PaCoRe: Learning to Scale Test-Time Compute with Parallel Coordinated Reasoning

TL;DR

This work introduces 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 far beyond sequential reasoning under a fixed context window.

Abstract

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.

Figures (5)

• Figure 1: Parallel Coordinated Reasoning (PaCoRe) performance. Left: On HMMT 2025, PaCoRe-8B demonstrates remarkable test-time scaling by increasing both parallel trajectories and coordinated rounds, yielding steady gains and ultimately surpassing GPT-5. Right: On LiveCodeBench, the RLVR-8B model fails to leverage increased test-time compute, while PaCoRe-8B model effectively unlocks this synthesis capability, yielding substantial gains as the test-time compute increases.
• Figure 2: Inference pipeline of PaCoRe. Each round launches broad parallel exploration, compacts the resulting trajectories into compacted messages, and feeds these messages together with the question forward to coordinate the next round. Repeating this process $\hat{R}$ times yields multi-million-token effective TTC while respecting fixed context limits, with the final compacted message serving as the system’s answer.
• Figure 3: PaCoRe Training dynamics.Left panels: The Training Reward and Response Length steadily increase, demonstrating the training stability and effectiveness. Right panels: Evaluation on HMMT 2025 and LiveCodeBench (2408-2505). Performance is reported using single round coordinated reasoning in PaCoRe inference setting with $\vec{K} = [16]$.
• Figure 4: Ablation of parallel reasoning and message passing.Left:Parallel scaling ($\vec{K} = [N, ]$) utilizes test-time compute more effectively than Sequential scaling ($\vec{K} = [1, \ldots, 1]$). Right:Message Passing is essential for test-time scaling. Without compaction ("W/O Message Passing"), performance degrades as test time scales and fundamentally limited by model context length, whereas standard PaCoRe ("W Message Passing") scales unboundedly and robustly. Pass@1 accuracy is evaluated on HMMT 2025.
• Figure 5: Evolution of synthesis-related linguistic features and emergent correctness across training steps.Left: Frequency of cross-checking words (including 'reference', '参考', 'Ref <number>', 'ref <number>') in generated solutions. Training elicits and magnifies this capability across domains; notably, the near-zero initial frequency in Code corroborates the poor test-time scaling of untrained models (Figure \ref{['fig:teaser']}). Right: The Emergent Correctness Rate tracks the probability of generating a correct solution given input messages that are all incorrect, averaged over 100-step intervals. The upward trend in both domains demonstrates that through large scale RL training, the model transcends naive strategies like majority voting or random selection to achieve genuine synthesis, recovering valid solutions even from entirely erroneous contexts.