Can LLMs Learn by Teaching for Better Reasoning? A Preliminary Study

TL;DR

This paper designs three methods, each mimicking one of the three levels of LbT: observing students' feedback, learning from the feedback, and learning iteratively, with the goals of improving answer accuracy without training or improving models' inherent capability with fine-tuning.

Abstract

Teaching to improve student models (e.g., knowledge distillation) is an extensively studied methodology in LLMs. However, for humans, teaching improves not only students but also teachers, by fostering more rigorous and clear reasoning as well as knowledge building. We ask: Can LLMs also learn by teaching (LbT) for better reasoning? If the answer is yes, we can potentially unlock the possibility of continuously advancing the models without solely relying on human-produced data or stronger models. In this paper, we provide a preliminary exploration on this question. We show that LbT ideas can be incorporated into existing LLM training/prompting pipelines and bring improvements. Specifically, we design three methods, each mimicking one of the three levels of LbT: observing students' feedback, learning from the feedback, and learning iteratively, with the goals of improving answer accuracy without training or improving models' inherent capability with fine-tuning. We reveal some findings: (1) Teaching materials that make it easier for students to learn have clearer and more accurate logic when using in-context learning as the student's "learning" method; (2) Weak-to-strong generalization: LbT might help improve strong models by teaching weak models; (3) Diversity in students might help: teaching multiple students could be better than teaching one student or the teacher itself. We hope that our exploration can inspire future research on LbT and more broadly adopting the advanced techniques in education to improve LLMs. The code and website are at https://github.com/imagination-research/lbt and https://sites.google.com/view/llm-learning-by-teaching.

Figures (7)

• Figure 1: Left:Learning from teacher aims at improving student LLMs with knowledge from the teacher LLMs. It is the essential idea behind common approaches including knowledge distillation and distillation via synthetic data. Right: In contrast, Learning by teaching aims at improving teacher LLMs through the teaching process using feedback from student LLMs.
• Figure 2: Two general pipelines for improving the answer quality and model capability. "P" stands for "Problem"; "R" stands for "Rationale"; "A" stands for "Answer".
• Figure 3: M1. The goal is to derive the best TA from the TR-TA pairs generated by the teacher LLM.
• Figure 4: Relative improvements of M1 over SC using LLaMA3-8B as the teacher and student on 181 MATH test problems with respect to: (Left) Number of TR-TA pairs. Error bars are calculated using the bootstrap sampling technique li2022alphacode, where 10 subsets are sampled from the 256 TR-TA pairs, and standard deviations are computed across these sets; (Middle) Difficulty level; (Right) The fraction of TPs when sorted by the cosine distance to the 2 closest problems from the training set.
• Figure 5: Baseline vs. M2. Both approaches use scores of TRs to craft preference data and finetune the teacher LLM with DPO. Left: The correctness score of TA. Right: The LbT score of TR and TA.