Surrogate Signals from Format and Length: Reinforcement Learning for
  Solving Mathematical Problems without Ground Truth Answers
Large Language Models have achieved remarkable success in natural language
processing tasks, with Reinforcement Learning playing a key role in adapting
them to specific applications. However, obtaining ground truth answers for
training LLMs in mathematical problem-solving is often challenging, costly, and
sometimes unfeasible. This research delves into the utilization of format and
length as surrogate signals to train LLMs for mathematical problem-solving,
bypassing the need for traditional ground truth answers.Our study shows that a
reward function centered on format correctness alone can yield performance
improvements comparable to the standard GRPO algorithm in early phases.
Recognizing the limitations of format-only rewards in the later phases, we
incorporate length-based rewards. The resulting GRPO approach, leveraging
format-length surrogate signals, not only matches but surpasses the performance
of the standard GRPO algorithm relying on ground truth answers in certain
scenarios, achieving 40.0\% accuracy on AIME2024 with a 7B base model. Through
systematic exploration and experimentation, this research not only offers a
practical solution for training LLMs to solve mathematical problems and
reducing the dependence on extensive ground truth data collection, but also
reveals the essence of why our label-free approach succeeds: base model is like
an excellent student who has already mastered mathematical and logical
reasoning skills, but performs poorly on the test paper, it simply needs to
develop good answering habits to achieve outstanding results in exams , in
other words, to unlock the capabilities it already possesses.
68355784bb7d114755346770
Rihui Xin
admin_assigned
2025-05-27T13:01:54.708Z
6835378ad0fbc64a8e718c45
/avatars/ab0553b3114cc4cfad9eaa034af3241d.svg
xinrihui
user
xinrihui
68355784bb7d114755346771
Han Liu
68355784bb7d114755346772
Zecheng Wang
admin_assigned
2025-05-27T13:02:02.524Z
67123ec5b832202bddc6e74a
https://cdn-avatars.huggingface.co/v1/production/uploads/no-auth/M87nMhWm9LXi0MqxODXVK.png
Zecheng Wang
user
wangzech
68355784bb7d114755346773
Yupeng Zhang
68355784bb7d114755346774
Dianbo Sui
admin_assigned
2025-05-27T13:02:22.250Z
643e8b572263cdc630f80fee
/avatars/93b11c28a58c5db71afd44e782493140.svg
Dianbo Sui
user
suidianbo
68355784bb7d114755346775
Xiaolin Hu
68355784bb7d114755346776
Bingning Wang
Surrogate Signals from Format and Length: Reinforcement Learning for
  Solving Mathematical Problems without Ground Truth Answers
Large Language Models have achieved remarkable success in natural language
processing tasks, with Reinforcement Learning playing a key role in adapting
them to specific applications. However, obtaining ground truth answers for
training LLMs in mathematical problem-solving is often challenging, costly, and
sometimes unfeasible. This research delves into the utilization of format and
length as surrogate signals to train LLMs for mathematical problem-solving,
bypassing the need for traditional ground truth answers.Our study shows that a
reward function centered on format correctness alone can yield performance
improvements comparable to the standard GRPO algorithm in early phases.
Recognizing the limitations of format-only rewards in the later phases, we
incorporate length-based rewards. The resulting GRPO approach, leveraging
format-length surrogate signals, not only matches but surpasses the performance
of the standard GRPO algorithm relying on ground truth answers in certain
scenarios, achieving 40.0\% accuracy on AIME2024 with a 7B base model. Through
systematic exploration and experimentation, this research not only offers a
practical solution for training LLMs to solve mathematical problems and
reducing the dependence on extensive ground truth data collection, but also
reveals the essence of why our label-free approach succeeds: base model is like
an excellent student who has already mastered mathematical and logical
reasoning skills, but performs poorly on the test paper, it simply needs to
develop good answering habits to achieve outstanding results in exams , in
other words, to unlock the capabilities it already possesses.
The research demonstrates that using format and length as surrogate signals can improve LLMs' performance in mathematical problem-solving, matching or surpassing traditional methods without extensive ground truth data.
Large Language Models Reinforcement Learning mathematical problem-solving GRPO algorithm format correctness length-based rewards AIME2024