English
Related papers

Related papers: Fractal Structure and Generalization Properties of…

200 papers

The classical statistical learning theory implies that fitting too many parameters leads to overfitting and poor performance. That modern deep neural networks generalize well despite a large number of parameters contradicts this finding and…

Machine Learning · Statistics 2022-10-18 Masaaki Imaizumi , Johannes Schmidt-Hieber

Generalization analyses of deep learning typically assume that the training converges to a fixed point. But, recent results indicate that in practice, the weights of deep neural networks optimized with stochastic gradient descent often…

Machine Learning · Computer Science 2022-08-22 Nisha Chandramoorthy , Andreas Loukas , Khashayar Gatmiry , Stefanie Jegelka

Fine-grained domain generalization (FGDG) is a more challenging task than traditional DG tasks due to its small inter-class variations and relatively large intra-class disparities. When domain distribution changes, the vulnerability of…

Computer Vision and Pattern Recognition · Computer Science 2025-03-27 Wenlong Yu , Dongyue Chen , Qilong Wang , Qinghua Hu

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

Machine Learning · Computer Science 2019-05-10 Baojian Zhou , Feng Chen , Yiming Ying

Neural networks typically generalize well when fitting the data perfectly, even though they are heavily overparameterized. Many factors have been pointed out as the reason for this phenomenon, including an implicit bias of stochastic…

Machine Learning · Computer Science 2025-02-04 Amit Peleg , Matthias Hein

Deep Neural Networks (DNNs) excel at many tasks, often rivaling or surpassing human performance. Yet their internal processes remain elusive, frequently described as "black boxes." While performance can be refined experimentally, achieving…

Disordered Systems and Neural Networks · Physics 2025-02-03 Sebastiano Ariosto

The notion of implicit bias, or implicit regularization, has been suggested as a means to explain the surprising generalization ability of modern-days overparameterized learning algorithms. This notion refers to the tendency of the…

Machine Learning · Computer Science 2020-12-23 Assaf Dauber , Meir Feder , Tomer Koren , Roi Livni

We describe new families of random fractals, referred to as "V-variable", which are intermediate between the notions of deterministic and of standard random fractals. The parameter V describes the degree of "variability" : at each…

Probability · Mathematics 2007-05-23 Michael Barnsley , John E. Hutchinson , Örjan Stenflo

We study the generalization error of stochastic learning algorithms from an information-theoretic perspective, with a particular emphasis on deriving sharper bounds for differentially private algorithms. It is well known that the…

Information Theory · Computer Science 2026-04-20 Yanxiao Liu , Chun Hei Michael Shiu , Lele Wang , Deniz Gündüz

We establish a data-dependent notion of algorithmic stability for Stochastic Gradient Descent (SGD), and employ it to develop novel generalization bounds. This is in contrast to previous distribution-free algorithmic stability results for…

Machine Learning · Computer Science 2018-02-19 Ilja Kuzborskij , Christoph H. Lampert

Generalization error bounds for deep neural networks trained by stochastic gradient descent (SGD) are derived by combining a dynamical control of an appropriate parameter norm and the Rademacher complexity estimate based on parameter norms.…

Machine Learning · Computer Science 2023-05-30 Mingze Wang , Chao Ma

Evolutionary Algorithms are naturally inspired approximation optimisation algorithms that usually interfere with science problems when common mathematical methods are unable to provide a good solution or finding the exact solution requires…

Artificial Intelligence · Computer Science 2021-02-03 Mohammed ElKomy

Developing a robust generalization measure for the performance of machine learning models is an important and challenging task. A lot of recent research in the area focuses on the model decision boundary when predicting generalization. In…

Machine Learning · Computer Science 2020-12-24 Valeri Alexiev

Machine learning models trained by different optimization algorithms under different data distributions can exhibit distinct generalization behaviors. In this paper, we analyze the generalization of models trained by noisy iterative…

Machine Learning · Statistics 2022-12-29 Hao Wang , Rui Gao , Flavio P. Calmon

Recent studies have shown that heavy tails can emerge in stochastic optimization and that the heaviness of the tails have links to the generalization error. While these studies have shed light on interesting aspects of the generalization…

Machine Learning · Statistics 2023-02-14 Anant Raj , Melih Barsbey , Mert Gürbüzbalaban , Lingjiong Zhu , Umut Şimşekli

Many machine learning tasks can be formulated as Regularized Empirical Risk Minimization (R-ERM), and solved by optimization algorithms such as gradient descent (GD), stochastic gradient descent (SGD), and stochastic variance reduction…

Machine Learning · Statistics 2016-09-28 Qi Meng , Yue Wang , Wei Chen , Taifeng Wang , Zhi-Ming Ma , Tie-Yan Liu

Stochastic gradient descent (SGD) has been widely studied in the literature from different angles, and is commonly employed for solving many big data machine learning problems. However, the averaging technique, which combines all iterative…

Machine Learning · Computer Science 2020-05-28 Zhishuai Guo , Yan Yan , Tianbao Yang

The ability of machine learning (ML) algorithms to generalize well to unseen data has been studied through the lens of information theory, by bounding the generalization error with the input-output mutual information (MI), i.e., the MI…

Machine Learning · Statistics 2024-06-07 Kimia Nadjahi , Kristjan Greenewald , Rickard Brüel Gabrielsson , Justin Solomon

We present an Expectation-Maximization algorithm for the fractal inverse problem: the problem of fitting a fractal model to data. In our setting the fractals are Iterated Function Systems (IFS), with similitudes as the family of…

Machine Learning · Statistics 2017-07-03 Peter Bloem , Steven de Rooij

We provide the first generalization error analysis for black-box learning through derivative-free optimization. Under the assumption of a Lipschitz and smooth unknown loss, we consider the Zeroth-order Stochastic Search (ZoSS) algorithm,…

Machine Learning · Computer Science 2023-02-13 Konstantinos E. Nikolakakis , Farzin Haddadpour , Dionysios S. Kalogerias , Amin Karbasi