Related papers: Newton Methods for Convolutional Neural Networks
Convolutional Neural Networks (CNNs) are pivotal in computer vision and Big Data analytics but demand significant computational resources when trained on large-scale datasets. Conventional training via back-propagation (BP) with losses like…
We propose a local modelling approach using deep convolutional neural networks (CNNs) for fine-grained image classification. Recently, deep CNNs trained from large datasets have considerably improved the performance of object recognition.…
In this paper a special piecewise linear system is studied. It is shown that, under a mild assumption, the semi-smooth Newton method applied to this system is well defined and the method generates a sequence that converges linearly to a…
Due to the advent of modern embedded systems and mobile devices with constrained resources, there is a great demand for incredibly efficient deep neural networks for machine learning purposes. There is also a growing concern of privacy and…
Convolutions are the core operation of deep learning applications based on Convolutional Neural Networks (CNNs). Current GPU architectures are highly efficient for training and deploying deep CNNs, and hence, these are largely used in…
Title: Comparison between layer-to-layer network training and conventional network training using Deep Convolutional Neural Networks Abstract: Convolutional neural networks (CNNs) are widely used in various applications due to their…
We consider variants of a recently-developed Newton-CG algorithm for nonconvex problems \citep{royer2018newton} in which inexact estimates of the gradient and the Hessian information are used for various steps. Under certain conditions on…
In this paper, we present some theoretical work to explain why simple gradient descent methods are so successful in solving non-convex optimization problems in learning large-scale neural networks (NN). After introducing a mathematical tool…
A novel convolution neural network model, abbreviated NL-CNN is proposed, where nonlinear convolution is emulated in a cascade of convolution + nonlinearity layers. The code for its implementation and some trained models are made publicly…
Convolutional neural network (CNN) is an important deep learning method. The convolution operation takes a large proportion of the total execution time for CNN. Feature maps for convolution operation are usually sparse. Multiplications and…
In this paper, an efficient modified Newton type algorithm is proposed for nonlinear unconstrianed optimization problems. The modified Hessian is a convex combination of the identity matrix (for steepest descent algorithm) and the Hessian…
An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…
This work studies the global convergence and implicit bias of Gauss Newton's (GN) when optimizing over-parameterized one-hidden layer networks in the mean-field regime. We first establish a global convergence result for GN in the…
DNN structures are continuously developing and achieving high performances in classification problems. Also, it is observed that success rates obtained with DNNs are higher than those obtained with traditional neural networks. In addition,…
First-order optimization methods, such as stochastic gradient descent (SGD) and its variants, are widely used in machine learning applications due to their simplicity and low per-iteration costs. However, they often require larger numbers…
Stochastic gradient descent (SGD) still is the workhorse for many practical problems. However, it converges slow, and can be difficult to tune. It is possible to precondition SGD to accelerate its convergence remarkably. But many attempts…
Nonconvex optimization problems such as the ones in training deep neural networks suffer from a phenomenon called saddle point proliferation. This means that there are a vast number of high error saddle points present in the loss function.…
The goal of this document is to provide a pedagogical introduction to the main concepts underpinning the training of deep neural networks using gradient descent; a process known as backpropagation. Although we focus on a very influential…
Deep convolutional neural networks (CNN) has become the most promising method for object recognition, repeatedly demonstrating record breaking results for image classification and object detection in recent years. However, a very deep CNN…
A scaled conjugate gradient method that accelerates existing adaptive methods utilizing stochastic gradients is proposed for solving nonconvex optimization problems with deep neural networks. It is shown theoretically that, whether with…