相关论文: Approximation capabilities of measure-preserving n…

It is known that $O(N)$ parameters are sufficient for neural networks to memorize arbitrary $N$ input-label pairs. By exploiting depth, we show that $O(N^{2/3})$ parameters suffice to memorize $N$ pairs, under a mild condition on the…

Neural networks are trained to learn an approximate mapping from an input domain to a target domain. Incorporating prior knowledge about true mappings is critical to learning a useful approximation. With current architectures, it is…

Various work has suggested that the memorability of an image is consistent across people, and thus can be treated as an intrinsic property of an image. Using computer vision models, we can make specific predictions about what people will…

The universal approximation property uniformly with respect to weakly compact families of measures is established for several classes of neural networks. To that end, we prove that these neural networks are dense in Orlicz spaces, thereby…

We show the existence of a deep neural network capable of approximating a wide class of high-dimensional approximations. The construction of the proposed neural network is based on a quasi-optimal polynomial approximation. We show that this…

We demonstrate that a very deep ResNet with stacked modules with one neuron per hidden layer and ReLU activation functions can uniformly approximate any Lebesgue integrable function in $d$ dimensions, i.e. $\ell_1(\mathbb{R}^d)$. Because of…

Deep neural networks (DNNs) are becoming increasingly important components of software, and are considered the state-of-the-art solution for a number of problems, such as image recognition. However, DNNs are far from infallible, and…

Deep neural networks are highly expressive machine learning models with the ability to interpolate arbitrary datasets. Deep nets are typically optimized via first-order methods and the optimization process crucially depends on the…

The universal approximation theorem, in one of its most general versions, says that if we consider only continuous activation functions $\sigma$, then a standard feedforward neural network with one hidden layer is able to approximate any…

Neural Posterior Estimation (NPE) enables rapid parameter inference for complex simulators with intractable likelihoods. NPE trains an inference network to estimate a probability density over parameters given data, typically assumed to be…

In studying the expressiveness of neural networks, an important question is whether there are functions which can only be approximated by sufficiently deep networks, assuming their size is bounded. However, for constant depths, existing…

Estimating the pose of an object from a monocular image is an inverse problem fundamental in computer vision. The ill-posed nature of this problem requires incorporating deformation priors to solve it. In practice, many materials do not…

To have a superior generalization, a deep learning neural network often involves a large size of training sample. With increase of hidden layers in order to increase learning ability, neural network has potential degradation in accuracy.…

This paper investigates the universal approximation capabilities of Hamiltonian Deep Neural Networks (HDNNs) that arise from the discretization of Hamiltonian Neural Ordinary Differential Equations. Recently, it has been shown that HDNNs…

Imitation learning considerably simplifies policy synthesis compared to alternative approaches by exploiting access to expert demonstrations. For such imitation policies, errors away from the training samples are particularly critical. Even…

Compressive imaging aims to recover a latent image from under-sampled measurements, suffering from a serious ill-posed inverse problem. Recently, deep neural networks have been applied to this problem with superior results, owing to the…

In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…

We develop a corrective mechanism for neural network approximation: the total available non-linear units are divided into multiple groups and the first group approximates the function under consideration, the second group approximates the…

We study the approximation of measurable functions on the hypercube by functions arising from affine neural networks. Our main achievement is an approximation of any measurable function $f \colon W_n \to [-1,1]$ up to a prescribed precision…

Variational methods that rely on a recognition network to approximate the posterior of directed graphical models offer better inference and learning than previous methods. Recent advances that exploit the capacity and flexibility in this…