相关论文: Universal approximation property of invertible neu…

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…

We propose a learning paradigm for the numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework…

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…

The Convolutional Neural Network (CNN) is one of the most prominent neural network architectures in deep learning. Despite its widespread adoption, our understanding of its universal approximation properties has been limited due to its…

Implicit neural representations (INRs) mark a fundamental shift in signal modeling, moving from discrete sampled data to continuous functional representations. By parameterizing signals as neural networks, INRs provide a unified framework…

We introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures. The architectures are codified using numbers from the ring of integers of non-Archimdean local fields. These rings have a natural…

Universal approximation theorems provide a mathematical explanation for the expressive power of neural networks. They assert that, under mild conditions on the activation function, feedforward neural networks are dense in broad function…

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…

Leveraging the infinite dimensional neural network architecture we proposed in arXiv:2109.13512v4 and which can process inputs from Fr\'echet spaces, and using the universal approximation property shown therein, we now largely extend the…

Physics-Informed Neural Networks (PINNs) are Neural Network architectures trained to emulate solutions of differential equations without the necessity of solution data. They are currently ubiquitous in the scientific literature due to their…

The unfolding of detector effects is crucial for the comparison of data to theory predictions. While traditional methods are limited to representing the data in a low number of dimensions, machine learning has enabled new unfolding…

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

Deep learning has been extensively employed as a powerful function approximator for modeling physics-based problems described by partial differential equations (PDEs). Despite their popularity, standard deep learning models often demand…

Inspired by biology, spiking neural networks (SNNs) process information via discrete spikes over time, offering an energy-efficient alternative to the classical computing paradigm and classical artificial neural networks (ANNs). In this…

We show that standard ResNet architectures can be made invertible, allowing the same model to be used for classification, density estimation, and generation. Typically, enforcing invertibility requires partitioning dimensions or restricting…

The universal approximation theorem is generalised to uniform convergence on the (noncompact) input space $\mathbb{R}^n$. All continuous functions that vanish at infinity can be uniformly approximated by neural networks with one hidden…

Autoencoders are able to learn useful data representations in an unsupervised matter and have been widely used in various machine learning and computer vision tasks. In this work, we present methods to train Invertible Neural Networks…

Modifications to a neural network's input and output layers are often required to accommodate the specificities of most practical learning tasks. However, the impact of such changes on architecture's approximation capabilities is largely…

A topological neural network (TNN), which takes data from a Tychonoff topological space instead of the usual finite dimensional space, is introduced. As a consequence, a distributional neural network (DNN) that takes Borel measures as data…

Implicit neural representation (INR) has proven to be accurate and efficient in various domains. In this work, we explore how different neural networks can be designed as a new texture INR, which operates in a continuous manner rather than…