Idea Search: Guiding Tree Search with Ideas to Explore Diverse Scientific Methods

As pretraining scaling laws approach saturation, Test-Time Scaling (TTS) has emerged as an important direction for improving reasoning by allocating inference-time compute to a fixed model prior. Viewed at a high level, TTS reframes inference as search over a space of partial reasoning states. While Chain-of-Thought (CoT) exposes intermediate steps, common instantiations rely on single-trajectory decoding, limiting recovery from early errors and exploration. This survey systematizes recent progress in tree-search-based reasoning, viewing inference as instance-specific optimization rather than decoding. We trace the evolution from uninformed search to Monte Carlo Tree Search (MCTS), highlighting how sampling-based control supports principled exploration-exploitation trade-offs. To unify a fragmented literature, we introduce a Unified Design Space spanning search topology, evaluation signals, and control dynamics, and advocate a standardized compute-reporting abstraction to make compute-accuracy trade-offs explicit and comparable.

Coding agents can recursively modify their own implementations, forming a loop of self-improvement. While prior work shows this can boost performance on coding benchmarks, existing approaches are costly and compute-intensive. We introduce a simple, sample-efficient self-improvement framework that significantly improves coding performance under strict budget constraints. We identify evaluation of candidate self-modifications as the main runtime bottleneck since prior approaches estimate their effectiveness by re-running a subset of benchmark tasks with the modified agent, which is time-consuming. We introduce Recursive Self Improvement via Fast Tree-search (SIFT), which augments these downstream task evaluations with an LLM-as-a-judge signal that performs pairwise comparisons between candidate patches, where the win-loss record is aggregated with a regularized Bradley-Terry model, and the resulting strength scores drive rank-based parent sampling inside a lightweight disaggregated tree search. Expensive downstream task evaluations are reserved only for the most promising nodes. Using a fully disaggregated tree search pipeline, the judge scores provide intermediate signal to guide exploration on promising candidate patches without being bottlenecked by slow evaluation runs. SIFT outperforms existing tree-search based self-evolution frameworks on the full Polyglot benchmark with significantly lower resource requirements in terms of CPU hours, wall clock time, and API cost.

Language models are increasingly used in scientific discovery to generate hypotheses, propose candidate solutions, implement systems, and iteratively refine them. At the core of these trial-and-error loops lies evaluation: the process of obtaining feedback on candidate solutions via verifiers, simulators, or task-specific scoring functions. While prior work has highlighted the importance of evaluation, it has not explicitly formulated the problem of how evaluation-driven discovery loops can be scaled up in a principled and effective manner to push the boundaries of scientific discovery, a problem this paper seeks to address. We introduce Simple Test-time Evaluation-driven Scaling (SimpleTES), a general framework that strategically combines parallel exploration, feedback-driven refinement, and local selection, revealing substantial gains unlocked by scaling evaluation-driven discovery loops along the right dimensions. Across 21 scientific problems spanning six domains, SimpleTES discovers state-of-the-art solutions using gpt-oss models, consistently outperforming both frontier-model baselines and sophisticated optimization pipelines. Particularly, we sped up the widely used LASSO algorithm by over 2x, designed quantum circuit routing policies that reduce gate overhead by 24.5%, and discovered new Erdos minimum overlap constructions that surpass the best-known results. Beyond novel discoveries, SimpleTES produces trajectory-level histories that naturally supervise feedback-driven learning. When post-trained on successful trajectories, models not only improve efficiency on seen problems but also generalize to unseen problems, discovering solutions that base models fail to uncover. Together, our results establish effective evaluation-driven loop scaling as a central axis for advancing LLM-driven scientific discovery, and provide a simple yet practical framework for realizing these gains.