Related papers: The inverse problem for neural networks

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…

Neural ordinary differential equations (Neural ODEs) propose the idea that a sequence of layers in a neural network is just a discretisation of an ODE, and thus can instead be directly modelled by a parameterised ODE. This idea has had…

Inverse problems correspond to a certain type of optimization problems formulated over appropriate input distributions. Recently, there has been a growing interest in understanding the computational hardness of these optimization problems,…

Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…

Finding model parameters from data is an essential task in science and engineering, from weather and climate forecasts to plasma control. Previous works have employed neural networks to greatly accelerate finding solutions to inverse…

It is often useful to perform integration over learned functions represented by neural networks. However, this integration is usually performed numerically, as analytical integration over learned functions (especially neural networks) is…

Recently deep neural networks have been widely and successfully applied in computer vision tasks and attracted growing interests in medical imaging. One barrier for the application of deep neural networks to medical imaging is the need of…

It is well known that the output of a Neural Network trained to disentangle between two classes has a probabilistic interpretation in terms of the a-posteriori Bayesian probability, provided that a unary representation is taken for the…

Modern discriminative predictors have been shown to match natural intelligences in specific perceptual tasks in image classification, object and part detection, boundary extraction, etc. However, a major advantage that natural intelligences…

This paper addresses the task of set prediction using deep feed-forward neural networks. A set is a collection of elements which is invariant under permutation and the size of a set is not fixed in advance. Many real-world problems, such as…

There is strong interest in developing mathematical methods that can be used to understand complex neural networks used in image analysis. In this paper, we introduce techniques from Linear Algebra to model neural network layers as maps…

We introduce inverse transport networks as a learning architecture for inverse rendering problems where, given input image measurements, we seek to infer physical scene parameters such as shape, material, and illumination. During training,…

Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step scheme. First, one trains the often neural network-based…

We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. Based on the understanding of propagation of waves and their nonlinear interactions, we…

A neural network consisting of piecewise affine building blocks, such as fully-connected layers and ReLU activations, is itself a piecewise affine function supported on a polyhedral complex. This complex has been previously studied to…

We study the problem of modeling a binary operation that satisfies some algebraic requirements. We first construct a neural network architecture for Abelian group operations and derive a universal approximation property. Then, we extend it…

Data inconsistency leads to a slow training process when deep neural networks are used for the inverse design of photonic devices, an issue that arises from the fundamental property of non-uniqueness in all inverse scattering problems. Here…

Many challenging image processing tasks can be described by an ill-posed linear inverse problem: deblurring, deconvolution, inpainting, compressed sensing, and superresolution all lie in this framework. Traditional inverse problem solvers…

Equivariant neural networks are neural networks with symmetry. Motivated by the theory of group representations, we decompose the layers of an equivariant neural network into simple representations. The nonlinear activation functions lead…

Employing deep neural networks as natural image priors to solve inverse problems either requires large amounts of data to sufficiently train expressive generative models or can succeed with no data via untrained neural networks. However,…