# SAM-on-the-Curve: Sharpness-Aware Mode Connectivity for Robust Weight-Space Interpolation

arXiv: https://arxiv.org/abs/2609.17748 · HTML: https://mlsanity.com/paper/2609.17748/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 25 references that are in the map.
- First posted on arXiv 15 Sep 2026.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [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)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [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)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2110.06296/) (2021)
- [Surrogate Gap Minimization Improves Sharpness-Aware Training](https://mlsanity.com/paper/2203.08065/) (2022)
- [Torchattacks: A PyTorch Repository for Adversarial Attacks](https://mlsanity.com/paper/2010.01950/) (2020)
- [Exploring Nonlinear Pathway in Parameter Space for Machine Unlearning](https://mlsanity.com/paper/2505.10859/) (2025)
- [MoCo-EA: Exploiting Adversarial Mode Connectivity for Efficient Evolutionary Attacks](https://mlsanity.com/paper/2605.18919/) (2026)

## Abstract (arXiv)

Deep neural networks that are independently trained to similar performance can be connected by low-loss parametric curves in weight space, a phenomenon known as Mode Connectivity (MC). This geometric property underpins practical techniques such as weight averaging, model ensembling, and model merging. We argue that low-loss connectivity is an incomplete geometric criterion: it controls loss only along a one-dimensional trajectory while leaving the surrounding weight-space neighborhood unconstrained, so the optimized curve may traverse sharp ridges that become fragile under distribution shift. We therefore reformulate mode connectivity as a neighborhood-robust path optimization problem, seeking a curve whose entire local neighborhood maintains low loss. We propose Sharp Mode Connectivity (SMC), which applies a first-order sharpness-aware approximation to the resulting minimax functional, enforcing flatness along the entire curve rather than only on it. We derive a practical optimization algorithm for connectivity paths under this sharpness-aware objective. Under severe blur corruptions from CIFAR-10-C, SMC achieves up to 6.09% absolute accuracy improvement over standard MC. Remarkably, SMC produces negative loss barriers, meaning that models obtained at interior points of the optimized path can outperform the average endpoint loss. These results, validated across ResNet-18, VGG16-BN, and ViT-Tiny on CIFAR-10 and ImageNet-100, establish path-wise flatness as a practical principle for robust weight-space interpolation.