# FAM: Relative Flatness Aware Minimization

arXiv: https://arxiv.org/abs/2307.02337 · HTML: https://mlsanity.com/paper/2307.02337/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 53 references that are in the map.
- First posted on arXiv 5 Jul 2023.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (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)
- [AutoAugment: Learning Augmentation Policies from Data](https://mlsanity.com/paper/1805.09501/) (2018)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [PyHessian: Neural Networks Through the Lens of the Hessian](https://mlsanity.com/paper/1912.07145/) (2019)
- [On the Stability of Fine-tuning BERT: Misconceptions, Explanations, and Strong Baselines](https://mlsanity.com/paper/2006.04884/) (2020)
- [Sentence Encoders on STILTs: Supplementary Training on Intermediate Labeled-data Tasks](https://mlsanity.com/paper/1811.01088/) (2018)
- [Surrogate Gap Minimization Improves Sharpness-Aware Training](https://mlsanity.com/paper/2203.08065/) (2022)
- [Towards Understanding Sharpness-Aware Minimization](https://mlsanity.com/paper/2206.06232/) (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)
- [Fisher-Rao Metric, Geometry, and Complexity of Neural Networks](https://mlsanity.com/paper/1711.01530/) (2017)
- [Relative Flatness and Generalization](https://mlsanity.com/paper/2001.00939/) (2020)
- [Shake-Shake regularization](https://mlsanity.com/paper/1705.07485/) (2017)
- [Hessian-based Analysis of Large Batch Training and Robustness to Adversaries](https://mlsanity.com/paper/1802.08241/) (2018)

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

- [Flatness is Necessary, Neural Collapse is Not: Rethinking Generalization via Grokking](https://mlsanity.com/paper/2509.17738/) (2025)
- [An accurate flatness measure to estimate the generalization performance of CNN models](https://mlsanity.com/paper/2603.09016/) (2026)

## Abstract (arXiv)

Flatness of the loss curve around a model at hand has been shown to empirically correlate with its generalization ability. Optimizing for flatness has been proposed as early as 1994 by Hochreiter and Schmidthuber, and was followed by more recent successful sharpness-aware optimization techniques. Their widespread adoption in practice, though, is dubious because of the lack of theoretically grounded connection between flatness and generalization, in particular in light of the reparameterization curse - certain reparameterizations of a neural network change most flatness measures but do not change generalization. Recent theoretical work suggests that a particular relative flatness measure can be connected to generalization and solves the reparameterization curse. In this paper, we derive a regularizer based on this relative flatness that is easy to compute, fast, efficient, and works with arbitrary loss functions. It requires computing the Hessian only of a single layer of the network, which makes it applicable to large neural networks, and with it avoids an expensive mapping of the loss surface in the vicinity of the model. In an extensive empirical evaluation we show that this relative flatness aware minimization (FAM) improves generalization in a multitude of applications and models, both in finetuning and standard training. We make the code available at github.