Learn Hard Problems During RL with Reference Guided Fine-tuning
Reinforcement learning (RL) for mathematical reasoning can suffer from reward sparsity: for challenging problems, LLM fails to sample any correct trajectories, preventing RL from receiving meaningful positive feedback. At the same time, there often exist human-written reference solutions along with the problem (e.g., problems from AoPS), but directly fine-tuning on these solutions offers no benefit because models often cannot imitate human proofs that lie outside their own reasoning distribution.
  We introduce Reference-Guided Fine-Tuning (ReGFT), a simple and effective method that utilizes human-written reference solutions to synthesize positive trajectories on hard problems and train on them before RL. For each problem, we provide the model with a partial reference solution and let it generate its own reasoning trace, ensuring the resulting trajectories remain in the model's reasoning space while still benefiting from reference guidance.
  Fine-tuning on these reference-guided trajectories increases the number of solvable problems and produces a checkpoint that receives more positive rewards during RL. Across three benchmarks (AIME24, AIME25, BeyondAIME), ReGFT consistently improves supervised accuracy, accelerates DAPO training, and raises the final performance plateau of RL. Our results show that ReGFT effectively overcomes reward sparsity and unlocks stronger RL-based mathematical reasoning.
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Yangzhen Wu
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Shanda Li
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Zixin Wen
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Xin Zhou
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Ameet Talwalkar
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Yiming Yang
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Wenhao Huang
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Tianle Cai
Learn Hard Problems During RL with Reference Guided Fine-tuning
Reinforcement learning (RL) for mathematical reasoning can suffer from reward sparsity: for challenging problems, LLM fails to sample any correct trajectories, preventing RL from receiving meaningful positive feedback. At the same time, there often exist human-written reference solutions along with the problem (e.g., problems from AoPS), but directly fine-tuning on these solutions offers no benefit because models often cannot imitate human proofs that lie outside their own reasoning distribution.
  We introduce Reference-Guided Fine-Tuning (ReGFT), a simple and effective method that utilizes human-written reference solutions to synthesize positive trajectories on hard problems and train on them before RL. For each problem, we provide the model with a partial reference solution and let it generate its own reasoning trace, ensuring the resulting trajectories remain in the model's reasoning space while still benefiting from reference guidance.
  Fine-tuning on these reference-guided trajectories increases the number of solvable problems and produces a checkpoint that receives more positive rewards during RL. Across three benchmarks (AIME24, AIME25, BeyondAIME), ReGFT consistently improves supervised accuracy, accelerates DAPO training, and raises the final performance plateau of RL. Our results show that ReGFT effectively overcomes reward sparsity and unlocks stronger RL-based mathematical reasoning.
Reference-Guided Fine-Tuning (ReGFT) addresses reward sparsity in reinforcement learning for mathematical reasoning by using human-written solutions to create guided training trajectories that improve model performance.
reinforcement learning mathematical reasoning reward sparsity supervised accuracy DAPO training reinforcement learning-based mathematical reasoning