Improving Large Language Model Fine-tuning for Solving Math Problems
Despite their success in many natural language tasks, solving math problems
remains a significant challenge for large language models (LLMs). A large gap
exists between LLMs' pass-at-one and pass-at-N performance in solving math
problems, suggesting LLMs might be close to finding correct solutions,
motivating our exploration of fine-tuning methods to unlock LLMs' performance.
Using the challenging MATH dataset, we investigate three fine-tuning
strategies: (1) solution fine-tuning, where we fine-tune to generate a detailed
solution for a given math problem; (2) solution-cluster re-ranking, where the
LLM is fine-tuned as a solution verifier/evaluator to choose among generated
candidate solution clusters; (3) multi-task sequential fine-tuning, which
integrates both solution generation and evaluation tasks together efficiently
to enhance the LLM performance. With these methods, we present a thorough
empirical study on a series of PaLM 2 models and find: (1) The quality and
style of the step-by-step solutions used for fine-tuning can make a significant
impact on the model performance; (2) While solution re-ranking and majority
voting are both effective for improving the model performance when used
separately, they can also be used together for an even greater performance
boost; (3) Multi-task fine-tuning that sequentially separates the solution
generation and evaluation tasks can offer improved performance compared with
the solution fine-tuning baseline. Guided by these insights, we design a
fine-tuning recipe that yields approximately 58.8% accuracy on the MATH dataset
with fine-tuned PaLM 2-L models, an 11.2% accuracy improvement over the
few-shot performance of pre-trained PaLM 2-L model with majority voting.
652df3d40c60de928ef8feaf
Yixin Liu
extracted_confirmed
2023-10-17T02:45:40.403Z
6244de1c1c560fb11edfca44
/avatars/36558928bd04be7f49837d4c603681d7.svg
Yixin Liu
user
henryL7
652df3d40c60de928ef8feb0
Avi Singh
652df3d40c60de928ef8feb1
C. Daniel Freeman
652df3d40c60de928ef8feb2
John D. Co-Reyes
652df3d40c60de928ef8feb3
Peter J. Liu
extracted_confirmed
2023-11-02T20:32:48.394Z
62ded294dcdc9043efaa4fc3
/avatars/1294078b8cd5c1901e4021253d877357.svg
Peter J Liu
user
peterjliu
Improving Large Language Model Fine-tuning for Solving Math Problems
Despite their success in many natural language tasks, solving math problems
remains a significant challenge for large language models (LLMs). A large gap
exists between LLMs' pass-at-one and pass-at-N performance in solving math
problems, suggesting LLMs might be close to finding correct solutions,
motivating our exploration of fine-tuning methods to unlock LLMs' performance.
Using the challenging MATH dataset, we investigate three fine-tuning
strategies: (1) solution fine-tuning, where we fine-tune to generate a detailed
solution for a given math problem; (2) solution-cluster re-ranking, where the
LLM is fine-tuned as a solution verifier/evaluator to choose among generated
candidate solution clusters; (3) multi-task sequential fine-tuning, which
integrates both solution generation and evaluation tasks together efficiently
to enhance the LLM performance. With these methods, we present a thorough
empirical study on a series of PaLM 2 models and find: (1) The quality and
style of the step-by-step solutions used for fine-tuning can make a significant
impact on the model performance; (2) While solution re-ranking and majority
voting are both effective for improving the model performance when used
separately, they can also be used together for an even greater performance
boost; (3) Multi-task fine-tuning that sequentially separates the solution
generation and evaluation tasks can offer improved performance compared with
the solution fine-tuning baseline. Guided by these insights, we design a
fine-tuning recipe that yields approximately 58.8% accuracy on the MATH dataset
with fine-tuned PaLM 2-L models, an 11.2% accuracy improvement over the
few-shot performance of pre-trained PaLM 2-L model with majority voting.
Three fine-tuning strategies significantly improve PaLM 2 models' performance in solving math problems on the MATH dataset.
solution fine-tuning solution-cluster re-ranking multi-task sequential fine-tuning PaLM 2 MATH dataset