Escaping Reasoning Basins: Basin-Aware Search for Inference-Time LLM Reasoning

Inference-time search (e.g., Tree of Thoughts, ToT) 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 \textit{reasoning basin collapse}. We introduce \textsc{BASIN}, a training-free selection method that penalizes repeated visits to the same reasoning basin, defined symbolically for arithmetic tasks or semantically via hypothesis clustering, thereby reallocating search across diverse reasoning strategies. Under matched inference budgets, \textsc{BASIN} improves over ToT by up to $+22$pp on Game of 24. To explain why this quality-agnostic penalty is effective, we introduce the \emph{redundancy gap} $\Delta$, which measures how differently search concentrates for correct versus incorrect predictions: standard ToT often operates near $\Delta \approx 0$, failing to distinguish correct from incorrect searches by their visit patterns, while \textsc{BASIN} consistently induces $\Delta > 0$, concentrating search on correct basins while dispersing incorrect ones. More broadly, \textsc{BASIN} suggests structure-aware selection as a simple and general approach to improving inference-time reasoning.