# X-KD: General Experiential Knowledge Distillation for Large Language Models

arXiv: https://arxiv.org/abs/2602.12674 · HTML: https://mlsanity.com/paper/2602.12674/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 15 of its 21 references that are in the map.
- First posted on arXiv 13 Feb 2026.

## Placed in

- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 15 of 15)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Don't Give Me the Details, Just the Summary! Topic-Aware Convolutional Neural Networks for Extreme Summarization](https://mlsanity.com/paper/1808.08745/) (2018)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [Sequence Level Training with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06732/) (2015)
- [A Survey on Knowledge Distillation of Large Language Models](https://mlsanity.com/paper/2402.13116/) (2024)
- [f-Divergence Minimization for Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/2307.15190/) (2023)
- [Less is More: Task-aware Layer-wise Distillation for Language Model Compression](https://mlsanity.com/paper/2210.01351/) (2022)
- [Scalable Bayesian Inverse Reinforcement Learning](https://mlsanity.com/paper/2102.06483/) (2021)

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

- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)

## Abstract (arXiv)

Knowledge Distillation (KD) for Large Language Models (LLMs) has become increasingly important as models grow in size and complexity. While existing distillation approaches focus on imitating teacher behavior, they often overlook the original learning environment that shaped the teacher's knowledge. Inspired by the experiential learning theory and inverse reinforcement learning, we propose Experiential Knowledge Distillation (X-KD), a novel and general framework that enables student models to learn in the teacher's original learning environment. X-KD adopts the Approximated Variational Reward Imitation Learning (AVRIL) framework to jointly model the teacher's original reward function and perform policy distillation, encouraging consistency between the student policy and the original reward function. Our derivation demonstrates that X-KD follows the supervised learning framework and applies to both sequence-level and divergence-based distillation methods, underlining the simplicity and flexibility of our approach. Empirical results show that X-KD outperforms the generalized KD and MiniLLM baselines on abstractive summarization, machine translation, and arithmetic reasoning tasks. Additionally, X-KD achieves better performance-diversity trade-off and data efficiency than baseline KD approaches.