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Recurrent neural networks are a powerful means to cope with time series. We show how autoregressive linear, i.e., linearly activated recurrent neural networks (LRNNs) can approximate any time-dependent function f(t). The approximation can…

Machine Learning · Computer Science 2025-10-01 Frieder Stolzenburg , Sandra Litz , Olivia Michael , Oliver Obst

In recent studies, linear recurrent neural networks (LRNNs) have achieved Transformer-level performance in natural language and long-range modeling, while offering rapid parallel training and constant inference cost. With the resurgence of…

Computation and Language · Computer Science 2024-04-10 Ting-Han Fan , Ta-Chung Chi , Alexander I. Rudnicky

Recurrent neural networks have gained widespread use in modeling sequential data. Learning long-term dependencies using these models remains difficult though, due to exploding or vanishing gradients. In this paper, we draw connections…

Machine Learning · Statistics 2019-02-27 Bo Chang , Minmin Chen , Eldad Haber , Ed H. Chi

Recurrent Neural Networks (RNNs) have been proven to be effective in modeling sequential data and they have been applied to boost a variety of tasks such as document classification, speech recognition and machine translation. Most of…

Computation and Language · Computer Science 2018-08-21 Zhiwei Wang , Yao Ma , Dawei Yin , Jiliang Tang

Deep Recurrent Neural Network architectures, though remarkably capable at modeling sequences, lack an intuitive high-level spatio-temporal structure. That is while many problems in computer vision inherently have an underlying high-level…

Computer Vision and Pattern Recognition · Computer Science 2016-04-12 Ashesh Jain , Amir R. Zamir , Silvio Savarese , Ashutosh Saxena

State-space models (SSMs) and transformers dominate the language modeling landscape. However, they are constrained to a lower computational complexity than classical recurrent neural networks (RNNs), limiting their expressivity. In…

Machine Learning · Computer Science 2025-06-13 Mark Schöne , Babak Rahmani , Heiner Kremer , Fabian Falck , Hitesh Ballani , Jannes Gladrow

Recurrent neural networks (RNNs) are a powerful model for sequential data. End-to-end training methods such as Connectionist Temporal Classification make it possible to train RNNs for sequence labelling problems where the input-output…

Neural and Evolutionary Computing · Computer Science 2013-03-26 Alex Graves , Abdel-rahman Mohamed , Geoffrey Hinton

Time series forecasting is prevalent in various real-world applications. Despite the promising results of deep learning models in time series forecasting, especially the Recurrent Neural Networks (RNNs), the explanations of time series…

Machine Learning · Computer Science 2023-08-29 Chaoqun Wang , Yijun Li , Xiangqian Sun , Qi Wu , Dongdong Wang , Zhixiang Huang

We present LrcSSM, a $\textit{non-linear}$ recurrent model that processes long sequences as fast as today's linear state-space layers. By forcing its Jacobian matrix to be diagonal, the full sequence can be solved in parallel, giving…

Machine Learning · Computer Science 2025-12-16 Mónika Farsang , Ramin Hasani , Daniela Rus , Radu Grosu

To understand the fundamental trade-offs between training stability, temporal dynamics and architectural complexity of recurrent neural networks~(RNNs), we directly analyze RNN architectures using numerical methods of ordinary differential…

Machine Learning · Computer Science 2019-05-01 Murphy Yuezhen Niu , Lior Horesh , Isaac Chuang

Deep learning (DL) in general and Recurrent neural networks (RNNs) in particular have seen high success levels in sequence based applications. This paper pertains to RNNs for time series modelling and forecasting. We propose a novel RNN…

Machine Learning · Computer Science 2022-07-12 Avinash Achar , Soumen Pachal

Recurrent Neural Networks (RNNs) have become the state-of-the-art choice for extracting patterns from temporal sequences. However, current RNN models are ill-suited to process irregularly sampled data triggered by events generated in…

Machine Learning · Computer Science 2016-11-01 Daniel Neil , Michael Pfeiffer , Shih-Chii Liu

Known as low energy consumption networks, spiking neural networks (SNNs) have gained a lot of attention within the past decades. While SNNs are increasing competitive with artificial neural networks (ANNs) for vision tasks, they are rarely…

Computation and Language · Computer Science 2024-12-25 Shuaijie Shen , Chao Wang , Renzhuo Huang , Yan Zhong , Qinghai Guo , Zhichao Lu , Jianguo Zhang , Luziwei Leng

This is a tutorial paper on Recurrent Neural Network (RNN), Long Short-Term Memory Network (LSTM), and their variants. We start with a dynamical system and backpropagation through time for RNN. Then, we discuss the problems of gradient…

Machine Learning · Computer Science 2023-04-25 Benyamin Ghojogh , Ali Ghodsi

Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…

Image captioning is a challenging task that combines the field of computer vision and natural language processing. A variety of approaches have been proposed to achieve the goal of automatically describing an image, and recurrent neural…

Computer Vision and Pattern Recognition · Computer Science 2018-05-24 Qingzhong Wang , Antoni B. Chan

The Linear Attention Recurrent Neural Network (LARNN) is a recurrent attention module derived from the Long Short-Term Memory (LSTM) cell and ideas from the consciousness Recurrent Neural Network (RNN). Yes, it LARNNs. The LARNN uses…

Machine Learning · Computer Science 2018-08-17 Guillaume Chevalier

Recent work has shown that convolutional networks can be substantially deeper, more accurate, and efficient to train if they contain shorter connections between layers close to the input and those close to the output. In this paper, we…

Computer Vision and Pattern Recognition · Computer Science 2018-01-30 Gao Huang , Zhuang Liu , Laurens van der Maaten , Kilian Q. Weinberger

Deep Learning networks have established themselves as providing state of art performance for semantic segmentation. These techniques are widely applied specifically to medical detection, segmentation and classification. The advent of the…

Image and Video Processing · Electrical Eng. & Systems 2021-02-02 Kaushik Dutta

Recurrent neural networks (RNN) as used in machine learning are commonly formulated in discrete time, i.e. as recursive maps. This brings a lot of advantages for training models on data, e.g. for the purpose of time series prediction or…

Dynamical Systems · Mathematics 2020-07-02 Zahra Monfared , Daniel Durstewitz