# Attributing Data for Sharpness-Aware Minimization

arXiv: https://arxiv.org/abs/2507.04059 · HTML: https://mlsanity.com/paper/2507.04059/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 68 references that are in the map.
- First posted on arXiv 5 Jul 2025.

## Builds on (most cited first, 30 of 53)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Adversarial Training for Free!](https://mlsanity.com/paper/1904.12843/) (2019)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [When Vision Transformers Outperform ResNets without Pre-training or Strong Data Augmentations](https://mlsanity.com/paper/2106.01548/) (2021)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [R-Drop: Regularized Dropout for Neural Networks](https://mlsanity.com/paper/2106.14448/) (2021)
- [Spectral Norm Regularization for Improving the Generalizability of Deep Learning](https://mlsanity.com/paper/1705.10941/) (2017)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [Mixed-Privacy Forgetting in Deep Networks](https://mlsanity.com/paper/2012.13431/) (2020)
- [Towards Understanding Sharpness-Aware Minimization](https://mlsanity.com/paper/2206.06232/) (2022)
- [Explaining Black Box Predictions and Unveiling Data Artifacts through Influence Functions](https://mlsanity.com/paper/2005.06676/) (2020)
- [Generalized Federated Learning via Sharpness Aware Minimization](https://mlsanity.com/paper/2206.02618/) (2022)
- [Efficient Sharpness-aware Minimization for Improved Training of Neural Networks](https://mlsanity.com/paper/2110.03141/) (2021)
- [Towards Efficient and Scalable Sharpness-Aware Minimization](https://mlsanity.com/paper/2203.02714/) (2022)

## Built on by (most cited first, 2 of 2)

- [In-Run Data Shapley for Adam Optimizer](https://mlsanity.com/paper/2602.00329/) (2026)
- [CoLA: A Choice Leakage Attack Framework to Expose Privacy Risks in Subset Training](https://mlsanity.com/paper/2604.12342/) (2026)

## Abstract (arXiv)

Sharpness-aware Minimization (SAM) improves generalization in large-scale model training by linking loss landscape geometry to generalization. However, challenges such as mislabeled noisy data and privacy concerns have emerged as significant issues. Data attribution, which identifies the contributions of specific training samples, offers a promising solution. However, directly rendering existing data influence evaluation tools such as influence functions (IF) to SAM will be inapplicable or inaccurate as SAM utilizes an inner loop to find model perturbations that maximize loss, which the outer loop then minimizes, resulting in a doubled computational structure. Additionally, this bilevel structure complicates the modeling of data influence on the parameters. In this paper, based on the IF, we develop two innovative data valuation methods for SAM, each offering unique benefits in different scenarios: the Hessian-based IF and the Gradient Trajectory-based IF. The first one provides a comprehensive estimation of data influence using a closed-form measure that relies only on the trained model weights. In contrast, the other IF for SAM utilizes gradient trajectory information during training for more accurate and efficient data assessment. Extensive experiments demonstrate their effectiveness in data evaluation and parameter tuning, with applications in identifying mislabeled data, model editing, and enhancing interpretability.