Related papers: Delay Differential Neural Networks
In this paper, the authors propose the utilization of Fibonacci Neural Networks (FNN) for solving arbitrary order differential equations. The FNN architecture comprises input, middle, and output layers, with various degrees of Fibonacci…
K-nearest neighbors (KNN) is one of the earliest and most established algorithms in machine learning. For regression tasks, KNN averages the targets within a neighborhood which poses a number of challenges: the neighborhood definition is…
Delay-Differential Equations (DDEs) are the most common representation for systems with delay. However, the DDE representation is limited. In network models with delay, the delayed channels are low-dimensional and accounting for this…
Neural ordinary differential equations (neural ODEs) have emerged as a novel network architecture that bridges dynamical systems and deep learning. However, the gradient obtained with the continuous adjoint method in the vanilla neural ODE…
Neural Disjunctive Normal Form (DNF) based models are powerful and interpretable approaches to neuro-symbolic learning and have shown promising results in classification and reinforcement learning settings without prior knowledge of the…
We present diffusion-convolutional neural networks (DCNNs), a new model for graph-structured data. Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from…
We propose a new approach, called as functional deep neural network (FDNN), for classifying multi-dimensional functional data. Specifically, a deep neural network is trained based on the principle components of the training data which shall…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
While deep neural networks (DNN) have become an effective computational tool, the prediction results are often criticized by the lack of interpretability, which is essential in many real-world applications such as health informatics.…
Discriminative features play an important role in image and object classification and also in other fields of research such as semi-supervised learning, fine-grained classification, out of distribution detection. Inspired by Linear…
Deep Neural Networks (DNNs) are becoming an important tool in modern computing applications. Accelerating their training is a major challenge and techniques range from distributed algorithms to low-level circuit design. In this survey, we…
This paper introduces Progressively Diffused Networks (PDNs) for unifying multi-scale context modeling with deep feature learning, by taking semantic image segmentation as an exemplar application. Prior neural networks, such as ResNet, tend…
Defect detection is a basic and essential task in automatic parts production, especially for automotive engine precision parts. In this paper, we propose a new idea to construct a deep convolutional network combining related knowledge of…
Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…
Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…
We present a lightweighted neural PDE representation to discover the hidden structure and predict the solution of different nonlinear PDEs. Our key idea is to leverage the prior of ``translational similarity'' of numerical PDE differential…
Despite their success and widespread adoption, the opaque nature of deep neural networks (DNNs) continues to hinder trust, especially in critical applications. Current interpretability solutions often yield inconsistent or oversimplified…
Randomized Neural Networks explore the behavior of neural systems where the majority of connections are fixed, either in a stochastic or a deterministic fashion. Typical examples of such systems consist of multi-layered neural network…
Stochastic control problems with delay are challenging due to the path-dependent feature of the system and thus its intrinsic high dimensions. In this paper, we propose and systematically study deep neural networks-based algorithms to solve…
We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problem by taking the continuum limits of both network width and depth. The proposed model captures the…