# The Bridge-Garden Dilemma in LLM Distillation: Why Mixing Hard and Soft Labels Works

arXiv: https://arxiv.org/abs/2605.26246 · HTML: https://mlsanity.com/paper/2605.26246/

## 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 63 of its 78 references that are in the map.
- First posted on arXiv 25 May 2026.

## Placed in

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

## Builds on (most cited first, 30 of 63)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [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)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [On the Efficacy of Knowledge Distillation](https://mlsanity.com/paper/1910.01348/) (2019)
- [Knowledge distillation: A good teacher is patient and consistent](https://mlsanity.com/paper/2106.05237/) (2021)
- [OpenCodeInterpreter: Integrating Code Generation with Execution and Refinement](https://mlsanity.com/paper/2402.14658/) (2024)
- [Knowledge Distillation from A Stronger Teacher](https://mlsanity.com/paper/2205.10536/) (2022)
- [TheoremQA: A Theorem-driven Question Answering dataset](https://mlsanity.com/paper/2305.12524/) (2023)
- [Direct Nash Optimization: Teaching Language Models to Self-Improve with General Preferences](https://mlsanity.com/paper/2404.03715/) (2024)
- [DistiLLM: Towards Streamlined Distillation for Large Language Models](https://mlsanity.com/paper/2402.03898/) (2024)
- [Stealing Part of a Production Language Model](https://mlsanity.com/paper/2403.06634/) (2024)
- [Knowledge Distillation with the Reused Teacher Classifier](https://mlsanity.com/paper/2203.14001/) (2022)

## Abstract (arXiv)

Knowledge distillation (KD) transfers knowledge from a large teacher model to a smaller student. In language modeling, the student is trained either on tokens sampled from the teacher (hard labels) or the teacher's full next-token distribution (soft labels). Despite soft labels appear strictly richer, we find that mixing hard and soft labels consistently yields better results. Crucially, we show that this gain cannot be explained by closer teacher matching during training. Instead, it comes from reduced exposure bias, the mismatch between training and inference distributions. To explain this phenomenon, we introduce the Bridge-Garden Decomposition theory, which categorizes generation steps into two types: Bridges, where the next token must be exact, and Gardens, where it can be flexible. We show that hard-only KD excels in Bridges by avoiding risky deviations, while soft-only KD preserves diversity in Gardens. A hybrid strategy handles both cases and, as a result, reduces exposure bias across the sequence. Guided by this theory, we develop a family of Bridge-Garden hybrid supervision methods that adaptively balance hard and soft labels. Across a primary suite of seven teacher-student pairs (including Qwen, Llama, Gemma, and DeepSeek) and benchmarks in reasoning and coding, our approach outperforms divergence-based and on-policy KD baselines while reducing training cost by 9.7x, enabling efficient model compression. Code is available at https://github.com/ghwang-s/bridge_garden_hybrid_kd_release.