相关论文: Approximation capabilities of measure-preserving n…
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…
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…
Due to the growing adoption of deep neural networks in many fields of science and engineering, modeling and estimating their uncertainties has become of primary importance. Despite the growing literature about uncertainty quantification in…
Although recent provable methods have been developed to compute preimage bounds for neural networks, their scalability is fundamentally limited by the #P-hardness of the problem. In this work, we adopt a novel probabilistic perspective,…
We present a new method to approximate posterior probabilities of Bayesian Network using Deep Neural Network. Experiment results on several public Bayesian Network datasets shows that Deep Neural Network is capable of learning joint…
There remains an important need for the development of image reconstruction methods that can produce diagnostically useful images from undersampled measurements. In magnetic resonance imaging (MRI), for example, such methods can facilitate…
In this article, we explore the effects of memory terms in continuous-layer Deep Residual Networks by studying Neural ODEs (NODEs). We investigate two types of models. On one side, we consider the case of Residual Neural Networks with…
In this work we study the properties of deep neural networks (DNN) with random weights. We formally prove that these networks perform a distance-preserving embedding of the data. Based on this we then draw conclusions on the size of the…
We explore unique considerations involved in fitting ML models to data with very high precision, as is often required for science applications. We empirically compare various function approximation methods and study how they scale with…
Probabilistic generative neural networks are useful for many applications, such as image classification, speech recognition and occlusion removal. However, the power budget for hardware implementations of neural networks can be extremely…
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…
We show that the error of iteratively magnitude-pruned networks empirically follows a scaling law with interpretable coefficients that depend on the architecture and task. We functionally approximate the error of the pruned networks,…
Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…
Multiplication layers are a key component in various influential neural network modules, including self-attention and hypernetwork layers. In this paper, we investigate the approximation capabilities of deep neural networks with…
Bayesian approaches for learning deep neural networks (BNN) have been received much attention and successfully applied to various applications. Particularly, BNNs have the merit of having better generalization ability as well as better…
Providing accurate uncertainty estimations is essential for producing reliable machine learning models, especially in safety-critical applications such as accelerator systems. Gaussian process models are generally regarded as the gold…
Although Deep Neural Networks (DNNs) have shown incredible performance in perceptive and control tasks, several trustworthy issues are still open. One of the most discussed topics is the existence of adversarial perturbations, which has…
Replacing non-polynomial functions (e.g., non-linear activation functions such as ReLU) in a neural network with their polynomial approximations is a standard practice in privacy-preserving machine learning. The resulting neural network,…
We propose a learning paradigm for the numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework…
In this paper we consider the limiting case of neural networks (NNs) architectures when the number of neurons in each hidden layer and the number of hidden layers tend to infinity thus forming a continuum, and we derive approximation errors…