Sharpness-Aware Teleportation on Riemannian Manifolds

Fuente: arXiv
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Main Authors: Truong, Tuan, Nguyen, Hoang-Phi, Luo, Haocheng, Pham, Tung, Harandi, Mehrtash, Phung, Dinh, Le, Trung
Format: Preprint
Published: 2023
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author Truong, Tuan
Nguyen, Hoang-Phi
Luo, Haocheng
Pham, Tung
Harandi, Mehrtash
Phung, Dinh
Le, Trung
author_facet Truong, Tuan
Nguyen, Hoang-Phi
Luo, Haocheng
Pham, Tung
Harandi, Mehrtash
Phung, Dinh
Le, Trung
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2309_17215
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Sharpness-Aware Teleportation on Riemannian Manifolds
Truong, Tuan
Nguyen, Hoang-Phi
Luo, Haocheng
Pham, Tung
Harandi, Mehrtash
Phung, Dinh
Le, Trung
Machine Learning
Artificial Intelligence
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.
title Sharpness-Aware Teleportation on Riemannian Manifolds
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2309.17215