# Towards the Fundamental Limits of Knowledge Transfer over Finite Domains

arXiv: https://arxiv.org/abs/2310.07838 · HTML: https://mlsanity.com/paper/2310.07838/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 66 of its 110 references that are in the map.
- First posted on arXiv 11 Oct 2023.

## Builds on (most cited first, 30 of 66)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Paying More Attention to Attention: Improving the Performance of Convolutional Neural Networks via Attention Transfer](https://mlsanity.com/paper/1612.03928/) (2016)
- [Relational Knowledge Distillation](https://mlsanity.com/paper/1904.05068/) (2019)
- [GLM-130B: An Open Bilingual Pre-trained Model](https://mlsanity.com/paper/2210.02414/) (2022)
- [Contrastive Representation Distillation](https://mlsanity.com/paper/1910.10699/) (2019)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [Born Again Neural Networks](https://mlsanity.com/paper/1805.04770/) (2018)
- [Similarity-Preserving Knowledge Distillation](https://mlsanity.com/paper/1907.09682/) (2019)
- [Do Deep Nets Really Need to be Deep?](https://mlsanity.com/paper/1312.6184/) (2013)
- [Dreaming to Distill: Data-free Knowledge Transfer via DeepInversion](https://mlsanity.com/paper/1912.08795/) (2019)
- [How Far Can Camels Go? Exploring the State of Instruction Tuning on Open Resources](https://mlsanity.com/paper/2306.04751/) (2023)
- [Decoupled Knowledge Distillation](https://mlsanity.com/paper/2203.08679/) (2022)
- [On the Efficacy of Knowledge Distillation](https://mlsanity.com/paper/1910.01348/) (2019)
- [Knowledge Distillation and Student-Teacher Learning for Visual Intelligence: A Review and New Outlooks](https://mlsanity.com/paper/2004.05937/) (2020)
- [Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning](https://mlsanity.com/paper/2012.09816/) (2020)
- [Knockoff Nets: Stealing Functionality of Black-Box Models](https://mlsanity.com/paper/1812.02766/) (2018)

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

- [A Survey on Knowledge Distillation of Large Language Models](https://mlsanity.com/paper/2402.13116/) (2024)
- [Iterative Data Smoothing: Mitigating Reward Overfitting and Overoptimization in RLHF](https://mlsanity.com/paper/2401.16335/) (2024)
- [Provable Weak-to-Strong Generalization via Benign Overfitting](https://mlsanity.com/paper/2410.04638/) (2024)
- [Revisiting Knowledge Distillation: The Hidden Role of Dataset Size](https://mlsanity.com/paper/2510.15516/) (2025)

## Abstract (arXiv)

We characterize the statistical efficiency of knowledge transfer through n samples from a teacher to a probabilistic student classifier with input space mathcal S over labels mathcal A. We show that privileged information at three progressive levels accelerates the transfer. At the first level, only samples with hard labels are known, via which the maximum likelihood estimator attains the minimax rate √|mathcal S||mathcal A|/n. The second level has the teacher probabilities of sampled labels available in addition, which turns out to boost the convergence rate lower bound to |mathcal S||mathcal A|/n. However, under this second data acquisition protocol, minimizing a naive adaptation of the cross-entropy loss results in an asymptotically biased student. We overcome this limitation and achieve the fundamental limit by using a novel empirical variant of the squared error logit loss. The third level further equips the student with the soft labels (complete logits) on mathcal A given every sampled input, thereby provably enables the student to enjoy a rate |mathcal S|/n free of |mathcal A|. We find any Kullback-Leibler divergence minimizer to be optimal in the last case. Numerical simulations distinguish the four learners and corroborate our theory.