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Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. However, most scholars agree that a convincing theoretical…
While deep learning algorithms demonstrate a great potential in scientific computing, its application to multi-scale problems remains to be a big challenge. This is manifested by the "frequency principle" that neural networks tend to learn…
This paper presents a numerical compression strategy for the boundary integral equation of acoustic scattering in two dimensions. These equations have oscillatory kernels that we represent in a basis of wave atoms, and compress by…
Beyond the scope of conventional metasurface which necessitates plenty of computational resources and time, an inverse design approach using machine learning algorithms promises an effective way for metasurfaces design. In this paper,…
Spiking neural network (SNN) is interesting both theoretically and practically because of its strong bio-inspiration nature and potentially outstanding energy efficiency. Unfortunately, its development has fallen far behind the conventional…
We propose a novel deep learning tool in order to study the evolution of dark energy models. The aim is to combine two architectures: the Recurrent Neural Networks (RNN) and the Bayesian Neural Networks (BNN), we named this full network as…
In the past decade, significant strides in deep learning have led to numerous groundbreaking applications. Despite these advancements, the understanding of the high generalizability of deep learning, especially in such an over-parametrized…
This article contributes to the current statistical theory of deep neural networks (DNNs). It was shown that DNNs are able to circumvent the so--called curse of dimensionality in case that suitable restrictions on the structure of the…
Analog computing has reemerged as a promising avenue for accelerating deep neural networks (DNNs) due to its potential to overcome the energy efficiency and scalability challenges posed by traditional digital architectures. However,…
In this work, we consider the approximation of parametric maps using the so-called Galerkin POD-NN method. This technique combines the computation of a reduced basis via proper orthogonal decomposition (POD) and artificial neural networks…
In this paper, we construct approximated solutions of Differential Equations (DEs) using the Deep Neural Network (DNN). Furthermore, we present an architecture that includes the process of finding model parameters through experimental data,…
For Deep Neural Networks (DNNs) to become useful in safety-critical applications, such as self-driving cars and disease diagnosis, they must be stable to perturbations in input and model parameters. Characterizing the sensitivity of a DNN…
We show expression rates and stability in Sobolev norms of deep feedforward ReLU neural networks (NNs) in terms of the number of parameters defining the NN for continuous, piecewise polynomial functions, on arbitrary, finite partitions…
We present a new deep-neural-network (DNN) based error correction code for fading channels with output feedback, called deep SNR-robust feedback (DRF) code. At the encoder, parity symbols are generated by a long short term memory (LSTM)…
Deep Neural Networks (DNNs) have emerged as a powerful mechanism and are being increasingly deployed in real-world safety-critical domains. Despite the widespread success, their complex architecture makes proving any formal guarantees about…
We propose a deep beamforming framework for enhancing target speaker(s) in multi-speaker environments. A deep neural network (DNN) is trained to estimate beamforming weights directly from noisy multichannel inputs while satisfying linear…
Deep neural networks (DNNs), particularly those using Rectified Linear Unit (ReLU) activation functions, have achieved remarkable success across diverse machine learning tasks, including image recognition, audio processing, and language…
Deep neural networks (DNN) have been a de facto standard for nowadays biometric recognition solutions. A serious, but still overlooked problem in these DNN-based recognition systems is their vulnerability against adversarial attacks.…
We introduce a method to reconstruct the kinematics of neutral-current deep inelastic scattering (DIS) using a deep neural network (DNN). Unlike traditional methods, it exploits the full kinematic information of both the scattered electron…
Recent achievements in end-to-end deep learning have encouraged the exploration of tasks dealing with highly structured data with unified deep network models. Having such models for compressing audio signals has been challenging since it…