C.2. Competitive Code Data
The competitive-code corpus combines roughly 29k gathered problems with about 14k additional open-source problems, followed by validation, deduplication, and checker-based quality control. Synthetic test cases are generated and verified, with fine-grained pass-rate rewards used in reinforcement-learning experiments.
- C.2. Competitive Code Data: About 29k competitive-programming problems are gathered and cleaned using format checks, test-case counts, and judging of submitted code.The process uses testlib to judge submissions.
- C.2. Competitive Code Data: Checker handling is broadened to support 64-bit integer comparison, while special-judge problems are given generated checkers or skipped.
- C.2. Competitive Code Data: About 14k additional problems from recent open-source datasets undergo deduplication and validation.
- C.2. Competitive Code Data: A generator-validator pipeline creates test cases and verifies them against ground-truth solutions and incorrect submissions.Fine-grained rewards based on test-case pass rates outperform simple binary rewards in RL experiments.
D. More Ablation Studies
The ablation fixes the first inference round at width K1 = 32 and varies the second-round width K2. Across both reported benchmarks, K2 = 4 performs best.
- D. More Ablation Studies: K2 = 4 yields the best performance on both benchmarks.
- D. More Ablation Studies: Table 8 reports the ablation over intermediate round width K2 under the fixed configuration K = [32, K2].