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Recurrent neural networks (RNNs) such as Long Short Term Memory (LSTM) networks have become popular in a variety of applications such as image processing, data classification, speech recognition, and as controllers in autonomous systems. In…

Nowadays, neural network models achieve state-of-the-art results in many areas as computer vision or speech processing. For sequential data, especially for Natural Language Processing (NLP) tasks, Recurrent Neural Networks (RNNs) and their…

Modelling long-term dependencies is a challenge for recurrent neural networks. This is primarily due to the fact that gradients vanish during training, as the sequence length increases. Gradients can be attenuated by transition operators…

Deep Neural Networks (DNNs) have provably enhanced the state-of-the-art Neural Machine Translation (NMT) with their capability in modeling complex functions and capturing complex linguistic structures. However NMT systems with deep…

Recurrent Neural Networks (RNNs) with Long Short-Term Memory units (LSTM) are widely used because they are expressive and are easy to train. Our interest lies in empirically evaluating the expressiveness and the learnability of LSTMs in the…

Countless learning tasks require dealing with sequential data. Image captioning, speech synthesis, and music generation all require that a model produce outputs that are sequences. In other domains, such as time series prediction, video…

We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems modulated via nonlinear…

State-space models (SSMs) are a class of networks for sequence learning that benefit from fixed state size and linear complexity with respect to sequence length, contrasting the quadratic scaling of typical attention mechanisms. Inspired…

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…

A key attribute that drives the unprecedented success of modern Recurrent Neural Networks (RNNs) on learning tasks which involve sequential data, is their ability to model intricate long-term temporal dependencies. However, a well…

Long-sequence state-space models (SSMs) such as Hyena and Mamba replace the quadratic complexity of self-attention with more efficient FFT and scan operations. However, modern accelerators like GPUs are poorly suited to these non-GEMM…

State space models (SSMs) have emerged as a powerful framework for modelling long-range dependencies in sequence data. Unlike traditional recurrent neural networks (RNNs) and convolutional neural networks (CNNs), SSMs offer a structured and…

Advanced deep learning architectures, particularly recurrent neural networks (RNNs), have been widely applied in audio, bioacoustic, and biomedical signal analysis, especially in data-scarce environments. While gated RNNs remain effective,…

Foundation models, now powering most of the exciting applications in deep learning, are almost universally based on the Transformer architecture and its core attention module. Many subquadratic-time architectures such as linear attention,…

In this work, we first analyze the memory behavior in three recurrent neural networks (RNN) cells; namely, the simple RNN (SRN), the long short-term memory (LSTM) and the gated recurrent unit (GRU), where the memory is defined as a function…

Long short-term memory (LSTM) recurrent neural networks (RNNs) have been shown to give state-of-the-art performance on many speech recognition tasks, as they are able to provide the learned dynamically changing contextual window of all…

Recurrent Neural Networks (RNNs) and their variants, such as Long-Short Term Memory (LSTM) networks, and Gated Recurrent Unit (GRU) networks, have achieved promising performance in sequential data modeling. The hidden layers in RNNs can be…

We develop a formal hierarchy of the expressive capacity of RNN architectures. The hierarchy is based on two formal properties: space complexity, which measures the RNN's memory, and rational recurrence, defined as whether the recurrent…

Recurrent neural networks (RNNs) notoriously struggle to learn long-term memories, primarily due to vanishing and exploding gradients. The recent success of state-space models (SSMs), a subclass of RNNs, to overcome such difficulties…

Speech recognition is largely taking advantage of deep learning, showing that substantial benefits can be obtained by modern Recurrent Neural Networks (RNNs). The most popular RNNs are Long Short-Term Memory (LSTMs), which typically reach…