Large language models (LLMs) like GPT-4 and PaLM 2 struggle with mathematical problem-solving due to the need for imagination, reasoning, and computation. However, with multiple attempts, LLMs show potential for improvement. Fine-tuning techniques such as supervised step-by-step solution fine-tuning, solution-cluster reranking, and sequential multi-tasking fine-tuning can enhance LLMs’ ability to generate and evaluate solutions. The research conducted by Yale and Google DeepMind explores these techniques and their impact on LLM performance.
Unlocking Math Problem-Solving Success with Advanced Fine-Tuning Techniques on Large Language Models
Even the most advanced large language models (LLMs) struggle with solving mathematical problems that require imagination, mathematical reasoning, and computation. However, there is potential for LLMs to improve their arithmetic problem-solving abilities by tackling the problem multiple times. For example, pre-trained models like PaLM 2-L can achieve up to 33.4% accuracy with greedy decoding and 79.4% accuracy when sampling 64 solutions using temperature sampling.
Fine-Tuning Techniques
To enhance LLMs’ capacity for solution development and assessment, researchers have explored three fine-tuning techniques:
- Supervised Step-by-Step Solution Fine-Tuning (SSFT): This technique involves adjusting the LLMs to provide the entire solution and answer.
- Solution-Cluster Reranking (SCR): By improving the LLM’s ability to evaluate solutions, SCR enhances the generator as a solution evaluator for candidate solution reranking. This approach combines majority voting with reranking to improve outcomes.
- Sequential Multi-Tasking Fine-Tuning: In addition to solution assessment, this technique aims to enhance the LLM’s performance in solution generation. By framing the solution assessment task as a natural language generation problem, the model can benefit from valuable supervision signals.
Key Findings
The research conducted on PaLM 2-S* and PaLM 2-L using the MATH dataset yielded the following conclusions:
- The quality and style of step-by-step solutions significantly influence the performance of the refined model through SSFT.
- Reranking only the most common solution clusters improves performance and computational efficiency, making it a recommended practice for future work.
- Training the model for both solution generation and evaluation tasks can effectively enhance the performance of the solution generation model.
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