Structure-Induced Information for Rerooting Levin Tree Search

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.

Deep search requires agents to answer complex questions through multi-step web search, browsing, evidence comparison, and synthesis. A central challenge is deciding how to search when several directions look plausible but only some will later lead to reliable evidence. If an agent greedily follows the current best-looking direction, it may keep extending a weak continuation. If it explores without discipline, it may waste budget on disconnected trials. We propose TreeSeeker, an inference-time framework for controlled trial-and-error in deep search. TreeSeeker organizes search as branch-and-return search over tree-structured states, where each branch is a tentative direction for a sub-goal. At each round, TreeSearch reads all sub-goal trees, identifies active goals, and uses textual UCB signals of value, uncertainty, and risk to select among exploiting a promising branch, exploring an uncertain alternative, or pruning an unproductive continuation and returning to an earlier branch point. TreeMem supports this control loop by keeping evidence, uncertainty, conflicts, progress, and failure cues attached to the branches that produced them, so trial outcomes can guide later decisions. Experiments on XBench-DeepSearch, BrowseComp, and BrowseComp-ZH show that TreeSeeker consistently outperforms strong open-source baselines, suggesting that explicit branch-and-return control complements stronger reasoning and tool execution.

Tree search is a central abstraction behind many language-agent reasoning and decision-making tasks: agents must explore actions, remember failures, and backtrack toward promising alternatives. Yet, we lack a theoretical understanding of how transformer-based policies acquire such search capabilities from the training dynamics of reinforcement learning (RL). We study this question in a stochastic $k$-ary tree environment, where an agentic transformer observes only its trajectory history through interaction and receives a terminal reward for reaching a hidden leaf goal node. We first construct a two-head transformer that implements randomized depth-first search (DFS): one head tracks previous actions, while the other detects failure outcomes and triggers backtracking. We then analyze the training dynamics of policy gradient under a depth-wise curriculum, showing that this same DFS mechanism emerges in stages from sparse reinforcement feedback without expert demonstrations. The resulting policy exhibits depth generalization: after training only on depth-$1$ and depth-$2$ trees, it succeeds on deeper full trees. We further show that, under imbalanced goal distributions, discounting the return leads to a ranked DFS policy that prioritizes higher-probability branches. Overall, our results identify a mechanistic normal form for transformer-based search, in which attention heads specialize and cooperate to extract decision-relevant traces from context and convert them into agentic action selection via RL training.