# Concept Distillation from Strong to Weak Models via Hypotheses-to-Theories Prompting

arXiv: https://arxiv.org/abs/2408.09365 · HTML: https://mlsanity.com/paper/2408.09365/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 40 references that are in the map.
- First posted on arXiv 18 Aug 2024.

## Builds on (most cited first, 21 of 21)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [A Survey on In-context Learning](https://mlsanity.com/paper/2301.00234/) (2022)
- [Automatic Prompt Optimization with "Gradient Descent" and Beam Search](https://mlsanity.com/paper/2305.03495/) (2023)
- [Learning To Retrieve Prompts for In-Context Learning](https://mlsanity.com/paper/2112.08633/) (2021)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [Hard Prompts Made Easy: Gradient-Based Discrete Optimization for Prompt Tuning and Discovery](https://mlsanity.com/paper/2302.03668/) (2023)
- [PromptAgent: Strategic Planning with Language Models Enables Expert-level Prompt Optimization](https://mlsanity.com/paper/2310.16427/) (2023)
- [EvoPrompt: Connecting LLMs with Evolutionary Algorithms Yields Powerful Prompt Optimizers](https://mlsanity.com/paper/2309.08532/) (2023)
- [Towards Understanding Knowledge Distillation](https://mlsanity.com/paper/2105.13093/) (2021)
- [Rephrase and Respond: Let Large Language Models Ask Better Questions for Themselves](https://mlsanity.com/paper/2311.04205/) (2023)
- [Large Language Models can Learn Rules](https://mlsanity.com/paper/2310.07064/) (2023)
- [In-Context Principle Learning from Mistakes](https://mlsanity.com/paper/2402.05403/) (2024)
- [Language Models for Text Classification: Is In-Context Learning Enough?](https://mlsanity.com/paper/2403.17661/) (2024)
- [How are Prompts Different in Terms of Sensitivity?](https://mlsanity.com/paper/2311.07230/) (2023)
- [PANDA: Prompt Transfer Meets Knowledge Distillation for Efficient Model Adaptation](https://mlsanity.com/paper/2208.10160/) (2022)
- [Failures Pave the Way: Enhancing Large Language Models through Tuning-free Rule Accumulation](https://mlsanity.com/paper/2310.15746/) (2023)
- [Evoke: Evoking Critical Thinking Abilities in LLMs via Reviewer-Author Prompt Editing](https://mlsanity.com/paper/2310.13855/) (2023)

## Built on by (most cited first, 1 of 1)

- [Agentic Multi-Source Grounding for Enhanced Query Intent Understanding: A DoorDash Case Study](https://mlsanity.com/paper/2603.01486/) (2026)

## Abstract (arXiv)

Hand-crafting high quality prompts to optimize the performance of language models is a complicated and labor-intensive process. Furthermore, when migrating to newer, smaller, or weaker models (possibly due to latency or cost gains), prompts need to be updated to re-optimize the task performance. We propose Concept Distillation (CD), an automatic prompt optimization technique for enhancing weaker models on complex tasks. CD involves: (1) collecting mistakes made by weak models with a base prompt (initialization), (2) using a strong model to generate reasons for these mistakes and create rules/concepts for weak models (induction), and (3) filtering these rules based on validation set performance and integrating them into the base prompt (deduction/verification). We evaluated CD on NL2Code and mathematical reasoning tasks, observing significant performance boosts for small and weaker language models. Notably, Mistral-7B's accuracy on Multi-Arith increased by 20%, and Phi-3-mini-3.8B's accuracy on HumanEval rose by 34%. Compared to other automated methods, CD offers an effective, cost-efficient strategy for improving weak models' performance on complex tasks and enables seamless workload migration across different language models without compromising performance.