# Robust Fine-Tuning of Deep Neural Networks with Hessian-based Generalization Guarantees

arXiv: https://arxiv.org/abs/2206.02659 · HTML: https://mlsanity.com/paper/2206.02659/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 74 of its 101 references that are in the map.
- First posted on arXiv 6 Jun 2022.

## Builds on (most cited first, 30 of 74)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (2017)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [Early-Learning Regularization Prevents Memorization of Noisy Labels](https://mlsanity.com/paper/2007.00151/) (2020)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [Multi-Task Deep Neural Networks for Natural Language Understanding](https://mlsanity.com/paper/1901.11504/) (2019)
- [A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks](https://mlsanity.com/paper/1707.09564/) (2017)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [Stronger generalization bounds for deep nets via a compression approach](https://mlsanity.com/paper/1802.05296/) (2018)

## Built on by (most cited first, 30 of 34)

- [Multimodal Prompting with Missing Modalities for Visual Recognition](https://mlsanity.com/paper/2303.03369/) (2023)
- [Generalization in Graph Neural Networks: Improved PAC-Bayesian Bounds on Graph Diffusion](https://mlsanity.com/paper/2302.04451/) (2023)
- [On the Impossible Safety of Large AI Models](https://mlsanity.com/paper/2209.15259/) (2022)
- [Position: Understanding LLMs Requires More Than Statistical Generalization](https://mlsanity.com/paper/2405.01964/) (2024)
- [Identification of Negative Transfers in Multitask Learning Using Surrogate Models](https://mlsanity.com/paper/2303.14582/) (2023)
- [Scalable Multitask Learning Using Gradient-based Estimation of Task Affinity](https://mlsanity.com/paper/2409.06091/) (2024)
- [DaWin: Training-free Dynamic Weight Interpolation for Robust Adaptation](https://mlsanity.com/paper/2410.03782/) (2024)
- [Understanding Multimodal LLMs Under Distribution Shifts: An Information-Theoretic Approach](https://mlsanity.com/paper/2502.00577/) (2025)
- [Boosting Multitask Learning on Graphs through Higher-Order Task Affinities](https://mlsanity.com/paper/2306.14009/) (2023)
- [Noise Stability Optimization for Finding Flat Minima: A Hessian-based Regularization Approach](https://mlsanity.com/paper/2306.08553/) (2023)
- [LENSLLM: Unveiling Fine-Tuning Dynamics for LLM Selection](https://mlsanity.com/paper/2505.03793/) (2025)
- [Graph Neural Networks for Road Safety Modeling: Datasets and Evaluations for Accident Analysis](https://mlsanity.com/paper/2311.00164/) (2023)
- [DALD: Improving Logits-based Detector without Logits from Black-box LLMs](https://mlsanity.com/paper/2406.05232/) (2024)
- [Pre-training LLM without Learning Rate Decay Enhances Supervised Fine-Tuning](https://mlsanity.com/paper/2603.16127/) (2026)
- [Efficient Ensemble for Fine-tuning Language Models on Multiple Datasets](https://mlsanity.com/paper/2505.21930/) (2025)
- [Koopman-based generalization bound: New aspect for full-rank weights](https://mlsanity.com/paper/2302.05825/) (2023)
- [A Theoretical Analysis of the Test Error of Finite-Rank Kernel Ridge Regression](https://mlsanity.com/paper/2310.00987/) (2023)
- [On the Generalization Ability of Unsupervised Pretraining](https://mlsanity.com/paper/2403.06871/) (2024)
- [Linear-Time Demonstration Selection for In-Context Learning via Gradient Estimation](https://mlsanity.com/paper/2508.19999/) (2025)
- [Scalable Multi-Objective and Meta Reinforcement Learning via Gradient Estimation](https://mlsanity.com/paper/2511.12779/) (2025)
- [Deep Learning with Kernels through RKHM and the Perron-Frobenius Operator](https://mlsanity.com/paper/2305.13588/) (2023)
- [Improving Robust Generalization by Direct PAC-Bayesian Bound Minimization](https://mlsanity.com/paper/2211.12624/) (2022)
- [Improving Continuous Sign Language Recognition with Adapted Image Models](https://mlsanity.com/paper/2404.08226/) (2024)
- [WinQ: Accelerating Quantization-Aware Training of Language Models Around Saddle Points](https://mlsanity.com/paper/2605.17471/) (2026)
- [Information-Theoretic Generalization Bounds for Transductive Learning and its Applications](https://mlsanity.com/paper/2311.04561/) (2023)
- [Unraveling the Hessian: A Key to Smooth Convergence in Loss Function Landscapes](https://mlsanity.com/paper/2409.11995/) (2024)
- [Why High-rank Neural Networks Generalize?: An Algebraic Framework with RKHSs](https://mlsanity.com/paper/2509.21895/) (2025)
- [Operator-Based Generalization Bound for Deep Learning: Insights on Multi-Task Learning](https://mlsanity.com/paper/2512.19184/) (2025)
- [On the Koopman-Based Generalization Bounds for Multi-Task Deep Learning](https://mlsanity.com/paper/2512.19199/) (2025)
- [Operator-Theoretic Generalization Bounds for Multitask Deep Learning](https://mlsanity.com/paper/2608.15982/) (2026)

## Abstract (arXiv)

We consider fine-tuning a pretrained deep neural network on a target task. We study the generalization properties of fine-tuning to understand the problem of overfitting, which has often been observed (e.g., when the target dataset is small or when the training labels are noisy). Existing generalization measures for deep networks depend on notions such as distance from the initialization (i.e., the pretrained network) of the fine-tuned model and noise stability properties of deep networks. This paper identifies a Hessian-based distance measure through PAC-Bayesian analysis, which is shown to correlate well with observed generalization gaps of fine-tuned models. Theoretically, we prove Hessian distance-based generalization bounds for fine-tuned models. We also describe an extended study of fine-tuning against label noise, where overfitting remains a critical problem. We present an algorithm and a generalization error guarantee for this algorithm under a class conditional independent noise model. Empirically, we observe that the Hessian-based distance measure can match the scale of the observed generalization gap of fine-tuned models in practice. We also test our algorithm on several image classification tasks with noisy training labels, showing gains over prior methods and decreases in the Hessian distance measure of the fine-tuned model.