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Neural networks are known to give better performance with increased depth due to their ability to learn more abstract features. Although the deepening of networks has been well established, there is still room for efficient feature…

Computer Vision and Pattern Recognition · Computer Science 2023-03-01 Dumindu Tissera , Rukshan Wijessinghe , Kasun Vithanage , Alex Xavier , Subha Fernando , Ranga Rodrigo

Deep Neural Networks (DNN) represent a performance-hungry application. Floating-Point (FP) and custom floating-point-like arithmetic satisfies this hunger. While there is need for speed, inference in DNNs does not seem to have any need for…

Machine Learning · Computer Science 2020-02-11 Christoph Lauter , Anastasia Volkova

Deep learning network training is usually computationally expensive and intuitively complex. We present a novel network architecture for custom training and weight evaluations. We reformulate the layers as ResNet-similar blocks with certain…

Computer Vision and Pattern Recognition · Computer Science 2020-07-15 Jishan Shaikh , Adya Sharma , Ankit Chouhan , Avinash Mahawar

This paper introduces a new parameterization of deep neural networks (both fully-connected and convolutional) with guaranteed $\ell^2$ Lipschitz bounds, i.e. limited sensitivity to input perturbations. The Lipschitz guarantees are…

Machine Learning · Computer Science 2023-06-07 Ruigang Wang , Ian R. Manchester

This article concerns the expressive power of depth in deep feed-forward neural nets with ReLU activations. Specifically, we answer the following question: for a fixed $d_{in}\geq 1,$ what is the minimal width $w$ so that neural nets with…

Machine Learning · Statistics 2018-03-13 Boris Hanin , Mark Sellke

In this work, we build a generic architecture of Convolutional Neural Networks to discover empirical properties of neural networks. Our first contribution is to introduce a state-of-the-art framework that depends upon few hyper parameters…

Computer Vision and Pattern Recognition · Computer Science 2017-03-07 Edouard Oyallon

Mixed-precision Deep Neural Networks achieve the energy efficiency and throughput needed for hardware deployment, particularly when the resources are limited, without sacrificing accuracy. However, the optimal per-layer bit precision that…

Machine Learning · Computer Science 2022-08-15 Mariam Rakka , Mohammed E. Fouda , Pramod Khargonekar , Fadi Kurdahi

We prove that for an $L$-layer fully-connected linear neural network, if the width of every hidden layer is $\tilde\Omega (L \cdot r \cdot d_{\mathrm{out}} \cdot \kappa^3 )$, where $r$ and $\kappa$ are the rank and the condition number of…

Machine Learning · Computer Science 2019-05-28 Simon S. Du , Wei Hu

We propose a new technique that boosts the convergence of training generative adversarial networks. Generally, the rate of training deep models reduces severely after multiple iterations. A key reason for this phenomenon is that a deep…

Machine Learning · Statistics 2018-06-15 Atsushi Nitanda , Taiji Suzuki

Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…

Machine Learning · Computer Science 2022-04-20 German Magai , Anton Ayzenberg

Recent work has focused on combining kernel methods and deep learning to exploit the best of the two approaches. Here, we introduce a new architecture of neural networks in which we replace the top dense layers of standard convolutional…

Machine Learning · Computer Science 2019-12-02 Luc Giffon , Stéphane Ayache , Thierry Artières , Hachem Kadri

Deep neural networks have a good success record and are thus viewed as the best architecture choice for complex applications. Their main shortcoming has been, for a long time, the vanishing gradient which prevented the numerical…

Machine Learning · Computer Science 2024-05-02 Bernhard Bermeitinger , Tomas Hrycej , Siegfried Handschuh

Question Answering with NLP has progressed through the evolution of advanced model architectures like BERT and BiDAF and earlier word, character, and context-based embeddings. As BERT has leapfrogged the accuracy of models, an element of…

Computation and Language · Computer Science 2021-09-02 Soumyendu Sarkar

How can we design neural networks that allow for stable universal approximation of maps between topologically interesting manifolds? The answer is with a coordinate projection. Neural networks based on topological data analysis (TDA) use…

Machine Learning · Computer Science 2022-10-04 Michael Puthawala , Matti Lassas , Ivan Dokmanic , Pekka Pankka , Maarten de Hoop

This paper investigates the approximation properties of deep neural networks with piecewise-polynomial activation functions. We derive the required depth, width, and sparsity of a deep neural network to approximate any H\"{o}lder smooth…

Numerical Analysis · Mathematics 2022-12-06 Denis Belomestny , Alexey Naumov , Nikita Puchkin , Sergey Samsonov

The reconstruction of a discrete surface from a point cloud is a fundamental geometry processing problem that has been studied for decades, with many methods developed. We propose the use of a deep neural network as a geometric prior for…

Computer Vision and Pattern Recognition · Computer Science 2019-04-08 Francis Williams , Teseo Schneider , Claudio Silva , Denis Zorin , Joan Bruna , Daniele Panozzo

Deep neural networks (DNNs) have significantly advanced machine learning, with model depth playing a central role in their successes. The dynamical system modeling approach has recently emerged as a powerful framework, offering new…

Machine Learning · Computer Science 2026-02-25 Jinshu Huang , Mingfei Sun , Chunlin Wu

We develop a new method for regularising neural networks. We learn a probability distribution over the activations of all layers of the model and then insert imputed values into the network during training. We obtain a posterior for an…

Machine Learning · Computer Science 2019-10-14 Matthew Willetts , Alexander Camuto , Stephen Roberts , Chris Holmes

The optimization foundations of deep linear networks have recently received significant attention. However, due to their inherent non-convexity and hierarchical structure, analyzing the loss functions of deep linear networks remains a…

Optimization and Control · Mathematics 2025-09-24 Po Chen , Rujun Jiang , Peng Wang

This paper investigates the foundations of deep learning through insight of geometry, algebra and differential calculus. At is core, artificial intelligence relies on assumption that data and its intrinsic structure can be embedded into…

Differential Geometry · Mathematics 2025-10-22 Tsemo Aristide