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As the emerging field of machine learning, deep learning shows excellent ability in solving complex learning problems. However, the size of the networks becomes increasingly large scale due to the demands of the practical applications,…

Implicit deep learning has received increasing attention recently due to the fact that it generalizes the recursive prediction rules of many commonly used neural network architectures. Its prediction rule is provided implicitly based on the…

The paper briefy reviews several recent results on hierarchical architectures for learning from examples, that may formally explain the conditions under which Deep Convolutional Neural Networks perform much better in function approximation…

The Rectified Power Unit (RePU) activation function, a differentiable generalization of the Rectified Linear Unit (ReLU), has shown promise in constructing neural networks due to its smoothness properties. However, deep RePU networks often…

Recurrent Neural Networks (RNNs) are used in applications that learn dependencies in data sequences, such as speech recognition, human activity recognition, and anomaly detection. In recent years, newer RNN variants, such as GRUs and LSTMs,…

We introduce SPLASH units, a class of learnable activation functions shown to simultaneously improve the accuracy of deep neural networks while also improving their robustness to adversarial attacks. SPLASH units have both a simple…

Deep neural network with rectified linear units (ReLU) is getting more and more popular recently. However, the derivatives of the function represented by a ReLU network are not continuous, which limit the usage of ReLU network to situations…

Convolutional neural network (CNN) is a class of artificial neural networks widely used in computer vision tasks. Most CNNs achieve excellent performance by stacking certain types of basic units. In addition to increasing the depth and…

Deep networks are gradually penetrating almost every domain in our lives due to their amazing success. However, with substantive performance accuracy improvements comes the price of \emph{irreproducibility}. Two identical models, trained on…

Recurrent Neural Networks (RNN) are known as powerful models for handling sequential data, and especially widely utilized in various natural language processing tasks. In this paper, we propose Contextual Recurrent Units (CRU) for enhancing…

We study layered neural networks of rectified linear units (ReLU) in a modelling framework for stochastic training processes. The comparison with sigmoidal activation functions is in the center of interest. We compute typical learning…

Layer normalization (LayerNorm) has been successfully applied to various deep neural networks to help stabilize training and boost model convergence because of its capability in handling re-centering and re-scaling of both inputs and weight…

In this paper, we introduce the Hyperbolic Tangent Exponential Linear Unit (TeLU), a novel neural network activation function, represented as $f(x) = x{\cdot}tanh(e^x)$. TeLU is designed to overcome the limitations of conventional…

Recently, a new recurrent neural network (RNN) named the Legendre Memory Unit (LMU) was proposed and shown to achieve state-of-the-art performance on several benchmark datasets. Here we leverage the linear time-invariant (LTI) memory…

The large number of ReLU non-linearity operations in existing deep neural networks makes them ill-suited for latency-efficient private inference (PI). Existing techniques to reduce ReLU operations often involve manual effort and sacrifice…

In this paper, a novel multi-head multi-layer perceptron (MLP) structure is presented for implicit neural representation (INR). Since conventional rectified linear unit (ReLU) networks are shown to exhibit spectral bias towards learning…

Recent results in nonparametric regression show that deep learning, i.e., neural network estimates with many hidden layers, are able to circumvent the so-called curse of dimensionality in case that suitable restrictions on the structure of…

In this letter, we investigate the discrete phase shift design of the intelligent reflecting surface (IRS) in a time division duplexing (TDD) multi-user multiple input multiple output (MIMO) system.We modify the design of deep reinforcement…

We theoretically discuss why deep neural networks (DNNs) performs better than other models in some cases by investigating statistical properties of DNNs for non-smooth functions. While DNNs have empirically shown higher performance than…

The impressive expressive power of deep neural networks (DNNs) underlies their widespread applicability. However, while the theoretical capacity of deep architectures is high, the practical expressive power achieved through successful…