# Characterizing the Training Dynamics of Private Fine-tuning with Langevin diffusion

arXiv: https://arxiv.org/abs/2402.18905 · HTML: https://mlsanity.com/paper/2402.18905/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 61 references that are in the map.
- First posted on arXiv 29 Feb 2024.

## Builds on (most cited first, 30 of 37)

- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [An Empirical Study of Training Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.02057/) (2021)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution](https://mlsanity.com/paper/2202.10054/) (2022)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Differentially Private Fine-tuning of Language Models](https://mlsanity.com/paper/2110.06500/) (2021)
- [On the Optimization of Deep Networks: Implicit Acceleration by Overparameterization](https://mlsanity.com/paper/1802.06509/) (2018)
- [Unlocking High-Accuracy Differentially Private Image Classification through Scale](https://mlsanity.com/paper/2204.13650/) (2022)
- [On the Theory of Transfer Learning: The Importance of Task Diversity](https://mlsanity.com/paper/2006.11650/) (2020)
- [Algorithmic Regularization in Learning Deep Homogeneous Models: Layers are Automatically Balanced](https://mlsanity.com/paper/1806.00900/) (2018)
- [Better Fine-Tuning by Reducing Representational Collapse](https://mlsanity.com/paper/2008.03156/) (2020)
- [Understanding Gradient Clipping in Private SGD: A Geometric Perspective](https://mlsanity.com/paper/2006.15429/) (2020)
- [On the Role of Neural Collapse in Transfer Learning](https://mlsanity.com/paper/2112.15121/) (2021)
- [Neural Collapse: A Review on Modelling Principles and Generalization](https://mlsanity.com/paper/2206.04041/) (2022)
- [Learning to See by Looking at Noise](https://mlsanity.com/paper/2106.05963/) (2021)
- [MiniViT: Compressing Vision Transformers with Weight Multiplexing](https://mlsanity.com/paper/2204.07154/) (2022)
- [Differential Privacy Dynamics of Langevin Diffusion and Noisy Gradient Descent](https://mlsanity.com/paper/2102.05855/) (2021)
- [What can linearized neural networks actually say about generalization?](https://mlsanity.com/paper/2106.06770/) (2021)
- [Global Convergence of Gradient Descent for Asymmetric Low-Rank Matrix Factorization](https://mlsanity.com/paper/2106.14289/) (2021)
- [Abide by the Law and Follow the Flow: Conservation Laws for Gradient Flows](https://mlsanity.com/paper/2307.00144/) (2023)
- [Why Is Public Pretraining Necessary for Private Model Training?](https://mlsanity.com/paper/2302.09483/) (2023)
- [On the Convergence and Calibration of Deep Learning with Differential Privacy](https://mlsanity.com/paper/2106.07830/) (2021)
- [Early Neuron Alignment in Two-layer ReLU Networks with Small Initialization](https://mlsanity.com/paper/2307.12851/) (2023)

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

- [DP-MemArc: Differential Privacy Transfer Learning for Memory Efficient Language Models](https://mlsanity.com/paper/2406.11087/) (2024)
- [On Optimal Hyperparameters for Differentially Private Deep Transfer Learning](https://mlsanity.com/paper/2510.20616/) (2025)
- [Mitigating Noise Detriment in Differentially Private Federated Learning with Model Pre-training](https://mlsanity.com/paper/2408.09478/) (2024)
- [Lower Bounds for Public-Private Learning under Distribution Shift](https://mlsanity.com/paper/2507.17895/) (2025)

## Abstract (arXiv)

We show that differentially private full fine-tuning (DP-FFT) can distort pre-trained backbone features based on both theoretical and empirical results. We identify the cause of the distortion as the misalignment between the pre-trained backbone and the randomly initialized linear head. We prove that a sequential fine-tuning strategy can mitigate the feature distortion: first-linear-probing-then-fine-tuning (DP-LP-FFT). A new approximation scheme allows us to derive approximate upper and lower bounds on the training loss of DP-LP and DP-FFT, in a simple but canonical setting of 2-layer neural networks with ReLU activation. Experiments on real-world datasets and architectures are consistent with our theoretical insights. We also derive new upper bounds for 2-layer linear networks without the approximation. Moreover, our theory suggests a trade-off of privacy budget allocation in multi-phase fine-tuning methods like DP-LP-FFT.