Generalization Bound of Gradient Flow through Training Trajectory and Data-dependent Kernel

• URL: http://arxiv.org/abs/2506.11357v1
• Date: Thu, 12 Jun 2025 23:17:09 GMT
• Title: Generalization Bound of Gradient Flow through Training Trajectory and Data-dependent Kernel
• Authors: Yilan Chen, Zhichao Wang, Wei Huang, Andi Han, Taiji Suzuki, Arya Mazumdar,
• Abstract summary: We establish a generalization bound for gradient flow that aligns with the classical Rademacher complexity for kernel methods.<n>Unlike static kernels such as NTK, the LPK captures the entire training trajectory, adapting to both data and optimization dynamics.
• Score: 55.82768375605861
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Gradient-based optimization methods have shown remarkable empirical success, yet their theoretical generalization properties remain only partially understood. In this paper, we establish a generalization bound for gradient flow that aligns with the classical Rademacher complexity bounds for kernel methods-specifically those based on the RKHS norm and kernel trace-through a data-dependent kernel called the loss path kernel (LPK). Unlike static kernels such as NTK, the LPK captures the entire training trajectory, adapting to both data and optimization dynamics, leading to tighter and more informative generalization guarantees. Moreover, the bound highlights how the norm of the training loss gradients along the optimization trajectory influences the final generalization performance. The key technical ingredients in our proof combine stability analysis of gradient flow with uniform convergence via Rademacher complexity. Our bound recovers existing kernel regression bounds for overparameterized neural networks and shows the feature learning capability of neural networks compared to kernel methods. Numerical experiments on real-world datasets validate that our bounds correlate well with the true generalization gap.

Related papers

• Kernel Sum of Squares for Data Adapted Kernel Learning of Dynamical Systems from Data: A global optimization approach [0.19999259391104385]
  This paper examines the application of the Kernel Sum of Squares (KSOS) method for enhancing kernel learning from data. Traditional kernel-based methods frequently struggle with selecting optimal base kernels and parameter tuning. KSOS mitigates these issues by leveraging a global optimization framework with kernel-based surrogate functions.
  arXiv  Detail & Related papers  (2024-08-12T19:32:28Z)
• Learning Analysis of Kernel Ridgeless Regression with Asymmetric Kernel Learning [33.34053480377887]
  This paper enhances kernel ridgeless regression with Locally-Adaptive-Bandwidths (LAB) RBF kernels. For the first time, we demonstrate that functions learned from LAB RBF kernels belong to an integral space of Reproducible Kernel Hilbert Spaces (RKHSs)
  arXiv  Detail & Related papers  (2024-06-03T15:28:12Z)
• Generalization Error Curves for Analytic Spectral Algorithms under Power-law Decay [13.803850290216257]
  We rigorously provide a full characterization of the generalization error curves of the kernel gradient descent method. Thanks to the neural tangent kernel theory, these results greatly improve our understanding of the generalization behavior of training the wide neural networks.
  arXiv  Detail & Related papers  (2024-01-03T08:00:50Z)
• Stable Nonconvex-Nonconcave Training via Linear Interpolation [51.668052890249726]
  This paper presents a theoretical analysis of linearahead as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss landscape and show how linear can help by leveraging the theory of nonexpansive operators.
  arXiv  Detail & Related papers  (2023-10-20T12:45:12Z)
• Benign Overfitting in Deep Neural Networks under Lazy Training [72.28294823115502]
  We show that when the data distribution is well-separated, DNNs can achieve Bayes-optimal test error for classification. Our results indicate that interpolating with smoother functions leads to better generalization.
  arXiv  Detail & Related papers  (2023-05-30T19:37:44Z)
• Generalization Properties of Stochastic Optimizers via Trajectory Analysis [48.38493838310503]
  We show that both the Fernique-Talagrand functional and the local powerlaw are predictive of generalization performance. We show that both our Fernique-Talagrand functional and the local powerlaw are predictive of generalization performance.
  arXiv  Detail & Related papers  (2021-08-02T10:58:32Z)
• Optimal Rates for Averaged Stochastic Gradient Descent under Neural Tangent Kernel Regime [50.510421854168065]
  We show that the averaged gradient descent can achieve the minimax optimal convergence rate. We show that the target function specified by the NTK of a ReLU network can be learned at the optimal convergence rate.
  arXiv  Detail & Related papers  (2020-06-22T14:31:37Z)
• On Learning Rates and Schr\"odinger Operators [105.32118775014015]
  We present a general theoretical analysis of the effect of the learning rate. We find that the learning rate tends to zero for a broad non- neural class functions.
  arXiv  Detail & Related papers  (2020-04-15T09:52:37Z)
• Spectrum Dependent Learning Curves in Kernel Regression and Wide Neural Networks [17.188280334580195]
  We derive analytical expressions for the generalization performance of kernel regression as a function of the number of training samples. Our expressions apply to wide neural networks due to an equivalence between training them and kernel regression with the Neural Kernel Tangent (NTK) We verify our theory with simulations on synthetic data and MNIST dataset.
  arXiv  Detail & Related papers  (2020-02-07T00:03:40Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.