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Despite the success of neural networks (NNs), there is still a concern among many over their "black box" nature. Why do they work? Here we present a simple analytic argument that NNs are in fact essentially polynomial regression models.…

Machine Learning · Computer Science 2019-04-11 Xi Cheng , Bohdan Khomtchouk , Norman Matloff , Pete Mohanty

Deep Neural Networks (DNNs) are a revolutionary force in the ongoing information revolution, and yet their intrinsic properties remain a mystery. In particular, it is widely known that DNNs are highly sensitive to noise, whether adversarial…

Machine Learning · Computer Science 2020-05-01 Netanel Raviv , Siddharth Jain , Pulakesh Upadhyaya , Jehoshua Bruck , Anxiao Jiang

Linear recurrent neural networks (LRNNs) provide a structured approach to sequence modeling that bridges classical linear dynamical systems and modern deep learning, offering both expressive power and theoretical guarantees on stability and…

In this paper we describe the implementation of semi-structured deep distributional regression, a flexible framework to learn conditional distributions based on the combination of additive regression models and deep networks. Our…

We propose a novel class of neural network-like parametrized functions, i.e., general transformation neural networks (GTNNs), for high-dimensional approximation. Conventional deep neural networks sometimes perform less accurately on…

Numerical Analysis · Mathematics 2026-02-25 Xiaoyang Wang , Yiqi Gu

Deep Neural Networks (DNN) have been widely employed in industry to address various Natural Language Processing (NLP) tasks. However, many engineers find it a big overhead when they have to choose from multiple frameworks, compare different…

Computation and Language · Computer Science 2019-10-21 Ming Gong , Linjun Shou , Wutao Lin , Zhijie Sang , Quanjia Yan , Ze Yang , Feixiang Cheng , Daxin Jiang

During the last decade, deep neural networks (DNN) have demonstrated impressive performances solving a wide range of problems in various domains such as medicine, finance, law, etc. Despite their great performances, they have long been…

Machine Learning · Computer Science 2020-10-13 Jiechieu Kameni Florentin Flambeau , Tsopze Norbert

Deep Neural Networks (DNNs) are rapidly gaining popularity in a variety of important domains. Formally, DNNs are complicated vector-valued functions which come in a variety of sizes and applications. Unfortunately, modern DNNs have been…

Machine Learning · Computer Science 2021-01-12 Matthew Sotoudeh , Aditya V. Thakur

Reservoir Computing Networks (RCNs) belong to a group of machine learning techniques that project the input space non-linearly into a high-dimensional feature space, where the underlying task can be solved linearly. Popular variants of RCNs…

Machine Learning · Computer Science 2022-05-31 Peter Steiner , Azarakhsh Jalalvand , Simon Stone , Peter Birkholz

Equivariant Graph Neural Networks (GNNs) have demonstrated significant success across various applications. To achieve completeness -- that is, the universal approximation property over the space of equivariant functions -- the network must…

Machine Learning · Computer Science 2025-10-16 Jiacheng Cen , Anyi Li , Ning Lin , Tingyang Xu , Yu Rong , Deli Zhao , Zihe Wang , Wenbing Huang

Feedforward neural networks (FNNs) can be viewed as non-linear regression models, where covariates enter the model through a combination of weighted summations and non-linear functions. Although these models have some similarities to the…

Methodology · Statistics 2024-05-02 Andrew McInerney , Kevin Burke

In traditional software programs, it is easy to trace program logic from variables back to input, apply assertion statements to block erroneous behavior, and compose programs together. Although deep learning programs have demonstrated…

Machine Learning · Computer Science 2021-10-27 Mike Wu , Noah Goodman , Stefano Ermon

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.…

Computer Vision and Pattern Recognition · Computer Science 2018-05-29 Mengnan Du , Ninghao Liu , Qingquan Song , Xia Hu

Deep Learning is considered to be a quite young in the area of machine learning research, found its effectiveness in dealing complex yet high dimensional dataset that includes but limited to images, text and speech etc. with multiple levels…

Computer Vision and Pattern Recognition · Computer Science 2016-10-19 Mrutyunjaya Panda

Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of…

Computer Vision and Pattern Recognition · Computer Science 2022-07-29 Yufei Hu , Nacim Belkhir , Jesus Angulo , Angela Yao , Gianni Franchi

The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose…

Machine Learning · Statistics 2020-07-16 Zhirui Hu , Zheng Tracy Ke , Jun S Liu

Neural networks are powerful function estimators, leading to their status as a paradigm of choice for modeling structured data. However, unlike other structured representations that emphasize the modularity of the problem -- e.g., factor…

Machine Learning · Computer Science 2022-06-20 Tsvetomila Mihaylova , Vlad Niculae , André F. T. Martins

In this paper, we introduce SciANN, a Python package for scientific computing and physics-informed deep learning using artificial neural networks. SciANN uses the widely used deep-learning packages Tensorflow and Keras to build deep neural…

Other Computer Science · Computer Science 2020-12-30 Ehsan Haghighat , Ruben Juanes

A challenging problem in many modern machine learning tasks is to process weight-space features, i.e., to transform or extract information from the weights and gradients of a neural network. Recent works have developed promising…

Machine Learning · Computer Science 2024-02-09 Allan Zhou , Chelsea Finn , James Harrison

Deep learning models have achieved state-of-the-art performance in many classification tasks. However, most of them cannot provide an interpretation for their classification results. Machine learning models that are interpretable are…

Machine Learning · Computer Science 2021-11-04 Miles Q. Li , Benjamin C. M. Fung , Adel Abusitta