  There is increasing interest in distilling task-specific knowledge from large
language models (LLM) to smaller student models. Nonetheless, LLM distillation
presents a dual challenge: 1) there is a high cost associated with querying the
teacher LLM, such as GPT-4, for gathering an ample number of demonstrations; 2)
the teacher LLM might provide imperfect outputs with a negative impact on the
student's learning process. To enhance sample efficiency within
resource-constrained, imperfect teacher scenarios, we propose a three-component
framework leveraging three signal types. The first signal is the student's
self-consistency (consistency of student multiple outputs), which is a proxy of
the student's confidence. Specifically, we introduce a ``teaching assistant''
(TA) model to assess the uncertainty of both the student's and the teacher's
outputs via confidence scoring, which serves as another two signals for student
training. Furthermore, we propose a two-stage training schema to first warm up
the student with a small proportion of data to better utilize student's signal.
Experiments have shown the superiority of our proposed framework for four
complex reasoning tasks. On average, our proposed two-stage framework brings a
relative improvement of up to 20.79% compared to fine-tuning without any
signals across datasets.
