FoE: Forest of Errors Makes the First Solution the Best in Large Reasoning Models

Computer Science > Artificial Intelligence [Submitted on 3 Apr 2026] FoE: Forest of Errors Makes the First Solution the Best in Large Reasoning Models Kehan Jiang, Haonan Dong, Zhaolu Kang, Zhengzhou Zhu, Guojie Song Recent Large Reasoning Models (LRMs) like DeepSeek-R1 have demonstrated remarkable success in complex reasoning tasks, exhibiting human-like patterns in exploring multiple alternative solutions. Upon closer inspection, however, we uncover a surprising phenomenon: The First is The Best, where alternative solutions are not merely suboptimal but potentially detrimental. This observation challenges widely accepted test-time scaling laws, leading us to hypothesize that errors within the reasoning path scale concurrently with test time. Through comprehensive empirical analysis, we characterize errors as a forest-structured Forest of Errors (FoE) and conclude that FoE makes the First the Best, which is underpinned by rigorous theoretical analysis. Leveraging these insights, we propose RED, a self-guided efficient reasoning framework comprising two components: I) Refining First, which suppresses FoE growth in the first solution; and II) Discarding Subs, which prunes subsequent FoE via dual-consistency. Extensive experiments across five benchmarks and six backbone models demonstrate that RED outperforms eight competitive baselines, achieving performance gains of up to 19.0% while reducing token consumption by 37.7% ~ 70.4%. Moreover, comparative experiments on FoE metrics shed light on how RED achieves effectiveness. Subjects: Artificial Intelligence (cs.AI); Computation and Language (cs.CL) Cite as: arXiv:2604.02967 [cs.AI]   (or arXiv:2604.02967v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2604.02967 Focus to learn more Submission history From: Haonan Dong [view email] [v1] Fri, 3 Apr 2026 11:03:02 UTC (1,732 KB) Access Paper: view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-04 Change to browse by: cs cs.CL References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)