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The training complexity of deep learning-based channel decoders scales exponentially with the codebook size and therefore with the number of information bits. Thus, neural network decoding (NND) is currently only feasible for very short…

To unleash the potential of quantum computers, noise effects on qubits' performance must be carefully managed. The decoders responsible for diagnosing noise-induced computational errors must use resources efficiently to enable scaling to…

Training deep neural networks on large datasets containing high-dimensional data requires a large amount of computation. A solution to this problem is data-parallel distributed training, where a model is replicated into several…

Surface codes reach high error thresholds when decoded with known algorithms, but the decoding time will likely exceed the available time budget, especially for near-term implementations. To decrease the decoding time, we reduce the…

High-order tensor decomposition has been widely adopted to obtain compact deep neural networks for edge deployment. However, existing studies focus primarily on its algorithmic advantages such as accuracy and compression ratio-while…

In this paper we propose a deep neural network model with an encoder-decoder architecture that translates images of math formulas into their LaTeX markup sequences. The encoder is a convolutional neural network (CNN) that transforms images…

We propose a novel \textit{capsule} based deep encoder-decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting Capsule Network (CapsNet)…

Finding efficient decoders for quantum error correcting codes adapted to realistic experimental noise in fault-tolerant devices represents a significant challenge. In this paper we introduce several decoding algorithms complemented by deep…

Many systems of partial differential equations have been proposed as simplified representations of complex collective behaviours in large networks of neurons. In this survey, we briefly discuss their derivations and then review the…

We present a novel discontinuous Galerkin algorithm for the solution of a class of Fokker-Planck collision operators. These operators arise in many fields of physics, and our particular application is for kinetic plasma simulations. In…

For problems in image processing and many other fields, a large class of effective neural networks has encoder-decoder-based architectures. Although these networks have made impressive performances, mathematical explanations of their…

When simulating partial differential equations, hybrid solvers combine coarse numerical solvers with learned correctors. They promise accelerated simulations while adhering to physical constraints. However, as shown in our theoretical…

We address the computational barrier of deploying advanced deep learning segmentation models in clinical settings by studying the efficacy of network compression through tensor decomposition. We propose a post-training Tucker factorization…

In the design of engineered components, rigorous vibration testing is essential for performance validation and identification of resonant frequencies and amplitudes encountered during operation. Performing this evaluation numerically via…

Neural operators have shown remarkable performance in approximating solutions of partial differential equations. However, their convergence behavior under grid refinement is still not well understood from the viewpoint of numerical…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

Deep learning algorithms are a key component of many state-of-the-art vision systems, especially as Convolutional Neural Networks (CNN) outperform most solutions in the sense of accuracy. To apply such algorithms in real-time applications,…

Semantic segmentation remains a computationally intensive algorithm for embedded deployment even with the rapid growth of computation power. Thus efficient network design is a critical aspect especially for applications like automated…

Recently, deep learning methods have shown significant improvements in communication systems. In this paper, we study the equalization problem over the nonlinear channel using neural networks. The joint equalizer and decoder based on neural…

As machine learning is applied to an increasing variety of complex problems, which are defined by high dimensional and complex data sets, the necessity for task oriented feature learning grows in importance. With the advancement of Deep…