# Sharpness-Aware Teleportation on Riemannian Manifolds

arXiv: https://arxiv.org/abs/2309.17215 · HTML: https://mlsanity.com/paper/2309.17215/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 52 references that are in the map.
- First posted on arXiv 29 Sep 2023.

## Builds on (most cited first, 30 of 31)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [NTU RGB+D: A Large Scale Dataset for 3D Human Activity Analysis](https://mlsanity.com/paper/1604.02808/) (2016)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [When Vision Transformers Outperform ResNets without Pre-training or Strong Data Augmentations](https://mlsanity.com/paper/2106.01548/) (2021)
- [First-Person Hand Action Benchmark with RGB-D Videos and 3D Hand Pose Annotations](https://mlsanity.com/paper/1704.02463/) (2017)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [Surrogate Gap Minimization Improves Sharpness-Aware Training](https://mlsanity.com/paper/2203.08065/) (2022)
- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [The Break-Even Point on Optimization Trajectories of Deep Neural Networks](https://mlsanity.com/paper/2002.09572/) (2020)
- [Generalized Federated Learning via Sharpness Aware Minimization](https://mlsanity.com/paper/2206.02618/) (2022)
- [Towards Efficient and Scalable Sharpness-Aware Minimization](https://mlsanity.com/paper/2203.02714/) (2022)
- [Orthogonal Convolutional Neural Networks](https://mlsanity.com/paper/1911.12207/) (2019)
- [Sharpness-Aware Minimization Improves Language Model Generalization](https://mlsanity.com/paper/2110.08529/) (2021)
- [Sharpness-Aware Training for Free](https://mlsanity.com/paper/2205.14083/) (2022)
- [When Do Flat Minima Optimizers Work?](https://mlsanity.com/paper/2202.00661/) (2022)
- [Global rates of convergence for nonconvex optimization on manifolds](https://mlsanity.com/paper/1605.08101/) (2016)
- [All You Need is Beyond a Good Init: Exploring Better Solution for Training Extremely Deep Convolutional Neural Networks with Orthonormality and Modulation](https://mlsanity.com/paper/1703.01827/) (2017)
- [Sharp-MAML: Sharpness-Aware Model-Agnostic Meta Learning](https://mlsanity.com/paper/2206.03996/) (2022)
- [Orthogonal Over-Parameterized Training](https://mlsanity.com/paper/2004.04690/) (2020)
- [SAM as an Optimal Relaxation of Bayes](https://mlsanity.com/paper/2210.01620/) (2022)
- [Computationally Tractable Riemannian Manifolds for Graph Embeddings](https://mlsanity.com/paper/2002.08665/) (2020)
- [Improving Convergence and Generalization Using Parameter Symmetries](https://mlsanity.com/paper/2305.13404/) (2023)
- [Flat Seeking Bayesian Neural Networks](https://mlsanity.com/paper/2302.02713/) (2023)

## Abstract (arXiv)

Recent studies highlight the effectiveness of flat minima in enhancing generalization, with sharpness-aware minimization (SAM) achieving state-of-the-art performance. Additionally, insights into the intrinsic geometry of the loss landscape have shown promise for improving model generalization. Building on these advancements, we introduce a novel sharpness-aware, geometry-aware teleportation mechanism to further enhance robustness and generalization. The core innovation of our approach is to decompose each iteration into a teleportation step within a local orbit and a sharpness-aware step that transitions between different orbits, leveraging the Riemannian quotient manifold. Our approach is grounded in a theoretical framework that analyzes the generalization gap between population loss and worst-case empirical loss within the context of Riemannian manifolds. To demonstrate the effectiveness of our method, we evaluate and compare our algorithm on diverse vision benchmarks with various datasets and Riemannian manifolds.