相关论文: Rational Neural Networks have Expressivity Advanta…

It is difficult to describe in mathematical terms what a neural network trained on data represents. On the other hand, there is a growing mathematical understanding of what neural networks are in principle capable of representing.…

It is well-known that overparametrized neural networks trained using gradient-based methods quickly achieve small training error with appropriate hyperparameter settings. Recent papers have proved this statement theoretically for highly…

In recent years, functional neural networks have been proposed and studied in order to approximate nonlinear continuous functionals defined on $L^p([-1, 1]^s)$ for integers $s\ge1$ and $1\le p<\infty$. However, their theoretical properties…

The input space of a neural network with ReLU-like activations is partitioned into multiple linear regions, each corresponding to a specific activation pattern of the included ReLU-like activations. We demonstrate that this partition…

This article is concerned with the approximation and expressive powers of deep neural networks. This is an active research area currently producing many interesting papers. The results most commonly found in the literature prove that neural…

In this paper, we introduce "Power Linear Unit" (PoLU) which increases the nonlinearity capacity of a neural network and thus helps improving its performance. PoLU adopts several advantages of previously proposed activation functions.…

`Biologically inspired' activation functions, such as the logistic sigmoid, have been instrumental in the historical advancement of machine learning. However in the field of deep learning, they have been largely displaced by rectified…

Lipschitz-constrained neural networks have several advantages over unconstrained ones and can be applied to a variety of problems, making them a topic of attention in the deep learning community. Unfortunately, it has been shown both…

Deep neural networks typically treat nonlinearities as fixed primitives (e.g., ReLU), limiting both interpretability and the granularity of control over the induced function class. While recent additive models (like KANs) attempt to address…

We explore the phase diagram of approximation rates for deep neural networks and prove several new theoretical results. In particular, we generalize the existing result on the existence of deep discontinuous phase in ReLU networks to…

This study explores the number of neurons required for a Rectified Linear Unit (ReLU) neural network to approximate multivariate monomials. We establish an exponential lower bound on the complexity of any shallow network approximating the…

The widespread use of Multi-layer perceptrons (MLPs) often relies on a fixed activation function (e.g., ReLU, Sigmoid, Tanh) for all nodes within the hidden layers. While effective in many scenarios, this uniformity may limit the networks…

In neural networks, non-linearity is introduced by activation functions. One commonly used activation function is Rectified Linear Unit (ReLU). ReLU has been a popular choice as an activation but has flaws. State-of-the-art functions like…

This paper studies the problem of range analysis for feedforward neural networks, which is a basic primitive for applications such as robustness of neural networks, compliance to specifications and reachability analysis of neural-network…

Deep learning researchers have a keen interest in proposing two new novel activation functions which can boost network performance. A good choice of activation function can have significant consequences in improving network performance. A…

This paper investigates the ability of finite samples to identify two-layer irreducible shallow networks with various nonlinear activation functions, including rectified linear units (ReLU) and analytic functions such as the logistic…

It is well-known that the expressivity of a neural network depends on its architecture, with deeper networks expressing more complex functions. In the case of networks that compute piecewise linear functions, such as those with ReLU…

Rational and neural network based approximations are efficient tools in modern approximation. These approaches are able to produce accurate approximations to nonsmooth and non-Lipschitz functions, including multivariate domain functions. In…

Even in recent neural network architectures such as Transformers and Extended LSTM (xLSTM), and traditional ones like Convolutional Neural Networks, Activation Functions are an integral part of nearly all neural networks. They enable more…

In this paper it is shown that $C_\beta$-smooth functions can be approximated by deep neural networks with ReLU activation function and with parameters $\{0,\pm \frac{1}{2}, \pm 1, 2\}$. The $l_0$ and $l_1$ parameter norms of considered…