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Deep artificial neural networks are powerful tools with many possible applications in nanophotonics. Here, we demonstrate how a deep neural network can be used as a fast, general purpose predictor of the full near-field and far-field…

We consider functions from the real numbers to the real numbers, output by a neural network with 1 hidden activation layer, arbitrary width, and ReLU activation function. We assume that the parameters of the neural network are chosen…

We propose an integral geometric approach for computing dual distributions for the parameter distributions of multilinear models. The dual distributions can be computed from, for example, the parameter distributions of conics, multiple view…

Deep neural nets have caused a revolution in many classification tasks. A related ongoing revolution -- also theoretically not understood -- concerns their ability to serve as generative models for complicated types of data such as images…

Nonlocal neural networks have been proposed and shown to be effective in several computer vision tasks, where the nonlocal operations can directly capture long-range dependencies in the feature space. In this paper, we study the nature of…

Social network analysis is an important problem in data mining. A fundamental step for analyzing social networks is to encode network data into low-dimensional representations, i.e., network embeddings, so that the network topology…

Topological neural networks (TNNs) are information processing architectures that model representations from data lying over topological spaces (e.g., simplicial or cell complexes) and allow for decentralized implementation through localized…

The proliferation of deep neural networks in various domains has seen an increased need for interpretability of these models. Preliminary work done along this line and papers that surveyed such, are focused on high-level representation…

A deep neural network (DNN) with piecewise linear activations can partition the input space into numerous small linear regions, where different linear functions are fitted. It is believed that the number of these regions represents the…

Artificial and biological agents cannon learn given completely random and unstructured data. The structure of data is encoded in the metric relationships between data points. In the context of neural networks, neuronal activity within a…

Randomized Neural Networks explore the behavior of neural systems where the majority of connections are fixed, either in a stochastic or a deterministic fashion. Typical examples of such systems consist of multi-layered neural network…

Linear networks provide valuable insights into the workings of neural networks in general. This paper identifies conditions under which the gradient flow provably trains a linear network, in spite of the non-strict saddle points present in…

An object-oriented approach to implementing artificial neural networks is introduced in this article. The networks obtained in this way are highly connected in that they admit edges between nodes in any layers of the network, and dynamic,…

Neural networks that process the parameters of other neural networks find applications in domains as diverse as classifying implicit neural representations, generating neural network weights, and predicting generalization errors. However,…

Understanding how information is represented in neural networks is a fundamental challenge in both neuroscience and artificial intelligence. Despite their nonlinear architectures, recent evidence suggests that neural networks encode…

Deep neural networks are widely used in various domains. However, the nature of computations at each layer of the deep networks is far from being well understood. Increasing the interpretability of deep neural networks is thus important.…

There is emerging interest in performing regression between distributions. In contrast to prediction on single instances, these machine learning methods can be useful for population-based studies or on problems that are inherently…

Drawing motivation from the manifold hypothesis, which posits that most high-dimensional data lies on or near low-dimensional manifolds, we apply manifold learning to the space of neural networks. We learn manifolds where datapoints are…

The process of aggregation is ubiquitous in almost all deep nets models. It functions as an important mechanism for consolidating deep features into a more compact representation, whilst increasing robustness to overfitting and providing…

Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…