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We study approximation and statistical learning properties of deep ReLU networks under structural assumptions that mitigate the curse of dimensionality. We prove minimax-optimal uniform approximation rates for $s$-H\"older smooth functions…

Artificial neural networks have achieved great success in many fields ranging from image recognition to video understanding. However, its high requirements for computing and memory resources have limited further development on processing…

Since real-world objects and their interactions are often multi-modal and multi-typed, heterogeneous networks have been widely used as a more powerful, realistic, and generic superclass of traditional homogeneous networks (graphs).…

This paper briefly analyzes the advantages and problems of AI mainstream technology and puts forward: To achieve stronger Artificial Intelligence, the end-to-end function calculation must be changed and adopt the technology system centered…

Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness. Most existing function approximation…

The empirical success of deep convolutional networks on tasks involving high-dimensional data such as images or audio suggests that they can efficiently approximate certain functions that are well-suited for such tasks. In this paper, we…

Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…

The design of compact deep neural networks is a crucial task to enable widespread adoption of deep neural networks in the real-world, particularly for edge and mobile scenarios. Due to the time-consuming and challenging nature of manually…

The success of deep neural networks (DNN) in machine perception applications such as image classification and speech recognition comes at the cost of high computation and storage complexity. Inference of uncompressed large scale DNN models…

Convolutional neural networks (CNNs) have been successfully applied to many recognition and learning tasks using a universal recipe; training a deep model on a very large dataset of supervised examples. However, this approach is rather…

In recent years, deep learning-based image compressive sensing (ICS) methods have achieved brilliant success. Many optimization-inspired networks have been proposed to bring the insights of optimization algorithms into the network structure…

Many approaches such as Quine-McCluskey algorithm, Karnaugh map solving, Petrick's method and McBoole's method have been devised to simplify Boolean expressions in order to optimize hardware implementation of digital circuits. However, the…

We propose o1Neuro, a new neural network model built on sparse indicator activation neurons, with two key statistical properties. (1) Constructive universal approximation: At the population level, a deep o1Neuro can approximate any…

In this paper, a universal approximation theorem (UAT) for shallow neural networks whose inputs belong to a topological vector space (TVS) and whose outputs take values in a Hausdorff locally convex TVS is established. The networks are…

Complex networks pervade various real-world systems, from the natural environment to human societies. The essence of these networks is in their ability to transition and evolve from microscopic disorder-where network topology and node…

We propose stochastic, non-parametric activation functions that are fully learnable and individual to each neuron. Complexity and the risk of overfitting are controlled by placing a Gaussian process prior over these functions. The result is…

Leveraging the infinite dimensional neural network architecture we proposed in arXiv:2109.13512v4 and which can process inputs from Fr\'echet spaces, and using the universal approximation property shown therein, we now largely extend the…

The universal approximation theorem is generalised to uniform convergence on the (noncompact) input space $\mathbb{R}^n$. All continuous functions that vanish at infinity can be uniformly approximated by neural networks with one hidden…

Understanding and predicting the human visual attentional mechanism is an active area of research in the fields of neuroscience and computer vision. In this work, we propose DeepFix, a first-of-its-kind fully convolutional neural network…

Capsule Network is a promising concept in deep learning, yet its true potential is not fully realized thus far, providing sub-par performance on several key benchmark datasets with complex data. Drawing intuition from the success achieved…