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Recently, neural networks in machine learning use rectified linear units (ReLUs) in early processing layers for better performance. Training these structures sometimes results in "dying ReLU units" with near-zero outputs. We first explore…

We propose the Hyperbolic Tangent Exponential Linear Unit (TeLU), a neural network hidden activation function defined as TeLU(x)=xtanh(exp(x)). TeLU's design is grounded in the core principles of key activation functions, achieving strong…

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…

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…

Sequence learning is dominated by Transformers and parallelizable recurrent neural networks (RNNs) such as state-space models, yet learning long-term dependencies remains challenging, and state-of-the-art designs trade power consumption for…

We consider neural networks with rational activation functions. The choice of the nonlinear activation function in deep learning architectures is crucial and heavily impacts the performance of a neural network. We establish optimal bounds…

Sequence modeling is a critical yet challenging task with wide-ranging applications, especially in time series forecasting for domains like weather prediction, temperature monitoring, and energy load forecasting. Transformers, with their…

How can local-search methods such as stochastic gradient descent (SGD) avoid bad local minima in training multi-layer neural networks? Why can they fit random labels even given non-convex and non-smooth architectures? Most existing theory…

Fault-tolerant Quantum Processing Units (QPUs) promise to deliver exponential speed-ups in select computational tasks, yet their integration into modern deep learning pipelines remains unclear. In this work, we take a step towards bridging…

Recently, Convolutional Neural Networks (CNNs) have shown promising performance in super-resolution (SR). However, these methods operate primarily on Low Resolution (LR) inputs for memory efficiency but this limits, as we demonstrate, their…

Deep neural networks, particularly those employing Rectified Linear Units (ReLU), are often perceived as complex, high-dimensional, non-linear systems. This complexity poses a significant challenge to understanding their internal learning…

Accurate emotion classification for online reviews is vital for business organizations to gain deeper insights into markets. Although deep learning has been successfully implemented in this area, accuracy and processing time are still major…

Two networks are equivalent if they produce the same output for any given input. In this paper, we study the possibility of transforming a deep neural network to another network with a different number of units or layers, which can be…

Deep learning, and in particular Recurrent Neural Networks (RNN) have shown superior accuracy in a large variety of tasks including machine translation, language understanding, and movie frame generation. However, these deep learning…

Neural network frameworks such as PyTorch and TensorFlow are the workhorses of numerous machine learning applications ranging from object recognition to machine translation. While these frameworks are versatile and straightforward to use,…

Most of convolutional neural networks share the same characteristic: each convolutional layer is followed by a nonlinear activation layer where Rectified Linear Unit (ReLU) is the most widely used. In this paper, we argue that the designed…

In this paper we investigate the family of functions representable by deep neural networks (DNN) with rectified linear units (ReLU). We give an algorithm to train a ReLU DNN with one hidden layer to *global optimality* with runtime…

Gated Linear Units (GLUs) have become essential components in the feed-forward networks of state-of-the-art Large Language Models (LLMs). However, they require twice as many memory reads compared to feed-forward layers without gating, due…

In recent years, the computational demands of deep learning applications have necessitated the introduction of energy-efficient hardware accelerators. Optical neural networks are a promising option; however, thus far they have been largely…

Tensor Core Units (TCUs) are hardware accelerators developed for deep neural networks, which efficiently support the multiplication of two dense $\sqrt{m}\times \sqrt{m}$ matrices, where $m$ is a given hardware parameter. In this paper, we…