# Adversarial Moment-Matching Distillation of Large Language Models

arXiv: https://arxiv.org/abs/2406.02959 · HTML: https://mlsanity.com/paper/2406.02959/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 21 of its 40 references that are in the map.
- First posted on arXiv 5 Jun 2024.

## Placed in

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

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

- [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)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [mT5: A massively multilingual pre-trained text-to-text transformer](https://mlsanity.com/paper/2010.11934/) (2020)
- [Super-NaturalInstructions: Generalization via Declarative Instructions on 1600+ NLP Tasks](https://mlsanity.com/paper/2204.07705/) (2022)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [SAMSum Corpus: A Human-annotated Dialogue Dataset for Abstractive Summarization](https://mlsanity.com/paper/1911.12237/) (2019)
- [UltraFeedback: Boosting Language Models with Scaled AI Feedback](https://mlsanity.com/paper/2310.01377/) (2023)
- [Unnatural Instructions: Tuning Language Models with (Almost) No Human Labor](https://mlsanity.com/paper/2212.09689/) (2022)
- [A Survey on Knowledge Distillation of Large Language Models](https://mlsanity.com/paper/2402.13116/) (2024)
- [DistiLLM: Towards Streamlined Distillation for Large Language Models](https://mlsanity.com/paper/2402.03898/) (2024)
- [Less is More: Task-aware Layer-wise Distillation for Language Model Compression](https://mlsanity.com/paper/2210.01351/) (2022)
- [Rethinking Kullback-Leibler Divergence in Knowledge Distillation for Large Language Models](https://mlsanity.com/paper/2404.02657/) (2024)
- [Text Generation by Learning from Demonstrations](https://mlsanity.com/paper/2009.07839/) (2020)
- [Sequence Model Imitation Learning with Unobserved Contexts](https://mlsanity.com/paper/2208.02225/) (2022)
- [Teacher Forcing Recovers Reward Functions for Text Generation](https://mlsanity.com/paper/2210.08708/) (2022)

## Built on by (most cited first, 4 of 4)

- [Language Model Distillation: A Temporal Difference Imitation Learning Perspective](https://mlsanity.com/paper/2505.20335/) (2025)
- [Short-Context Dominance: How Much Local Context Natural Language Actually Needs?](https://mlsanity.com/paper/2512.08082/) (2025)
- [Online Knowledge Distillation with Reward Guidance](https://mlsanity.com/paper/2505.18952/) (2025)
- [Revisiting On-policy Adversarial Black-Box Distillation: Calibrating Groupwise Reward Geometry for Effective Advantage Construction](https://mlsanity.com/paper/2609.39757/) (2026)

## Abstract (arXiv)

Knowledge distillation (KD) has been shown to be highly effective in guiding a student model with a larger teacher model and achieving practical benefits in improving the computational and memory efficiency for large language models (LLMs). State-of-the-art KD methods for LLMs mostly rely on minimizing explicit distribution distance between teacher and student probability predictions. Instead of optimizing these mandatory behaviour cloning objectives, we explore an imitation learning strategy for KD of LLMs. In particular, we minimize the imitation gap by matching the action-value moments of the teacher's behavior from both on- and off-policy perspectives. To achieve this action-value moment-matching goal, we propose an adversarial training algorithm to jointly estimate the moment-matching distance and optimize the student policy to minimize it. Results from both task-agnostic instruction-following experiments and task-specific experiments demonstrate the effectiveness of our method and achieve new state-of-the-art performance.