Tree of Thoughts as a Classical Heuristic Search Problem: Formal Foundations and Design Patterns

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.

Tree of Thought (ToT) search has become a promising direction for improving the reasoning capabilities of large language models, but deploying these methods in practice raises a question that has received little systematic attention: how do different search strategies behave under varying compute budgets, model sizes, and problem difficulties? In this work, we evaluate two representative ToT methods; DPTS, a Monte Carlo tree search based approach, and SSDP, a semantic deduplication based approach, across two mathematical reasoning benchmarks (Math500 and GSM8K), two model scales (Llama-3B and Llama-8B), and four token budgets (3k--10k). Our analysis reveals that the two methods exhibit limitations that pull in opposite directions. DPTS suffers from a cold-start bottleneck at low budgets: it requires sufficient exploration before its value estimates become reliable, making it a poor fit for resource-constrained settings despite strong scaling behavior at higher budgets. SSDP, on the other hand, reaches candidate solutions efficiently but is prone to frontier depletion; its aggressive node merging permanently discards unexplored paths, leaving it unable to improve regardless of how much budget remains. Together, these findings suggest that neither a fixed exploration strategy nor a fixed pruning strategy is sufficient across compute continuum. We argue that effective search for scientific reasoning agents requires strategies that can adapt their behavior based on search progress and available resources.

Although advances such as chain-of-thought, tree-of-thought or reinforcement learning have improved the performance of LLMs in reasoning and planning tasks, they are still brittle and have not achieved human-level performance in many domains, and often suffer from high time and token costs. Inspired by the success of width-based search in planning, we explore how the concept of novelty can be transferred to language domains and how it can improve tree-of-thought reasoning. A tree of thoughts relies on building possible "paths" of consecutive ideas or thoughts. These are generated by repeatedly prompting an LLM. In our paper, a measurable concept of novelty is proposed that describes the uniqueness of a new node (thought) in comparison to nodes previously seen in the search tree. Novelty is estimated by prompting an LLM and making use of embedded general knowledge from pre-training. This metric can then be used to prune branches and reduce the scope of the search. Although this method introduces more prompts per state, the overall token cost can be reduced by pruning and reducing the overall tree size. This procedure is tested and compared using several benchmarks in language-based planning and general reasoning.