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stat.ML updates on arXiv.org

Adaptive multi-fidelity optimization with fast learning rates Enhancing AI and Dynamical Subseasonal Forecasts with Probabilistic Bias Correction Sample Complexity Bounds for Stochastic Shortest Path with a Generative Model The Harder Path: Last Iterate Convergence for Uncoupled Learning in Zero-Sum Games with Bandit Feedback Stylistic-STORM (ST-STORM) : Perceiving the Semantic Nature of Appearance Collective Kernel EFT for Pre-activation ResNets PRIM-cipal components analysis One-Shot Generative Flows: Existence and Obstructions Structural interpretability in SVMs with truncated orthogonal polynomial kernels Amortized Optimal Transport from Sliced Potentials MinShap: A Modified Shapley Value Approach for Feature Selection Unsupervised feature selection using Bayesian Tucker decomposition Multi-User mmWave Beam and Rate Adaptation via Combinatorial Satisficing Bandits Best of both worlds: Stochastic & adversarial best-arm identification Scalable Model-Based Clustering with Sequential Monte Carlo Expert-Guided Class-Conditional Goodness-of-Fit Scores for Interpretable Classification with Informative Missingness: An Application to Seismic Monitoring Lightweight Geometric Adaptation for Training Physics-Informed Neural Networks Gating Enables Curvature: A Geometric Expressivity Gap in Attention Zeroth-Order Optimization at the Edge of Stability Differentially Private Conformal Prediction CLion: Efficient Cautious Lion Optimizer with Enhanced Generalization Generative Augmented Inference Improving Machine Learning Performance with Synthetic Augmentation PAC-MCTS: Bias-Aware Pruning for Robust LLM-Guided Search and Planning Path-Sampled Integrated Gradients Heat and Matérn Kernels on Matchings Doubly Outlier-Robust Online Infinite Hidden Markov Model Momentum Further Constrains Sharpness at the Edge of Stochastic Stability Multistage Conditional Compositional Optimization BOAT: Navigating the Sea of In Silico Predictors for Antibody Design via Multi-Objective Bayesian Optimization
Tight Generalization Error Bounds for Stochastic Gradient...
Wenjun Xiong, Juan Ding, Xinlei Zuo, Qizhai Li · 2025-06-23 · via stat.ML updates on arXiv.org

Stochastic Gradient Descent (SGD) is fundamental for training deep neural networks, especially in non-convex settings. Understanding SGD's generalization properties is crucial for ensuring robust model performance on unseen data. In this paper, we analyze the generalization error bounds of SGD for non-convex learning by introducing the Type II perturbed SGD (T2pm-SGD), which accommodates both sub-Gaussian and bounded loss functions. The generalization error bound is decomposed into two components: the trajectory term and the flatness term. Our analysis improves the trajectory term to $O(n^{-1})$, significantly enhancing the previous $O((nb)^{-1/2})$ bound for bounded losses, where n is the number of training samples and b is the batch size. By selecting an optimal variance for the perturbation noise, the overall bound is further refined to $O(n^{-2/3})$. For sub-Gaussian loss functions, a tighter trajectory term is also achieved. In both cases, the flatness term remains stable across iterations and is smaller than those reported in previous literature, which increase with iterations. This stability, ensured by T2pm-SGD, leads to tighter generalization error bounds for both loss function types. Our theoretical results are validated through extensive experiments on benchmark datasets, including MNIST and CIFAR-10, demonstrating the effectiveness of T2pm-SGD in establishing tighter generalization bounds.