Implementation:Iamhankai Forest of Thought Monte Carlo Tree

Knowledge Sources	Forest-of-Thought Forest-of-Thought
Domains	Search_Algorithms, Reasoning
Last Updated	2026-02-14 03:00 GMT

Overview

Concrete tool for executing single-tree MCTS reasoning provided by the Forest-of-Thought repository.

Description

The monte_carlo_tree function implements the core MCTS loop for a single reasoning tree. It generates an initial answer, then iteratively refines it through UCB-guided selection, hint-based expansion, reward scoring, and backpropagation. The function maintains full tree state including reward banks, UCB values, and activation signals for tracking which answers are "mature" enough for forest-level aggregation.

Usage

Called by Monte_Carlo_Forest.mctsr_run() once per tree in the forest. Each tree operates independently with the same question but may produce different answers due to stochastic LLM generation.

Code Reference

Source Location

Repository: Forest-of-Thought
File: run_with_mcf_stop_noearly.py
Lines: L223-312

Signature

def monte_carlo_tree(DATA_NAME, query, max_iter=16, ans_format=''):
    """
    Execute MCTS for iterative answer refinement on a single problem.

    Args:
        DATA_NAME (str): Dataset identifier for label extraction.
        query (str): The input question to solve.
        max_iter (int): Maximum MCTS iterations (default 16).
        ans_format (str): Expected answer format specification.

    Returns:
        tuple: (
            tree_ans (str): Best selected answer,
            is_activate (bool): Whether answer is mature,
            activated_answers_list (list[str]): Extracted answer labels,
            activated_answer_scores (list[float]): Reward scores,
            answers_list (list[str]): All generated raw answers,
            to_explore (list): Explorable nodes,
            to_explore_reward (dict): Node-to-reward mapping,
            ucb_bank (dict): UCB values for all nodes
        )
    """

Import

# Defined inline in main script
from run_with_mcf_stop_noearly import monte_carlo_tree

I/O Contract

Inputs

Name	Type	Required	Description
DATA_NAME	str	Yes	Dataset name for format-aware label extraction
query	str	Yes	Math problem to solve via MCTS
max_iter	int	No	Number of MCTS iterations (default 16)
ans_format	str	No	Expected answer format hint

Outputs

Name	Type	Description
tree_ans	str	Best answer selected by the tree
is_activate	bool	True if the tree produced a mature answer
activated_answers_list	list[str]	Extracted answer labels from all iterations
activated_answer_scores	list[float]	Reward scores for each answer
answers_list	list[str]	All raw generated answer strings
to_explore	list	Remaining explorable nodes
to_explore_reward	dict	Reward mapping for explorable nodes
ucb_bank	dict	UCB values for all explored nodes

Usage Examples

# Single tree MCTS execution (called internally by Monte_Carlo_Forest)
tree_ans, is_activate, act_answers, act_scores, all_answers, \
    to_explore, rewards, ucb = monte_carlo_tree(
        DATA_NAME="math",
        query="Find all real numbers x such that x^2 - 5x + 6 = 0",
        max_iter=8,
        ans_format="\\boxed{}"
    )

print(f"Best answer: {tree_ans}")
print(f"Activated: {is_activate}")
print(f"Answer labels: {act_answers}")

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