Related papers: Fractional Deep Neural Network via Constrained Opt…
Interpretation of Deep Neural Networks (DNNs) training as an optimal control problem with nonlinear dynamical systems has received considerable attention recently, yet the algorithmic development remains relatively limited. In this work, we…
In this article, we investigate the existence of a deep neural network (DNN) capable of approximating solutions to partial integro-differential equations while circumventing the curse of dimensionality. Using the Feynman-Kac theorem, we…
We propose a unified framework for delay differential equations (DDEs) based on deep neural networks (DNNs) - the neural delay differential equations (NDDEs), aimed at solving the forward and inverse problems of delay differential…
Recurrent neural networks have gained widespread use in modeling sequential data. Learning long-term dependencies using these models remains difficult though, due to exploding or vanishing gradients. In this paper, we draw connections…
Deep neural networks (DNN) have an impressive ability to invert very complex models, i.e. to learn the generative parameters from a model's output. Once trained, the forward pass of a DNN is often much faster than traditional,…
Learning with recurrent neural networks (RNNs) on long sequences is a notoriously difficult task. There are three major challenges: 1) complex dependencies, 2) vanishing and exploding gradients, and 3) efficient parallelization. In this…
The paper proposes a new testing approach for Deep Neural Networks (DNN) using gradient-free optimization to find perturbation chains that successfully falsify the tested DNN, going beyond existing grid-based or combinatorial testing.…
We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a…
We introduce an all-optical Diffractive Deep Neural Network (D2NN) architecture that can learn to implement various functions after deep learning-based design of passive diffractive layers that work collectively. We experimentally…
Deep neural networks (DNNs) play an important role in machine learning due to its outstanding performance compared to other alternatives. However, DNNs are not suitable for safety-critical applications since DNNs can be easily fooled by…
Deep neural networks (DNNs) have achieved the state of the art performance in numerous fields. However, DNNs need high computation times, and people always expect better performance in a lower computation. Therefore, we study the human…
Recent advances in solving ordinary differential equations (ODEs) with neural networks have been remarkable. Neural networks excel at serving as trial functions and approximating solutions within functional spaces, aided by gradient…
The computation and storage requirements for Deep Neural Networks (DNNs) are usually high. This issue limits their deployability on ubiquitous computing devices such as smart phones, wearables and autonomous drones. In this paper, we…
Deep neural networks (DNNs) depend on the storage of a large number of parameters, which consumes an important portion of the energy used during inference. This paper considers the case where the energy usage of memory elements can be…
We investigate the potential of applying (D)NN ((deep) neural networks) for approximating nonlinear mappings arising in the finite element discretization of nonlinear PDEs (partial differential equations). As an application, we apply the…
We introduce the Distributed-order fRActional Graph Operating Network (DRAGON), a novel continuous Graph Neural Network (GNN) framework that incorporates distributed-order fractional calculus. Unlike traditional continuous GNNs that utilize…
Deep Neural Networks (DNNs) require very large amounts of computation both for training and for inference when deployed in the field. Many different algorithms have been proposed to implement the most computationally expensive layers of…
Optical machine learning offers advantages in terms of power efficiency, scalability and computation speed. Recently, an optical machine learning method based on Diffractive Deep Neural Networks (D2NNs) has been introduced to execute a…
We present an architecture of a recurrent neural network (RNN) with a fully-connected deep neural network (DNN) as its feature extractor. The RNN is equipped with both causal temporal prediction and non-causal look-ahead, via…
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…