Related papers: On the Approximation of Bi-Lipschitz Maps by Inver…

Invertible neural networks (INNs) are neural network architectures with invertibility by design. Thanks to their invertibility and the tractability of Jacobian, INNs have various machine learning applications such as probabilistic modeling,…

Deep neural networks have achieved substantial success across various scientific computing tasks. A pivotal challenge within this domain is the rapid and parallel approximation of matrix inverses, critical for numerous applications. Despite…

We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs). INNs are a class of implicit learning models that use implicit equations as layers and have been shown to exhibit several notable…

With the remarkable empirical success of neural networks across diverse scientific disciplines, rigorous error and convergence analysis are also being developed and enriched. However, there has been little theoretical work focusing on…

Robot localization is an inverse problem of finding a robot's pose using a map and sensor measurements. In recent years, Invertible Neural Networks (INNs) have successfully solved ambiguous inverse problems in various fields. This paper…

We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with…

Neural ODEs and i-ResNet are recently proposed methods for enforcing invertibility of residual neural models. Having a generic technique for constructing invertible models can open new avenues for advances in learning systems, but so far…

How can we design neural networks that allow for stable universal approximation of maps between topologically interesting manifolds? The answer is with a coordinate projection. Neural networks based on topological data analysis (TDA) use…

Invertible neural networks (INNs) have been used to design generative models, implement memory-saving gradient computation, and solve inverse problems. In this work, we show that commonly-used INN architectures suffer from exploding…

Physics informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for PDEs. We focus on a particular class of inverse problems, the so-called data assimilation or unique…

Most problems in natural language processing can be approximated as inverse problems such as analysis and generation at variety of levels from morphological (e.g., cat+Plural <-> cats) to semantic (e.g., (call + 1 2) <-> "Calculate one plus…

We study the problem of reconstructing solutions of inverse problems when only noisy measurements are available. We assume that the problem can be modeled with an infinite-dimensional forward operator that is not continuously invertible.…

This paper introduces an Interpretable Neural Network (INN) incorporating spatial information to tackle the opaque parameterization process of random weighted neural networks. The INN leverages spatial information to elucidate the…

In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse…

Measure-preserving neural networks are well-developed invertible models, however, their approximation capabilities remain unexplored. This paper rigorously analyses the approximation capabilities of existing measure-preserving neural…

Recently, deep neural networks (DNNs) have become powerful tools for solving inverse scattering problems. However, the approximation and generalization rates of DNNs for solving these problems remain largely under-explored. In this work, we…

Neural network systems describe complex mappings that can be very difficult to understand. In this paper, we study the inverse problem of determining the input images that get mapped to specific neural network classes. Ultimately, we expect…

Invertible neural networks based on coupling flows (CF-INNs) have various machine learning applications such as image synthesis and representation learning. However, their desirable characteristics such as analytic invertibility come at the…

We describe generalizations of the universal approximation theorem for neural networks to maps invariant or equivariant with respect to linear representations of groups. Our goal is to establish network-like computational models that are…

While the interaction of ultra-intense ultra-short laser pulses with near- and overcritical plasmas cannot be directly observed, experimentally accessible quantities (observables) often only indirectly give information about the underlying…