Related papers: Universal approximation property of ODENet and Res…
Approximation capability of reservoir systems whose reservoir is a recurrent neural network (RNN) is discussed. We show what we call uniform strong universality of RNN reservoir systems for a certain class of dynamical systems. This means…
The celebrated universal approximation theorems for neural networks roughly state that any reasonable function can be arbitrarily well-approximated by a network whose parameters are appropriately chosen real numbers. This paper examines the…
Deep residual networks (ResNets) made a recent breakthrough in deep learning. The core idea of ResNets is to have shortcut connections between layers that allow the network to be much deeper while still being easy to optimize avoiding…
We introduce the Universal Manipulation Policy Network (UMPNet) -- a single image-based policy network that infers closed-loop action sequences for manipulating arbitrary articulated objects. To infer a wide range of action trajectories,…
One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…
In this paper, we propose to provide a general ensemble learning framework based on deep learning models. Given a group of unit models, the proposed deep ensemble learning framework will effectively combine their learning results via a…
Recent advances in solving ordinary differential equations (ODEs) with neural networks have been remarkable. Neural networks excel at serving as trial functions and approximating solutions within functional spaces, aided by gradient…
Inspired by recent theoretical arguments, physics-informed echo state network (ESN) is discussed on the attempt to train a reservoir model absolutely in physics-informed manner. As the plainest work on such a purpose, an ODE (ordinary…
This paper concerns the universal approximation property with neural networks in variable Lebesgue spaces. We show that, whenever the exponent function of the space is bounded, every function can be approximated with shallow neural networks…
The study of universal approximation of arbitrary functions $f: \mathcal{X} \to \mathcal{Y}$ by neural networks has a rich and thorough history dating back to Kolmogorov (1957). In the case of learning finite dimensional maps, many authors…
The classical Universal Approximation Theorem holds for neural networks of arbitrary width and bounded depth. Here we consider the natural `dual' scenario for networks of bounded width and arbitrary depth. Precisely, let $n$ be the number…
Transformers have become the dominant architecture in modern machine learning, yet the theoretical understanding of their training dynamics remains limited. This paper develops a rigorous mathematical framework for analyzing gradient-based…
Accurate prediction of enzyme kinetic parameters is essential for understanding catalytic mechanisms and guiding enzyme engineering.However, existing deep learning-based enzyme-substrate interaction (ESI) predictors often exhibit…
Semantic segmentation is pixel-wise classification which retains critical spatial information. The "feature map reuse" has been commonly adopted in CNN based approaches to take advantage of feature maps in the early layers for the later…
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…
Deep neural operators (DNOs) have been utilized to approximate nonlinear mappings between function spaces. However, DNOs face the challenge of increased dimensionality and computational cost associated with unaligned observation data. In…
Deep learning architectures are highly diverse. To prove their universal approximation properties, existing works typically rely on model-specific proofs. Generally, they construct a dedicated mathematical formulation for each architecture…
Reaction-diffusion systems represent one of the most fundamental formulations used to describe a wide range of physical, chemical, and biological processes. With the increasing adoption of neural networks, recent research has focused on…
In this paper, we propose a deep neural network approximation to the evolution operator for time dependent PDE systems over long time period by recursively using one single neural network propagator, in the form of POD-DeepONet with…
Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…