Related papers: A Deep Neural Network for Knot Placement in B-spli…
In recent years, deep learning has been connected with optimal control as a way to define a notion of a continuous underlying learning problem. In this view, neural networks can be interpreted as a discretization of a parametric Ordinary…
Determining the optimal depth of a neural network is a fundamental yet challenging problem, typically resolved through resource-intensive experimentation. This paper introduces a formal theoretical framework to address this question by…
Dropout Regularization, serving to reduce variance, is nearly ubiquitous in Deep Learning models. We explore the relationship between the dropout rate and model complexity by training 2,000 neural networks configured with random…
This paper proposes a deep Convolutional Neural Network(CNN) with strong generalization ability for structural topology optimization. The architecture of the neural network is made up of encoding and decoding parts, which provide down- and…
The performance of Deep Neural Networks (DNNs) keeps elevating in recent years with increasing network depth and width. To enable DNNs on edge devices like mobile phones, researchers proposed several network compression methods including…
In this paper we summarise the work discussed in Ref. [1] and [2] (q-alg/9505003), in which we introduced a method helpful in solving the problem of knot classification. We also present results obtained since then.
We propose a distributed approach to train deep neural networks (DNNs), which has guaranteed convergence theoretically and great scalability empirically: close to 6 times faster on instance of ImageNet data set when run with 6 machines. The…
Network compression reduces the computational complexity and memory consumption of deep neural networks by reducing the number of parameters. In SVD-based network compression, the right rank needs to be decided for every layer of the…
Network alignment is the problem of matching the nodes of two graphs, maximizing the similarity of the matched nodes and the edges between them. This problem is encountered in a wide array of applications-from biological networks to social…
Nowadays, the number of layers and of neurons in each layer of a deep network are typically set manually. While very deep and wide networks have proven effective in general, they come at a high memory and computation cost, thus making them…
With the increasing number of base stations (BSs) and network densification in 5G, interference management using link scheduling and power control are vital for better utilization of radio resources. However, the complexity of solving link…
Deep learning is a powerful tool for solving nonlinear differential equations, but usually, only the solution corresponding to the flattest local minimizer can be found due to the implicit regularization of stochastic gradient descent. This…
While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear…
Deep networks realize complex mappings that are often understood by their locally linear behavior at or around points of interest. For example, we use the derivative of the mapping with respect to its inputs for sensitivity analysis, or to…
We introduce a new numerical method based on machine learning to approximate the solution of elliptic partial differential equations with collocation using a set of sigmoidal functions. We show that a feedforward neural network with a…
This paper explores the use of artificial neural networks for the stable and data-driven selection of the frequency parameter in hyperbolic polynomial penalized splines (HP-splines). This parameter defines the underlying spline space and is…
Based on the continuous interpretation of deep learning cast as an optimal control problem, this paper investigates the benefits of employing B-spline basis functions to parameterize neural network controls across the layers. Rather than…
The paper aims to investigate relevant computational issues of deep neural network architectures with an eye to the interaction between the optimization algorithm and the classification performance. In particular, we aim to analyze the…
The success of deep neural networks (DNNs) is attributable to three factors: increased compute capacity, more complex models, and more data. These factors, however, are not always present, especially for edge applications such as autonomous…
In the deep-learning community new algorithms are published at an incredible pace. Therefore, solving an image classification problem for new datasets becomes a challenging task, as it requires to re-evaluate published algorithms and their…