From Reasoning to Super-Intelligence: A Search-Theoretic Perspective

Chain-of-Thought (CoT) reasoning has emerged as a powerful tool for enhancing the problem-solving capabilities of large language models (LLMs). However, the theoretical foundations of learning from CoT data remain underdeveloped, and existing approaches -- such as Supervised Fine-Tuning (SFT), Reinforcement Learning (RL), Tree-of-Thoughts (ToT), and Monte Carlo Tree Search (MCTS) -- often fail on complex reasoning tasks. In this work, we identify core obstacles that hinder effective CoT learning, including distribution drift, lack of embedded search, and exponential inference costs. We introduce the Diligent Learner, a new learning paradigm that explicitly models reasoning as a depth-first search guided by a validator and supports backtracking upon failure. Under two mild and realistic assumptions, we prove that the Diligent Learner can efficiently learn from CoT data while existing methods fail to do so. This framework offers a path toward building scalable and reliable reasoning systems trained on naturally occurring, incomplete data -- paving the way for the development of Large Reasoning Models (LRMs) with robust, interpretable problem-solving abilities.