Sharpness-Aware Minimization with Z-Score Gradient Filtering

Deep neural networks achieve high performance across many domains but can still face challenges in generalization when optimization is influenced by small or noisy gradient components. Sharpness-Aware Minimization improves generalization by perturbing parameters toward directions of high curvature, but it uses the entire gradient vector, which means that small or noisy components may affect the ascent step and cause the optimizer to miss optimal solutions. We propose Z-Score Filtered Sharpness-Aware Minimization, which applies Z-score based filtering to gradients in each layer. Instead of using all gradient components, a mask is constructed to retain only the top percentile with the largest absolute Z-scores. The percentile threshold Q<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> determines how many components are kept, so that the ascent step focuses on directions that stand out most compared to the average of the layer. This selective perturbation refines the search toward flatter minima while reducing the influence of less significant gradients.