اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدExistence, Stability And Scalability Of Orthogonal Convolutional Neural Networks
123
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Imposing orthogonal transformations between layers of a neural network has been considered for several years now. This facilitates their learning, by limiting the explosion/vanishing of the gradient; decorrelates the features; improves the robustness. In this framework, this paper studies theoretical properties of orthogonal convolutional layers. More precisely, we establish necessary and sufficient conditions on the layer architecture guaranteeing the existence of an orthogonal convolutional transform. These conditions show that orthogonal convolutional transforms exist for almost all architectures used in practice. Recently, a regularization term imposing the orthogonality of convolutional layers has been proposed. We make the link between this regularization term and orthogonality measures. In doing so, we show that this regularization strategy is stable with respect to numerical and optimization errors and remains accurate when the size of the signals/images is large. This holds for both row and column orthogonality. Finally, we confirm these theoretical results with experiments, and also empirically study the landscape of the regularization term.
قيم البحث
اقرأ أيضاً
Deep convolutional neural networks are hindered by training instability and feature redundancy towards further performance improvement. A promising solution is to impose orthogonality on convolutional filters. We develop an efficient approach to im
pose filter orthogonality on a convolutional layer based on the doubly block-Toeplitz matrix representation of the convolutional kernel instead of using the common kernel orthogonality approach, which we show is only necessary but not sufficient for ensuring orthogonal convolutions. Our proposed orthogonal convolution requires no additional parameters and little computational overhead. This method consistently outperforms the kernel orthogonality alternative on a wide range of tasks such as image classification and inpainting under supervised, semi-supervised and unsupervised settings. Further, it learns more diverse and expressive features with better training stability, robustness, and generalization. Our code is publicly available at https://github.com/samaonline/Orthogonal-Convolutional-Neural-Networks.
Neural networks are becoming an increasingly important tool in applications. However, neural networks are not widely used in statistical genetics. In this paper, we propose a new neural networks method called expectile neural networks. When the size
of parameter is too large, the standard maximum likelihood procedures may not work. We use sieve method to constrain parameter space. And we prove its consistency and normality under nonparametric regression framework.
Inspired by convolutional neural networks on 1D and 2D data, graph convolutional neural networks (GCNNs) have been developed for various learning tasks on graph data, and have shown superior performance on real-world datasets. Despite their success,
there is a dearth of theoretical explorations of GCNN models such as their generalization properties. In this paper, we take a first step towards developing a deeper theoretical understanding of GCNN models by analyzing the stability of single-layer GCNN models and deriving their generalization guarantees in a semi-supervised graph learning setting. In particular, we show that the algorithmic stability of a GCNN model depends upon the largest absolute eigenvalue of its graph convolution filter. Moreover, to ensure the uniform stability needed to provide strong generalization guarantees, the largest absolute eigenvalue must be independent of the graph size. Our results shed new insights on the design of new & improved graph convolution filters with guaranteed algorithmic stability. We evaluate the generalization gap and stability on various real-world graph datasets and show that the empirical results indeed support our theoretical findings. To the best of our knowledge, we are the first to study stability bounds on graph learning in a semi-supervised setting and derive generalization bounds for GCNN models.
In this paper, we study the properties of robust nonparametric estimation using deep neural networks for regression models with heavy tailed error distributions. We establish the non-asymptotic error bounds for a class of robust nonparametric regress
ion estimators using deep neural networks with ReLU activation under suitable smoothness conditions on the regression function and mild conditions on the error term. In particular, we only assume that the error distribution has a finite p-th moment with p greater than one. We also show that the deep robust regression estimators are able to circumvent the curse of dimensionality when the distribution of the predictor is supported on an approximate lower-dimensional set. An important feature of our error bound is that, for ReLU neural networks with network width and network size (number of parameters) no more than the order of the square of the dimensionality d of the predictor, our excess risk bounds depend sub-linearly on d. Our assumption relaxes the exact manifold support assumption, which could be restrictive and unrealistic in practice. We also relax several crucial assumptions on the data distribution, the target regression function and the neural networks required in the recent literature. Our simulation studies demonstrate that the robust methods can significantly outperform the least squares method when the errors have heavy-tailed distributions and illustrate that the choice of loss function is important in the context of deep nonparametric regression.
Recently it was shown in several papers that backpropagation is able to find the global minimum of the empirical risk on the training data using over-parametrized deep neural networks. In this paper a similar result is shown for deep neural networks
with the sigmoidal squasher activation function in a regression setting, and a lower bound is presented which proves that these networks do not generalize well on a new data in the sense that they do not achieve the optimal minimax rate of convergence for estimation of smooth regression functions.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
