Generalization Bounds of Stochastic Gradient Descent in Homogeneous Neural Networks

• URL: http://arxiv.org/abs/2602.22936v1
• Date: Thu, 26 Feb 2026 12:26:32 GMT
• Title: Generalization Bounds of Stochastic Gradient Descent in Homogeneous Neural Networks
• Authors: Wenquan Ma, Yang Sui, Jiaye Teng, Bohan Wang, Jing Xu, Jingqin Yang,
• Abstract summary: We show that homogeneous networks encompass fully-connected and neural convolutional neural networks with ReReRe activations.<n>This finding is broadly applicable, as homogeneous networks encompass fully-connected and neural networks with ReReRe activations.
• Score: 29.858071115963472
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Algorithmic stability is among the most potent techniques in generalization analysis. However, its derivation usually requires a stepsize $η_t = \mathcal{O}(1/t)$ under non-convex training regimes, where $t$ denotes iterations. This rigid decay of the stepsize potentially impedes optimization and may not align with practical scenarios. In this paper, we derive the generalization bounds under the homogeneous neural network regimes, proving that this regime enables slower stepsize decay of order $Ω(1/\sqrt{t})$ under mild assumptions. We further extend the theoretical results from several aspects, e.g., non-Lipschitz regimes. This finding is broadly applicable, as homogeneous neural networks encompass fully-connected and convolutional neural networks with ReLU and LeakyReLU activations.

Related papers

• Gradient Descent as a Perceptron Algorithm: Understanding Dynamics and Implicit Acceleration [67.12978375116599]
  We show that the steps of gradient descent (GD) reduce to those of generalized perceptron algorithms.<n>This helps explain the optimization dynamics and the implicit acceleration phenomenon observed in neural networks.
  arXiv  Detail & Related papers  (2025-12-12T14:16:35Z)
• Generalization of Scaled Deep ResNets in the Mean-Field Regime [55.77054255101667]
  We investigate emphscaled ResNet in the limit of infinitely deep and wide neural networks. Our results offer new insights into the generalization ability of deep ResNet beyond the lazy training regime.
  arXiv  Detail & Related papers  (2024-03-14T21:48:00Z)
• Convergence of Gradient Descent for Recurrent Neural Networks: A Nonasymptotic Analysis [16.893624100273108]
  We analyze recurrent neural networks with diagonal hidden-to-hidden weight matrices trained with gradient descent in the supervised learning setting. We prove that gradient descent can achieve optimality emphwithout massive over parameterization. Our results are based on an explicit characterization of the class of dynamical systems that can be approximated and learned by recurrent neural networks.
  arXiv  Detail & Related papers  (2024-02-19T15:56:43Z)
• Neural Networks with Sparse Activation Induced by Large Bias: Tighter Analysis with Bias-Generalized NTK [86.45209429863858]
  We study training one-hidden-layer ReLU networks in the neural tangent kernel (NTK) regime. We show that the neural networks possess a different limiting kernel which we call textitbias-generalized NTK We also study various properties of the neural networks with this new kernel.
  arXiv  Detail & Related papers  (2023-01-01T02:11:39Z)
• The Asymmetric Maximum Margin Bias of Quasi-Homogeneous Neural Networks [26.58848653965855]
  We introduce the class of quasi-homogeneous models, which is expressive enough to describe nearly all neural networks with homogeneous activations. We find that gradient flow implicitly favors a subset of the parameters, unlike in the case of a homogeneous model where all parameters are treated equally.
  arXiv  Detail & Related papers  (2022-10-07T21:14:09Z)
• Stability and Generalization Analysis of Gradient Methods for Shallow Neural Networks [59.142826407441106]
  We study the generalization behavior of shallow neural networks (SNNs) by leveraging the concept of algorithmic stability. We consider gradient descent (GD) and gradient descent (SGD) to train SNNs, for both of which we develop consistent excess bounds.
  arXiv  Detail & Related papers  (2022-09-19T18:48:00Z)
• Critical Initialization of Wide and Deep Neural Networks through Partial Jacobians: General Theory and Applications [6.579523168465526]
  We introduce emphpartial Jacobians of a network, defined as derivatives of preactivations in layer $l$ with respect to preactivations in layer $l_0leq l$. We derive recurrence relations for the norms of partial Jacobians and utilize these relations to analyze criticality of deep fully connected neural networks with LayerNorm and/or residual connections.
  arXiv  Detail & Related papers  (2021-11-23T20:31:42Z)
• Path Regularization: A Convexity and Sparsity Inducing Regularization for Parallel ReLU Networks [75.33431791218302]
  We study the training problem of deep neural networks and introduce an analytic approach to unveil hidden convexity in the optimization landscape. We consider a deep parallel ReLU network architecture, which also includes standard deep networks and ResNets as its special cases.
  arXiv  Detail & Related papers  (2021-10-18T18:00:36Z)
• A global convergence theory for deep ReLU implicit networks via over-parameterization [26.19122384935622]
  Implicit deep learning has received increasing attention recently. This paper analyzes the gradient flow of Rectified Linear Unit (ReLU) activated implicit neural networks.
  arXiv  Detail & Related papers  (2021-10-11T23:22:50Z)
• An efficient projection neural network for $\ell_1$-regularized logistic regression [10.517079029721257]
  This paper presents a simple projection neural network for $ell_$-regularized logistics regression. The proposed neural network does not require any extra auxiliary variable nor any smooth approximation. We also investigate the convergence of the proposed neural network by using the Lyapunov theory and show that it converges to a solution of the problem with any arbitrary initial value.
  arXiv  Detail & Related papers  (2021-05-12T06:13:44Z)
• Generalization bound of globally optimal non-convex neural network training: Transportation map estimation by infinite dimensional Langevin dynamics [50.83356836818667]
  We introduce a new theoretical framework to analyze deep learning optimization with connection to its generalization error. Existing frameworks such as mean field theory and neural tangent kernel theory for neural network optimization analysis typically require taking limit of infinite width of the network to show its global convergence.
  arXiv  Detail & Related papers  (2020-07-11T18:19:50Z)

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.