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How Edge of Stability Hinders SCAFFOLD in Federated Optimization
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arXiv Machine Learning
Aug 27
How Edge of Stability Hinders SCAFFOLD in Federated Optimization
The paper investigates why the SCAFFOLD algorithm, designed to be robust to data heterogeneity in federated learning, often underperforms compared to the simpler FedAvg. It identifies the presence of Edge of Stability (EoS) dynamics and progressive sharpening as key factors, showing that both algorithms exhibit EoS behavior across various architectures and hyperparameters. Crucially, the study finds that at the EoS, SCAFFOLD’s ability to estimate the global gradient deteriorates, as indicated by a weakened correlation between sharpness and gradient estimation error, explaining its limited practical advantage.
arXiv AI
Jun 2
Stability Analysis of Sharpness-Aware Minimization
arXiv:2301. 06308v2 Announce Type: replace-cross Abstract: Sharpness-aware minimization (SAM) is a training method that seeks to find flat minima in deep learning, resulting in state-of-the-art performance across various domains.
arXiv Machine Learning
Jun 4
Edge of Stability Selectively Shapes Learning Across the Data Distribution
arXiv:2606. 04212v1 Announce Type: new Abstract: Existing analyses of the edge of stability (EoS) treat it as a global property of optimization.
arXiv AI
Jul 21
Singularity-aware Optimization via Randomized Geometric Probing: Towards Stable Non-smooth Optimization
arXiv:2605. 29547v2 Announce Type: replace-cross Abstract: Deep learning optimization relies heavily on the assumption of smooth loss landscapes, a condition systematically violated by modern architectures due to non-smooth components such as ReLU activations and quantization operators.
arXiv Machine Learning
Jun 17
Edge Flow: A Tractable and Predictive Continuous-Time Model for Gradient Descent at the Edge of Stability
arXiv:2606. 18080v1 Announce Type: new Abstract: Gradient descent in deep learning may operate at the edge of stability (EoS), a regime in which the largest eigenvalue of the loss Hessian hovers near the stability threshold $2/\eta$, where $\eta$ is the learning rate.
arXiv Machine Learning
Jul 8
Leveraging Extragradient for Effective Sharpness-Aware Minimization in Deep Learning
arXiv:2607. 06151v1 Announce Type: new Abstract: Generalization remains a pivotal challenge in deep learning, where traditional optimizers like Stochastic Gradient Descent (SGD) often converge to sharp minima, leading to overfitting and reduced performance on unseen data.