Related papers: A comparison of rational and neural network based …
We study the computational complexity of (deterministic or randomized) algorithms based on point samples for approximating or integrating functions that can be well approximated by neural networks. Such algorithms (most prominently…
Deep neural networks have achieved substantial success across various scientific computing tasks. A pivotal challenge within this domain is the rapid and parallel approximation of matrix inverses, critical for numerous applications. Despite…
Recent advances in neuroscience have revealed many principles about neural processing. In particular, many biological systems were found to reconfigure/recruit single neurons to generate multiple kinds of decisions. Such findings have the…
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…
Answering complex questions that require multi-step multi-type reasoning over raw text is challenging, especially when conducting numerical reasoning. Neural Module Networks(NMNs), follow the programmer-interpreter framework and design…
Deep neural networks have achieved success across a wide range of applications, including as models of human behavior and neural representations in vision tasks. However, neural network training and human learning differ in fundamental…
In recent studies [1][13][12] Recurrent Neural Networks were used for generative processes and their surprising performance can be explained by their ability to create good predictions. In addition, data compression is also based on…
Recent advances in machine learning have led to a surge in adoption of neural networks for various tasks, but lack of interpretability remains an issue for many others in which an understanding of the features influencing the prediction is…
Two neural-network-based numerical schemes are proposed to solve the classical obstacle problems. The schemes are based on the universal approximation property of neural networks, and the cost functions are taken as the energy minimization…
The layered structure of deep neural networks hinders the use of numerous analysis tools and thus the development of its interpretability. Inspired by the success of functional brain networks, we propose a novel framework for…
Neural networks are known to be effective function approximators. Recently, deep neural networks have proven to be very effective in pattern recognition, classification tasks and human-level control to model highly nonlinear realworld…
One of the arguments to explain the success of deep learning is the powerful approximation capacity of deep neural networks. Such capacity is generally accompanied by the explosive growth of the number of parameters, which, in turn, leads…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
The scientific community is able to present a new set of solutions to practical problems that substantially improve the performance of modern technology in terms of efficiency and speed of computation due to the advancement in neural…
Neural network-based function approximation plays a pivotal role in the advancement of scientific computing and machine learning. Yet, training such models faces several challenges: (i) each target function often requires training a new…
Recent years have witnessed the great success of deep neural networks in many research areas. The fundamental idea behind the design of most neural networks is to learn similarity patterns from data for prediction and inference, which lacks…
We show that suitably regular functions can be approximated in the $\mathcal{C}^1$-norm both with rational functions and rational neural networks, including approximation rates with respect to width and depth of the network, and degree of…
Artificial neural networks (ANNs) perform extraordinarily on numerous tasks including classification or prediction, e.g., speech processing and image classification. These new functions are based on a computational model that is enabled to…
Neural networks have achieved success in a wide array of perceptual tasks but often fail at tasks involving both perception and higher-level reasoning. On these more challenging tasks, bespoke approaches (such as modular symbolic…
Artificial Neural Networks are powerful function approximators capable of modelling solutions to a wide variety of problems, both supervised and unsupervised. As their size and expressivity increases, so too does the variance of the model,…