Inference-time search with large language models (LLMs) often concentrates on a small set of structurally or semantically similar trajectories, leaving alternatives underexplored---a failure mode we call reasoning basin collapse. We introduce BASIN, a training-free, structure-aware selection method that groups reasoning states into basins and penalizes repeated visits to the same strategy, thereby reallocating search across genuinely distinct reasoning paths under a fixed compute budget.

Under matched inference budgets, BASIN improves over Tree of Thoughts (ToT) by up to $+22$pp on Game of 24 and $+6.7$pp on MuSR. A quality-aware variant, QA-BASIN, further improves robustness by preserving high-quality basins when unconditional diversification over-explores.

To explain when basin-aware selection helps, we introduce the redundancy gap $Δ$, which measures how differently search concentrates for correct versus incorrect predictions: standard ToT often operates near $Δ\approx 0$, while BASIN consistently shifts $Δ$ positive. More broadly, BASIN suggests structure-aware selection as a simple and general approach to improving inference-time reasoning.

Code can be found at https://github.com/GitHubLuCheng/basin.