When performing inference‑time search with large language models (LLMs), the process often concentrates on a narrow set of structurally or semantically similar trajectories, leaving many alternative solutions unexplored. This failure mode is termed reasoning basin collapse. To address it, the authors introduce BASIN, a training‑free, structure‑aware selection method. BASIN groups reasoning states into distinct basins and penalizes repeated visits to the same strategy, thereby reallocating the fixed compute budget toward genuinely different reasoning paths.
Under matched inference budgets, BASIN outperforms Tree of Thoughts (ToT) by up to $+22$ percentage points on Game of 24 and $+6.7$ points on MuSR. A quality‑aware variant, QA‑BASIN, further improves robustness by preserving high‑quality basins when unconditional diversification would otherwise over‑explore.
To quantify the benefit of basin‑aware selection, the paper defines the redundancy gap $\Delta$, measuring how differently search concentrates for correct versus incorrect predictions. Standard ToT typically operates near $\Delta \approx 0$, indicating little distinction between good and bad paths, whereas BASIN consistently shifts $\Delta$ positive, showing a bias toward correct trajectories.
Overall, BASIN suggests that structure‑aware selection is a simple and general approach to enhance inference‑time reasoning. The implementation is publicly available at https://github.com/GitHubLuCheng/basin.
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