Related papers: Radius-margin bounds for deep neural networks
We present a formulation of deep learning that aims at producing a large margin classifier. The notion of margin, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically…
The classical hinge-loss support vector machines (SVMs) model is sensitive to outlier observations due to the unboundedness of its loss function. To circumvent this issue, recent studies have focused on non-convex loss functions, such as…
Recent research has used margin theory to analyze the generalization performance for deep neural networks (DNNs). The existed results are almost based on the spectrally-normalized minimum margin. However, optimizing the minimum margin…
While deep learning models and techniques have achieved great empirical success, our understanding of the source of success in many aspects remains very limited. In an attempt to bridge the gap, we investigate the decision boundary of a…
Deep learning methods minimise the empirical risk using loss functions such as the cross entropy loss. When minimising the empirical risk, the generalisation of the learnt function still depends on the performance on the training data, the…
This paper addresses the problem of nearly optimal Vapnik--Chervonenkis dimension (VC-dimension) and pseudo-dimension estimations of the derivative functions of deep neural networks (DNNs). Two important applications of these estimations…
Vapnik-Chervonenkis (VC) dimension is a fundamental measure of the generalization capacity of learning algorithms. However, apart from a few special cases, it is hard or impossible to calculate analytically. Vapnik et al. [10] proposed a…
We investigate the use of Deep Neural Networks for the classification of image datasets where texture features are important for generating class-conditional discriminative representations. To this end, we first derive the size of the…
Support Vector Machines (SVMs) based on hinge loss have been extensively discussed and applied to various binary classification tasks. These SVMs achieve a balance between margin maximization and the minimization of slack due to outliers.…
We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, as well as the Jacobian of the networks. Through introducing a new characterization of the…
We show that deep Heaviside networks (DHNs) have limited expressiveness but that this can be overcome by including either skip connections or neurons with linear activation. We provide lower and upper bounds for the Vapnik-Chervonenkis (VC)…
Despite being so vital to success of Support Vector Machines, the principle of separating margin maximisation is not used in deep learning. We show that minimisation of margin variance and not maximisation of the margin is more suitable for…
We study the generalization capabilities of Group Convolutional Neural Networks (GCNNs) with ReLU activation function by deriving upper and lower bounds for their Vapnik-Chervonenkis (VC) dimension. Specifically, we analyze how factors such…
Understanding the generalization of deep neural networks is one of the most important tasks in deep learning. Although much progress has been made, theoretical error bounds still often behave disparately from empirical observations. In this…
Support Vector Machines (SVMs) are among the most fundamental tools for binary classification. In its simplest formulation, an SVM produces a hyperplane separating two classes of data using the largest possible margin to the data. The focus…
People believe that depth plays an important role in success of deep neural networks (DNN). However, this belief lacks solid theoretical justifications as far as we know. We investigate role of depth from perspective of margin bound. In…
We prove that overparametrized neural networks are able to generalize with a test error that is independent of the level of overparametrization, and independent of the Vapnik-Chervonenkis (VC) dimension. We prove explicit bounds that only…
Using a support vector machine requires to set two types of hyperparameters: the soft margin parameter C and the parameters of the kernel. To perform this model selection task, the method of choice is cross-validation. Its leave-one-out…
Ventricular volume and its progression are known to be linked to several brain diseases such as dementia and schizophrenia. Therefore accurate measurement of ventricle volume is vital for longitudinal studies on these disorders, making…
Largest theoretical contribution to Neural Networks comes from VC Dimension which characterizes the sample complexity of classification model in a probabilistic view and are widely used to study the generalization error. So far in the…