Related papers: How ConvNets model Non-linear Transformations

Invariances to translations have imbued convolutional neural networks with powerful generalization properties. However, we often do not know a priori what invariances are present in the data, or to what extent a model should be invariant to…

Deep learning on point clouds has made a lot of progress recently. Many point cloud dedicated deep learning frameworks, such as PointNet and PointNet++, have shown advantages in accuracy and speed comparing to those using traditional 3D…

In certain situations, neural networks are trained upon data that obey underlying symmetries. However, the predictions do not respect the symmetries exactly unless embedded in the network structure. In this work, we introduce architectures…

Exploiting data invariances is crucial for efficient learning in both artificial and biological neural circuits. Understanding how neural networks can discover appropriate representations capable of harnessing the underlying symmetries of…

Deep neural network algorithms are difficult to analyze because they lack structure allowing to understand the properties of underlying transforms and invariants. Multiscale hierarchical convolutional networks are structured deep…

This work introduces the Topological CNN (TCNN), which encompasses several topologically defined convolutional methods. Manifolds with important relationships to the natural image space are used to parameterize image filters which are used…

Hypernetworks, or hypernets for short, are neural networks that generate weights for another neural network, known as the target network. They have emerged as a powerful deep learning technique that allows for greater flexibility,…

Developing robust and interpretable vision systems is a crucial step towards trustworthy artificial intelligence. In this regard, a promising paradigm considers embedding task-required invariant structures, e.g., geometric invariance, in…

Tensor networks (TN) have found a wide use in machine learning, and in particular, TN and deep learning bear striking similarities. In this work, we propose the quantum-classical hybrid tensor networks (HTN) which combine tensor networks…

In recent years, there has been a surge in applying deep learning to various challenging design problems in communication networks. The early attempts adopt neural architectures inherited from applications such as computer vision, which…

It is widely believed that the success of deep convolutional networks is based on progressively discarding uninformative variability about the input with respect to the problem at hand. This is supported empirically by the difficulty of…

Inverse problems exist in many domains such as phase imaging, image processing, and computer vision. These problems are often solved with application-specific algorithms, even though their nature remains the same: mapping input image(s) to…

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…

Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…

Current Deep Learning approaches have been very successful using convolutional neural networks (CNN) trained on large graphical processing units (GPU)-based computers. Three limitations of this approach are: 1) they are based on a simple…

While deep learning is successful in a number of applications, it is not yet well understood theoretically. A satisfactory theoretical characterization of deep learning however, is beginning to emerge. It covers the following questions: 1)…

State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of…

Optimization for deep networks is currently a very active area of research. As neural networks become deeper, the ability in manually optimizing the network becomes harder. Mini-batch normalization, identification of effective respective…

As object recognition becomes an increasingly common ML task, and recent research demonstrating CNNs vulnerability to attacks and small image perturbations necessitate fully understanding the foundations of object recognition. We focus on…

Early diagnosis of interstitial lung diseases is crucial for their treatment, but even experienced physicians find it difficult, as their clinical manifestations are similar. In order to assist with the diagnosis, computer-aided diagnosis…