# K2P: Label-Free Knowledge to Prompt Distillation

arXiv: https://arxiv.org/abs/2609.38898 · HTML: https://mlsanity.com/paper/2609.38898/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Knowledge distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 10 of its 51 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Placed in

- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 10 of 10)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [DSPy: Compiling Declarative Language Model Calls into Self-Improving Pipelines](https://mlsanity.com/paper/2310.03714/) (2023)
- [GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning](https://mlsanity.com/paper/2507.19457/) (2025)
- [Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning](https://mlsanity.com/paper/2209.14610/) (2022)
- [ReasoningBank: Scaling Agent Self-Evolving with Reasoning Memory](https://mlsanity.com/paper/2509.25140/) (2025)

## Abstract (arXiv)

Knowledge distillation can transfer reasoning from stronger teachers to frozen students through reusable prompts, but avoiding weight updates does not eliminate supervision. Without ground-truth answers, teacher solutions are unverified, and agreement with the teacher can reward shared mistakes. We introduce Knowledge-to-Prompt (K2P) for label-free knowledge distillation to prompts. K2P synthesizes reusable instructions from teacher solutions, refines them using paired teacher and student responses, and guides search and selection with answer agreement. It retains candidates that adaptive search may undervalue and selects on reserved questions. Deployment uses only the frozen student and selected prompt. Our theory separates generation and selection gaps and gives conditions under which agreement-guided construction yields accuracy guarantees despite imperfect teacher references. Across reasoning tasks and students, K2P outperforms label-free alternatives overall and remains competitive with supervised prompt optimization. Ablations and archive diagnostics assess the contributions of teacher solutions and refinement, while revealing the limits of agreement-guided selection.