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In this paper, we explore some basic questions on the complexity of training neural networks with ReLU activation function. We show that it is NP-hard to train a two-hidden layer feedforward ReLU neural network. If dimension of the input…

Computational Complexity · Computer Science 2020-11-05 Digvijay Boob , Santanu S. Dey , Guanghui Lan

Recurrent Neural Networks are powerful machine learning frameworks that allow for data to be saved and referenced in a temporal sequence. This opens many new possibilities in fields such as handwriting analysis and speech recognition. This…

Machine Learning · Computer Science 2021-09-14 Joseph M. Ackerson , Dave Rushit , Seliya Jim

We study the problem of compressing recurrent neural networks (RNNs). In particular, we focus on the compression of RNN acoustic models, which are motivated by the goal of building compact and accurate speech recognition systems which can…

Computation and Language · Computer Science 2016-05-03 Rohit Prabhavalkar , Ouais Alsharif , Antoine Bruguier , Ian McGraw

Recurrent neural networks (RNNs) are powerful and effective for processing sequential data. However, RNNs are usually considered "black box" models whose internal structure and learned parameters are not interpretable. In this paper, we…

Machine Learning · Statistics 2016-11-23 Scott Wisdom , Thomas Powers , James Pitton , Les Atlas

We investigate the computational complexity of neural network verification in quantised settings. We distinguish three classes of Feedforward Neural Networks (FNNs): rational FNNs with exact rational weights, quantised FNNs whose weights…

Computational Complexity · Computer Science 2026-05-29 Eric Alsmann , Martin Lange , Marco Sälzer

Recurrent neural networks (RNNs), including long short-term memory (LSTM) RNNs, have produced state-of-the-art results on a variety of speech recognition tasks. However, these models are often too large in size for deployment on mobile…

Machine Learning · Computer Science 2016-04-12 Zhiyun Lu , Vikas Sindhwani , Tara N. Sainath

This paper aims to discuss and analyze the potentialities of Recurrent Neural Networks (RNN) in control design applications. The main families of RNN are considered, namely Neural Nonlinear AutoRegressive eXogenous, (NNARX), Echo State…

Systems and Control · Electrical Eng. & Systems 2022-05-11 Fabio Bonassi , Marcello Farina , Jing Xie , Riccardo Scattolini

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…

Computation and Language · Computer Science 2017-05-03 Juan Andrés Laura , Gabriel Masi , Luis Argerich

Over the past few years, neural networks have re-emerged as powerful machine-learning models, yielding state-of-the-art results in fields such as image recognition and speech processing. More recently, neural network models started to be…

Computation and Language · Computer Science 2015-10-06 Yoav Goldberg

The proliferation of large-scale and structurally complex data has spurred the integration of machine learning methods into statistical modeling. Recurrent neural networks (RNNs), a foundational class of models for time-dependent data, can…

Machine Learning · Statistics 2026-05-05 Yuxi Cai , Lan Li , Feiqing Huang , Guodong Li

Recurrent neural networks (RNNs) are powerful architectures to model sequential data, due to their capability to learn short and long-term dependencies between the basic elements of a sequence. Nonetheless, popular tasks such as speech or…

One of the fundamental principles of contemporary linguistics states that language processing requires the ability to extract recursively nested tree structures. However, it remains unclear whether and how this code could be implemented in…

Computation and Language · Computer Science 2021-01-08 Yair Lakretz , Théo Desbordes , Jean-Rémi King , Benoît Crabbé , Maxime Oquab , Stanislas Dehaene

Single-hidden layer feed forward neural networks (SLFNs) are widely used in pattern classification problems, but a huge bottleneck encountered is the slow speed and poor performance of the traditional iterative gradient-based learning…

Machine Learning · Computer Science 2019-10-28 Jie He , Tao Chen , Zhijun Zhang

We present recurrent transformer networks (RTNs) for obtaining dense correspondences between semantically similar images. Our networks accomplish this through an iterative process of estimating spatial transformations between the input…

Computer Vision and Pattern Recognition · Computer Science 2018-10-30 Seungryong Kim , Stephen Lin , Sangryul Jeon , Dongbo Min , Kwanghoon Sohn

Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep…

Methodology · Statistics 2018-02-08 Patrick L. McDermott , Christopher K. Wikle

Despite the tremendous empirical success of neural models in natural language processing, many of them lack the strong intuitions that accompany classical machine learning approaches. Recently, connections have been shown between…

Computation and Language · Computer Science 2018-08-29 Hao Peng , Roy Schwartz , Sam Thomson , Noah A. Smith

Random Neural Networks (RNNs) are a class of Neural Networks (NNs) that can also be seen as a specific type of queuing network. They have been successfully used in several domains during the last 25 years, as queuing networks to analyze the…

Neural and Evolutionary Computing · Computer Science 2016-09-19 Sebastián Basterrech , Gerardo Rubino

Recurrent neural networks (RNNs) are temporal networks and cumulative in nature that have shown promising results in various natural language processing tasks. Despite their success, it still remains a challenge to understand their hidden…

Computation and Language · Computer Science 2018-08-07 Pankaj Gupta , Hinrich Schütze

Recent work has shown that the training of a one-hidden-layer, scalar-output fully-connected ReLU neural network can be reformulated as a finite-dimensional convex program. Unfortunately, the scale of such a convex program grows…

Machine Learning · Computer Science 2021-05-27 Yatong Bai , Tanmay Gautam , Yu Gai , Somayeh Sojoudi

Recurrent neural networks (RNNs) have been successfully applied to various natural language processing (NLP) tasks and achieved better results than conventional methods. However, the lack of understanding of the mechanisms behind their…

Computation and Language · Computer Science 2017-10-31 Yao Ming , Shaozu Cao , Ruixiang Zhang , Zhen Li , Yuanzhe Chen , Yangqiu Song , Huamin Qu
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