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Effective activation functions introduce non-linear transformations, providing neural networks with stronger fitting capa-bilities, which help them better adapt to real data distributions. Huawei Noah's Lab believes that dynamic activation…

Neural networks can be trained to solve regression problems by using gradient-based methods to minimize the square loss. However, practitioners often prefer to reformulate regression as a classification problem, observing that training on…

In recent years, Quantum Machine Learning (QML) has increasingly captured the interest of researchers. Among the components in this domain, activation functions hold a fundamental and indispensable role. Our research focuses on the…

The mathematical complexity and high dimensionality of neural networks slow both training and deployment, demanding heavy computational resources. This has driven the search for alternative architectures built from novel components,…

In this article we study high-dimensional approximation capacities of shallow and deep artificial neural networks (ANNs) with the rectified linear unit (ReLU) activation. In particular, it is a key contribution of this work to reveal that…

Tremendous progress has been made in sequential processing with the recent advances in recurrent neural networks. However, recurrent architectures face the challenge of exploding/vanishing gradients during training, and require significant…

One of the most popular estimation methods in Bayesian neural networks (BNN) is mean-field variational inference (MFVI). In this work, we show that neural networks with ReLU activation function induce posteriors, that are hard to fit with…

Networks are widely used in many fields for their powerful ability to provide vivid representations of relationships between variables. However, many of them may be corrupted by experimental noise or inappropriate network inference methods…

The reason behind CNNs capability to learn high-dimensional complex features from the images is the non-linearity introduced by the activation function. Several advanced activation functions have been discovered to improve the training…

Most deep neural networks use simple, fixed activation functions, such as sigmoids or rectified linear units, regardless of domain or network structure. We introduce differential equation units (DEUs), an improvement to modern neural…

In recent years novel activation functions have been proposed to improve the performance of neural networks, and they show superior performance compared to the ReLU counterpart. However, there are environments, where the availability of…

Rectified linear units, or ReLUs, have become the preferred activation function for artificial neural networks. In this paper we consider two basic learning problems assuming that the underlying data follow a generative model based on a…

Many super-resolution (SR) models are optimized for high performance only and therefore lack efficiency due to large model complexity. As large models are often not practical in real-world applications, we investigate and propose novel loss…

Single image super-resolution (SISR) aims to recover the high-resolution (HR) image from its low-resolution (LR) input image. With the development of deep learning, SISR has achieved great progress. However, It is still a challenge to…

Federated learning (FL) enables multiple clients to collaboratively train machine learning models under the coordination of a central server, while maintaining privacy. However, the server cannot directly monitor the local training…

We present a Statistical Mechanics (SM) model of deep neural networks, connecting the energy-based and the feed forward networks (FFN) approach. We infer that FFN can be understood as performing three basic steps: encoding, representation…

Activation in deep neural networks is fundamental to achieving non-linear mappings. Traditional studies mainly focus on finding fixed activations for a particular set of learning tasks or model architectures. The research on flexible…

The performance of deep network learning strongly depends on the choice of the non-linear activation function associated with each neuron. However, deciding on the best activation is non-trivial, and the choice depends on the architecture,…

Neural networks are a powerful class of functions that can be trained with simple gradient descent to achieve state-of-the-art performance on a variety of applications. Despite their practical success, there is a paucity of results that…

Training deep neural networks is a challenging non-convex optimization problem. Recent work has proven that the strong duality holds (which means zero duality gap) for regularized finite-width two-layer ReLU networks and consequently…