Related papers: A General Method for Proving Networks Universal Ap…

Complex-valued neural networks have attracted increasing attention in recent years, while it remains open on the advantages of complex-valued neural networks in comparison with real-valued networks. This work takes one step on this…

Deep Matching (DM) is a popular high-quality method for quasi-dense image matching. Despite its name, however, the original DM formulation does not yield a deep neural network that can be trained end-to-end via backpropagation. In this…

It is well known that Artificial Neural Networks are universal approximators. The classical result proves that, given a continuous function on a compact set on an n-dimensional space, then there exists a one-hidden-layer feedforward network…

Due to the widespread use of complex machine learning models in real-world applications, it is becoming critical to explain model predictions. However, these models are typically black-box deep neural networks, explained post-hoc via…

We establish fundamental mathematical limits on universal approximation theorem (UAT) system alignment by proving that catastrophic failures are an inescapable feature of any useful computational system. Our central thesis is that for any…

Quantum machine learning (QML), as an interdisciplinary field bridging quantum computing and machine learning, has garnered significant attention in recent years. Currently, the field as a whole faces challenges due to incomplete…

We investigate the expressive power of deep residual neural networks idealized as continuous dynamical systems through control theory. Specifically, we consider two properties that arise from supervised learning, namely universal…

Universal approximation theorems are the foundations of classical neural networks, providing theoretical guarantees that the latter are able to approximate maps of interest. Recent results have shown that this can also be achieved in a…

As deep learning applications continue to become more diverse, an interesting question arises: Can general problem solving arise from jointly learning several such diverse tasks? To approach this question, deep multi-task learning is…

The classical universal approximation (UA) theorem for neural networks establishes mild conditions under which a feedforward neural network can approximate a continuous function $f$ with arbitrary accuracy. A recent result shows that neural…

Molecular modeling is an important topic in drug discovery. Decades of research have led to the development of high quality scalable molecular force fields. In this paper, we show that neural networks can be used to train a universal…

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…

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…

We investigate the approximation capabilities of dense neural networks. While universal approximation theorems establish that sufficiently large architectures can approximate arbitrary continuous functions if there are no restrictions on…

The approximation capabilities of Deep Q-Networks (DQNs) are commonly justified by general Universal Approximation Theorems (UATs) that do not leverage the intrinsic structural properties of the optimal Q-function, the solution to a Bellman…

Deep neural networks are widely used for nonlinear function approximation with applications ranging from computer vision to control. Although these networks involve the composition of simple arithmetic operations, it can be very challenging…

Deep learning models have gained great success in many real-world applications. However, most existing networks are typically designed in heuristic manners, thus lack of rigorous mathematical principles and derivations. Several recent…

Neural networks are increasingly evolving towards training large models with big data, a method that has demonstrated superior performance across many tasks. However, this approach introduces an urgent problem: current deep learning models…

This paper studies the approximation capabilities of neural networks that combine layer normalization (LN) with linear layers. We prove that networks consisting of two linear layers with parallel layer normalizations (PLNs) inserted between…

A practical limitation of deep neural networks is their high degree of specialization to a single task and visual domain. Recently, inspired by the successes of transfer learning, several authors have proposed to learn instead universal,…