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Related papers: Sharper Generalization Bounds for Transformer

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Can transformers generalize efficiently on problems that require dealing with examples with different levels of difficulty? We introduce a new task tailored to assess generalization over different complexities and present results that…

We address two fundamental questions about graph neural networks (GNNs). First, we prove that several important graph properties cannot be computed by GNNs that rely entirely on local information. Such GNNs include the standard message…

Machine Learning · Computer Science 2020-02-17 Vikas K. Garg , Stefanie Jegelka , Tommi Jaakkola

We present a general approach to deriving bounds on the generalization error of randomized learning algorithms. Our approach can be used to obtain bounds on the average generalization error as well as bounds on its tail probabilities, both…

Information Theory · Computer Science 2020-09-10 Fredrik Hellström , Giuseppe Durisi

The scaling behavior, in which test performance often improves as model size and data increase, is a central empirical phenomenon in modern deep learning, yet its theoretical basis remains incomplete. In this paper, we study depth expansion…

Machine Learning · Computer Science 2026-05-12 Daning Cheng , Zeyu Liu , Jun Sun , Fen Xia , Boyang Zhang , Dongping Liu , Yunquan Zhang

We derive generalization error bounds for stationary univariate autoregressive (AR) models. We show that imposing stationarity is enough to control the Gaussian complexity without further regularization. This lets us use structural risk…

Machine Learning · Statistics 2011-06-06 Daniel J. McDonald , Cosma Rohilla Shalizi , Mark Schervish

As state-of-the-art neural networks are deployed on reasoning and algorithmic tasks, exactness guarantees become increasingly important. However, high average-case accuracy can still mask inconsistent behaviors. This motivates exact…

Machine Learning · Computer Science 2026-05-25 Artur Back de Luca , Kimon Fountoulakis

We propose a new bound for generalization of neural networks using Koopman operators. Whereas most of existing works focus on low-rank weight matrices, we focus on full-rank weight matrices. Our bound is tighter than existing norm-based…

Machine Learning · Computer Science 2024-03-19 Yuka Hashimoto , Sho Sonoda , Isao Ishikawa , Atsushi Nitanda , Taiji Suzuki

Similarity learning has received a large amount of interest and is an important tool for many scientific and industrial applications. In this framework, we wish to infer the distance (similarity) between points with respect to an arbitrary…

Machine Learning · Statistics 2016-11-30 Michael Rabadi

We analyze the sample complexity of full-batch Gradient Descent (GD) in the setup of non-smooth Stochastic Convex Optimization. We show that the generalization error of GD, with common choice of hyper-parameters, can be $\tilde \Theta(d/m +…

Machine Learning · Computer Science 2024-04-12 Roi Livni

Deep nets generalize well despite having more parameters than the number of training samples. Recent works try to give an explanation using PAC-Bayes and Margin-based analyses, but do not as yet result in sample complexity bounds better…

Machine Learning · Computer Science 2018-11-28 Sanjeev Arora , Rong Ge , Behnam Neyshabur , Yi Zhang

In this paper, we use tools from rate-distortion theory to establish new upper bounds on the generalization error of statistical distributed learning algorithms. Specifically, there are $K$ clients whose individually chosen models are…

Machine Learning · Statistics 2022-11-23 Milad Sefidgaran , Romain Chor , Abdellatif Zaidi

Transformers have been recently adapted for large scale image classification, achieving high scores shaking up the long supremacy of convolutional neural networks. However the optimization of image transformers has been little studied so…

Computer Vision and Pattern Recognition · Computer Science 2021-04-08 Hugo Touvron , Matthieu Cord , Alexandre Sablayrolles , Gabriel Synnaeve , Hervé Jégou

Existing generalization bounds fail to explain crucial factors that drive the generalization of modern neural networks. Since such bounds often hold uniformly over all parameters, they suffer from over-parametrization and fail to account…

Machine Learning · Statistics 2023-11-14 Songyan Hou , Parnian Kassraie , Anastasis Kratsios , Andreas Krause , Jonas Rothfuss

Transformer networks have achieved remarkable empirical success across a wide range of applications, yet their theoretical expressive power remains insufficiently understood. In this paper, we study the expressive capabilities of…

Machine Learning · Computer Science 2026-03-04 Linyan Gu , Lihua Yang , Feng Zhou

This note examines the behavior of generalization capabilities - as defined by out-of-sample mean squared error (MSE) - of Linear Gaussian (with a fixed design matrix) and Linear Least Squares regression. Particularly, we consider a…

Statistics Theory · Mathematics 2021-09-21 Karthik Duraisamy

Learning representations on large graphs is a long-standing challenge due to the inter-dependence nature. Transformers recently have shown promising performance on small graphs thanks to its global attention for capturing all-pair…

Machine Learning · Computer Science 2024-09-16 Qitian Wu , Kai Yang , Hengrui Zhang , David Wipf , Junchi Yan

Recent studies demonstrated that the adversarially robust learning under $\ell_\infty$ attack is harder to generalize to different domains than standard domain adaptation. How to transfer robustness across different domains has been a key…

Machine Learning · Computer Science 2023-02-27 Yuyang Deng , Nidham Gazagnadou , Junyuan Hong , Mehrdad Mahdavi , Lingjuan Lyu

Transformers serve as the foundational architecture for large language and video generation models, such as GPT, BERT, SORA and their successors. Empirical studies have demonstrated that real-world data and learning tasks exhibit…

Machine Learning · Computer Science 2026-05-19 Zhaiming Shen , Alex Havrilla , Rongjie Lai , Alexander Cloninger , Wenjing Liao

We study inductive bias in Transformers in the infinitely over-parameterized Gaussian process limit and argue transformers tend to be biased towards more permutation symmetric functions in sequence space. We show that the representation…

Machine Learning · Computer Science 2024-05-29 Itay Lavie , Guy Gur-Ari , Zohar Ringel

Large-scale transformers achieve impressive results on program synthesis benchmarks, yet their true generalization capabilities remain obscured by data contamination and opaque training corpora. To rigorously assess whether models are truly…

Machine Learning · Computer Science 2026-05-01 Henrik Voigt , Michael Habeck , Joachim Giesen