Think in Parallel, Answer as One: Logit Averaging for Open-Ended Reasoning

Abstract: Majority voting has proven effective for close-ended question answering by aggregating parallel reasoning traces. However, it is not directly applicable to open-ended reasoning, such as code generation and web-based deep research, where a "majority" over complete solutions is ill-defined. We introduce ThinkMerge, a training-free, plug-and-play decoding strategy that runs K parallel reasoning traces and averages their next-token logits at synchronization points to produce a single coherent output. ThinkMerge integrates seamlessly with vLLM/SGLang and remains compatible with standard decoding techniques such as Top-p/Top-k. Empirically, it matches or surpasses majority voting on AIME and GPQA, while delivering consistent gains on open-ended coding tasks: on LiveCodeBench (hard), pass@1 improves by +8.28% for DeepCoder-14B-Preview and +7.58% for Qwen3-8B. Beyond code, we further show that ThinkMerge improves web-based deep-research agents (e.g., WebSailor-7B/32B) across GAIA, BrowseComp-en/zh, and XbenchDeepSearch. These results demonstrate that parallel test-time scaling can benefit open-ended reasoning without relying on voting over complete outputs.