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Paper · 2502.06773 · 2025

On the Emergence of Thinking in LLMs I: Searching for the Right Intuition

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 13 functions out of this paper's own repositories and ran 11 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
GuanghaoYe/Emergence-of-Thinking canonical 11 of 13
FunctionStatusWhere it lives
choice_answer_clean Ran GuanghaoYe/Emergence-of-Thinking/evaluation/grader.py
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extract_multi_choice_answer Ran GuanghaoYe/Emergence-of-Thinking/evaluation/parser.py
code served (permissive licence) · get_code("ed2f4689128f9885")
is_choice Ran GuanghaoYe/Emergence-of-Thinking/evaluation/eval_math_data_parallel.py
code served (permissive licence) · get_code("32a0caa6856c96c1")
is_digit Ran GuanghaoYe/Emergence-of-Thinking/evaluation/grader.py
code served (permissive licence) · get_code("fb37d3c84b18e368")
is_execution_success Ran GuanghaoYe/Emergence-of-Thinking/evaluation/trajectory.py
code served (permissive licence) · get_code("581f3949cfdcffa2")
is_multi_choice Ran GuanghaoYe/Emergence-of-Thinking/evaluation/eval_math_data_parallel.py
code served (permissive licence) · get_code("17fa07643a5a08e5")
lower_keys Ran GuanghaoYe/Emergence-of-Thinking/evaluation/utils.py
code served (permissive licence) · get_code("0af0b06d6cf22524")
majority_voting Ran GuanghaoYe/Emergence-of-Thinking/evaluation/evaluate.py
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parse_digits Ran GuanghaoYe/Emergence-of-Thinking/evaluation/grader.py
code served (permissive licence) · get_code("7d4b7f8c3875b126")
text_to_trajectory Ran GuanghaoYe/Emergence-of-Thinking/evaluation/trajectory.py
code served (permissive licence) · get_code("7e48538d19cc0d8f")
trajectory_to_text Ran GuanghaoYe/Emergence-of-Thinking/evaluation/trajectory.py
code served (permissive licence) · get_code("0d7ae684ec6c7537")
generate_completions Not yet run GuanghaoYe/Emergence-of-Thinking/evaluation/model_utils.py
code served (permissive licence) · get_code("25f1381fe69df071")
load_hf_lm_and_tokenizer Not yet run GuanghaoYe/Emergence-of-Thinking/evaluation/model_utils.py
code served (permissive licence) · get_code("ee71a94d9dd1b8e9")

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Abstract

Recent AI advancements, such as OpenAI's new models, are transforming LLMs into LRMs (Large Reasoning Models) that perform reasoning during inference, taking extra time and compute for higher-quality outputs. We aim to uncover the algorithmic framework for training LRMs. Methods like self-consistency, PRM, and AlphaZero suggest reasoning as guided search. We ask: what is the simplest, most scalable way to enable search in LLMs? We propose a post-training framework called Reinforcement Learning via Self-Play (RLSP). RLSP involves three steps: (1) supervised fine-tuning with human or synthetic demonstrations of the reasoning process, (2) using an exploration reward signal to encourage diverse and efficient reasoning behaviors, and (3) RL training with an outcome verifier to ensure correctness while preventing reward hacking. Our key innovation is to decouple exploration and correctness signals during PPO training, carefully balancing them to improve performance and efficiency. Empirical studies in the math domain show that RLSP improves reasoning. On the Llama-3.1-8B-Instruct model, RLSP can boost performance by 23% in MATH-500 test set; On AIME 2024 math problems, Qwen2.5-32B-Instruct improved by 10% due to RLSP. However, a more important finding of this work is that the models trained using RLSP, even with the simplest exploration reward that encourages the model to take more intermediate steps, showed several emergent behaviors such as backtracking, exploration of ideas, and verification. These findings demonstrate that RLSP framework might be enough to enable emergence of complex reasoning abilities in LLMs when scaled. Lastly, we propose a theory as to why RLSP search strategy is more suitable for LLMs inspired by a remarkable result that says CoT provably increases computational power of LLMs, which grows as the number of steps in CoT \cite{li2024chain,merrill2023expresssive}.

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