相关论文: Rethinking the ill-posedness of the spectral funct…

Under investigation is the problem of finding the best approximation of a function in a Hilbert space subject to convex constraints and prescribed nonlinear transformations. We show that in many instances these prescriptions can be…

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…

Understanding feature representation for deep neural networks (DNNs) remains an open question within the general field of explainable AI. We use principal component analysis (PCA) to study the performance of a k-nearest neighbors classifier…

The prospect of nonparametric reconstructions of cosmological parameters from observational data sets has been a popular topic in the literature for a number of years. This has mainly taken the form of a technique based on Gaussian…

Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…

We present Spectral Inference Networks, a framework for learning eigenfunctions of linear operators by stochastic optimization. Spectral Inference Networks generalize Slow Feature Analysis to generic symmetric operators, and are closely…

The approximate nearest neighbor problem ($\epsilon$-ANN) in high dimensional Euclidean space has been mainly addressed by Locality Sensitive Hashing (LSH), which has polynomial dependence in the dimension, sublinear query time, but…

Reconstructing an image from its Radon transform is a fundamental computed tomography (CT) task arising in applications such as X-ray scans. In many practical scenarios, a full 180-degree scan is not feasible, or there is a desire to reduce…

Invariance under symmetry is an important problem in machine learning. Our paper looks specifically at equivariant neural networks where transformations of inputs yield homomorphic transformations of outputs. Here, steerable CNNs have…

In this paper, we demonstrate the expressibility of artificial neural networks (ANNs) in quantum many-body physics by showing that a feed-forward neural network with a small number of hidden layers can be trained to approximate with high…

Bilevel optimization offers a methodology to learn hyperparameters in imaging inverse problems, yet its integration with automatic differentiation techniques remains challenging. On the one hand, inverse problems are typically solved by…

This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…

The image reconstruction problem consists in finding an approximation of a function f starting from its Radon transform Rf. This problem arises in the ambit of medical imaging when one tries to reconstruct the internal structure of the…

Current research in Computer Vision has shown that Convolutional Neural Networks (CNN) give state-of-the-art performance in many classification tasks and Computer Vision problems. The embedding of CNN, which is the internal representation…

Electron tomography is a powerful tool for understanding the morphology of materials in three dimensions, but conventional reconstruction algorithms typically suffer from missing-wedge artifacts and data misalignment imposed by experimental…

In this paper, we discuss the computational complexity of reconstructing the state of a linear system from sensor measurements that have been corrupted by an adversary. The first result establishes that the problem is, in general, NP-hard.…

Inverse problems consist of recovering a signal from a collection of noisy measurements. These problems can often be cast as feasibility problems; however, additional regularization is typically necessary to ensure accurate and stable…

State of the art methods in astronomical image reconstruction rely on the resolution of a regularized or constrained optimization problem. Solving this problem can be computationally intensive and usually leads to a quadratic or at least…

Organisms in nature have evolved to exhibit flexibility in face of changes to the environment and/or to themselves. Artificial neural networks (ANNs) have proven useful for controlling of artificial agents acting in environments. However,…

Spectral computations of infinite-dimensional operators are notoriously difficult, yet ubiquitous in the sciences. Indeed, despite more than half a century of research, it is still unknown which classes of operators allow for computation of…