Related papers: Semantic Segmentation using Neural Ordinary Differ…
The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin.…
Continuous-depth neural networks, such as the Neural Ordinary Differential Equations (ODEs), have aroused a great deal of interest from the communities of machine learning and data science in recent years, which bridge the connection…
Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…
Neural ordinary differential equations (NODEs) treat computation of intermediate feature vectors as trajectories of ordinary differential equation parameterized by a neural network. In this paper, we propose a novel model, delay…
Semantic segmentation consists of predicting a semantic label for each image pixel. While existing deep learning approaches achieve high accuracy, they often overlook the ordinal relationships between classes, which can provide critical…
Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to…
Despite outstanding semantic scene segmentation in closed-worlds, deep neural networks segment novel instances poorly, which is required for autonomous agents acting in an open world. To improve out-of-distribution (OOD) detection for…
The recently-introduced class of ordinary differential equation networks (ODE-Nets) establishes a fruitful connection between deep learning and dynamical systems. In this work, we reconsider formulations of the weights as…
Deep residual networks (ResNets) have shown state-of-the-art performance in various real-world applications. Recently, the ResNets model was reparameterized and interpreted as solutions to a continuous ordinary differential equation or…
Deep neural networks have shown outstanding performance in computer vision tasks such as semantic segmentation and have defined the state-of-the-art. However, these segmentation models are trained on a closed and predefined set of semantic…
Fast data acquisition in Magnetic Resonance Imaging (MRI) is vastly in demand and scan time directly depends on the number of acquired k-space samples. The data-driven methods based on deep neural networks have resulted in promising…
Semantic segmentation models classify pixels into a set of known (``in-distribution'') visual classes. When deployed in an open world, the reliability of these models depends on their ability not only to classify in-distribution pixels but…
Unlike conventional grid and mesh based methods for solving partial differential equations (PDEs), neural networks have the potential to break the curse of dimensionality, providing approximate solutions to problems where using classical…
It has been found that residual networks are an Euler discretization of solutions to Ordinary Differential Equations (ODEs). In this paper, we explore a deeper relationship between Transformer and numerical methods of ODEs. We show that a…
Although ordinary differential equations (ODEs) provide insights for designing network architectures, its relationship with the non-residual convolutional neural networks (CNNs) is still unclear. In this paper, we present a novel ODE model…
A neural ordinary differential equation (neural ODE) is a machine learning model that is commonly described as a continuous-depth generalization of a residual network (ResNet) with a single residual block, or conversely, the ResNet can be…
Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…
We propose a novel second-order optimization framework for training the emerging deep continuous-time models, specifically the Neural Ordinary Differential Equations (Neural ODEs). Since their training already involves expensive gradient…
We study the ability of neural networks to calculate feedback control signals that steer trajectories of continuous time non-linear dynamical systems on graphs, which we represent with neural ordinary differential equations (neural ODEs).…
Semantic segmentation is a fundamental task in visual scene understanding. We focus on the supervised setting, where ground-truth semantic annotations are available. Based on knowledge about the high regularity of real-world scenes, we…