相关论文: Order Theory in the Context of Machine Learning

Solving constrained nonlinear optimization problems (CNLPs) is a longstanding problem that arises in various fields, e.g., economics, computer science, and engineering. We propose optimization-informed neural networks (OINN), a deep…

Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…

Convolutional Neural Networks (CNN) have been pivotal to the success of many state-of-the-art classification problems, in a wide variety of domains (for e.g. vision, speech, graphs and medical imaging). A commonality within those domains is…

The paper briefy reviews several recent results on hierarchical architectures for learning from examples, that may formally explain the conditions under which Deep Convolutional Neural Networks perform much better in function approximation…

Large-scale dynamics of the oceans and the atmosphere are governed by primitive equations (PEs). Due to the nonlinearity and nonlocality, the numerical study of the PEs is generally challenging. Neural networks have been shown to be a…

In machine learning and neuroscience, certain computational structures and algorithms are known to yield disentangled representations without us understanding why, the most striking examples being perhaps convolutional neural networks and…

In this paper, we propose a novel approach for implicit data representation to evaluate similarity of input data using a trained neural network. In contrast to the previous approach, which uses gradients for representation, we utilize only…

Convergence of deep neural networks as the depth of the networks tends to infinity is fundamental in building the mathematical foundation for deep learning. In a previous study, we investigated this question for deep ReLU networks with a…

In this paper we are concerned with the approximation of functions by single hidden layer neural networks with ReLU activation functions on the unit circle. In particular, we are interested in the case when the number of data-points exceeds…

In this paper we study an emerging class of neural networks based on the morphological operators of dilation and erosion. We explore these networks mathematically from a tropical geometry perspective as well as mathematical morphology. Our…

In recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches…

Graph Convolutional Neural Networks (GCNN) are becoming a preferred model for data processing on irregular domains, yet their analysis and principles of operation are rarely examined due to the black box nature of NNs. To this end, we…

Each year, deep learning demonstrates new and improved empirical results with deeper and wider neural networks. Meanwhile, with existing theoretical frameworks, it is difficult to analyze networks deeper than two layers without resorting to…

We propose an algorithm capable of identifying and eliminating irrelevant layers of a neural network during the early stages of training. In contrast to weight or filter-level pruning, layer pruning reduces the harder to parallelize…

Nowadays, Deep Neural Networks are among the main tools used in various sciences. Convolutional Neural Network is a special type of DNN consisting of several convolution layers, each followed by an activation function and a pooling layer.…

Mathematical definitions of polyhedrons and perceptron networks are discussed. The formalization of polyhedrons is done in a rather traditional way. For networks, previously proposed systems are developed. Perceptron networks in disjunctive…

We seek to improve deep neural networks by generalizing the pooling operations that play a central role in current architectures. We pursue a careful exploration of approaches to allow pooling to learn and to adapt to complex and variable…

We propose a novel approach to image classification inspired by complex nonlinear biological visual processing, whereby classical convolutional neural networks (CNNs) are equipped with learnable higher-order convolutions. Our model…

In current deep network architectures, deeper layers in networks tend to contain hundreds of independent neurons which makes it hard for humans to understand how they interact with each other. By organizing the neurons by correlation,…

Contrast is a crucial factor in visual information processing. It is desired for a visual system - irrespective of being biological or artificial - to "perceive" the world robustly under large potential changes in illumination. In this…