相关论文: Universal approximation property of invertible neu…

Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…

Inverse problems arise almost everywhere in science and engineering where we need to infer on a quantity from indirect observation. The cases of medical, biomedical, and industrial imaging systems are the typical examples. A very high…

We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…

Deep neural networks (DNNs) lack the precise semantics and definitive probabilistic interpretation of probabilistic graphical models (PGMs). In this paper, we propose an innovative solution by constructing infinite tree-structured PGMs that…

Artificial intelligence (AI) has revolutionized software development, shifting from task-specific codes (Software 1.0) to neural network-based approaches (Software 2.0). However, applying this transition in engineering software presents…

We propose a new way of constructing invertible neural networks by combining simple building blocks with a novel set of composition rules. This leads to a rich set of invertible architectures, including those similar to ResNets. Inversion…

Physics-informed neural networks (PINNs) are an influential method of solving differential equations and estimating their parameters given data. However, since they make use of neural networks, they provide only a point estimate of…

Constraining linear layers in neural networks to respect symmetry transformations from a group $G$ is a common design principle for invariant networks that has found many applications in machine learning. In this paper, we consider a…

Deep neural networks are vulnerable to adversarial attacks and hard to interpret because of their black-box nature. The recently proposed invertible network is able to accurately reconstruct the inputs to a layer from its outputs, thus has…

Physics Informed Neural Networks (PINNs) have been emerging as a powerful computational tool for solving differential equations. However, the applicability of these models is still in its initial stages and requires more standardization to…

Deep learning has achieved remarkable success across many domains, but it has also created a growing demand for interpretability in model predictions. Although many explainable machine learning methods have been proposed, post-hoc…

In this study, we explore the integration of Neural Networks, a powerful class of functions known for their exceptional approximation capabilities. Our primary emphasis is on the integration of multi-layer Neural Networks, a challenging…

Deep neural networks (DNNs) achieve remarkable predictive performance but remain difficult to interpret, largely due to overparameterization that obscures the minimal structure required for interpretation. Here we introduce DeepIn, a…

Our ability to interact with the world around us relies on being able to infer what actions objects afford -- often referred to as affordances. The neural mechanisms of object-action associations are realized in the visuomotor pathway where…

Data in tabular format is frequently occurring in real-world applications. Graph Neural Networks (GNNs) have recently been extended to effectively handle such data, allowing feature interactions to be captured through representation…

The many variations of Implicit Neural Representations (INRs), where a neural network is trained as a continuous representation of a signal, have tremendous practical utility for downstream tasks including novel view synthesis, video…

Several recent works have empirically observed that Convolutional Neural Nets (CNNs) are (approximately) invertible. To understand this approximate invertibility phenomenon and how to leverage it more effectively, we focus on a theoretical…

A common assumption about neural networks is that they can learn an appropriate internal representations on their own, see e.g. end-to-end learning. In this work we challenge this assumption. We consider two simple tasks and show that the…

Neural networks have recently gained attention in solving inverse problems. One prominent methodology are Physics-Informed Neural Networks (PINNs) which can solve both forward and inverse problems. In the paper at hand, full waveform…

Neural networks successfully capture the computational power of the human brain for many tasks. Similarly inspired by the brain architecture, Nearest Neighbor (NN) representations is a novel approach of computation. We establish a firmer…