# How Is Uncertainty Propagated in Knowledge Distillation?

arXiv: https://arxiv.org/abs/2601.18909 · HTML: https://mlsanity.com/paper/2601.18909/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in General knowledge distillation methods, one of 12 directions in Knowledge distillation.
- Builds on 19 of its 48 references that are in the map.
- First posted on arXiv 26 Jan 2026.

## Placed in

- Knowledge distillation / [General knowledge distillation methods](https://mlsanity.com/distill/general-knowledge-distillation-methods/)

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [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)
- [Does Knowledge Distillation Really Work?](https://mlsanity.com/paper/2106.05945/) (2021)
- [Efficient Methods for Natural Language Processing: A Survey](https://mlsanity.com/paper/2209.00099/) (2022)
- [Mitigating Membership Inference Attacks by Self-Distillation Through a Novel Ensemble Architecture](https://mlsanity.com/paper/2110.08324/) (2021)
- [A Survey of Large Language Model Agents for Question Answering](https://mlsanity.com/paper/2503.19213/) (2025)
- [Beyond Answers: Transferring Reasoning Capabilities to Smaller LLMs Using Multi-Teacher Knowledge Distillation](https://mlsanity.com/paper/2402.04616/) (2024)
- [A Survey on Model Compression and Acceleration for Pretrained Language Models](https://mlsanity.com/paper/2202.07105/) (2022)
- [Meta-KD: A Meta Knowledge Distillation Framework for Language Model Compression across Domains](https://mlsanity.com/paper/2012.01266/) (2020)
- [The Efficiency Spectrum of Large Language Models: An Algorithmic Survey](https://mlsanity.com/paper/2312.00678/) (2023)
- [Smoothing Out Hallucinations: Mitigating LLM Hallucination with Smoothed Knowledge Distillation](https://mlsanity.com/paper/2502.11306/) (2025)
- [On the Generalization vs Fidelity Paradox in Knowledge Distillation](https://mlsanity.com/paper/2505.15442/) (2025)

## Abstract (arXiv)

Knowledge distillation transfers behavior from a teacher to a student model, but the process is inherently stochastic: teacher outputs, student training, and student inference can all be random. Collapsing these uncertainties to a single point estimate can distort what is learned. We systematically study how uncertainty propagates through knowledge distillation across three representative model classes--linear regression, feed-forward neural networks, and large language models (LLMs)--and propose simple corrections. We distinguish inter-student uncertainty (variance across independently distilled students) from intra-student uncertainty (variance of a single student's predictive distribution), showing that standard single-response knowledge distillation suppresses intra-student variance while leaving substantial inter-student variability. To address these mismatches, we introduce two variance-aware strategies: averaging multiple teacher responses, which reduces noise at rate O(1/k), and variance-weighting, which combines teacher and student estimates via inverse-variance weighting to yield a minimum-variance estimator. We provide formal guarantees in linear regression, validate the methods in neural networks, and demonstrate empirical gains in LLM distillation, including reduced systematic noise and hallucination. These results reframe knowledge distillation as an uncertainty transformation and show that variance-aware distillation produces more stable students that better reflect teacher uncertainty.