相关论文: Replacing K-infinity Function with Leaky ReLU in B…

For random piecewise linear systems T of the interval that are expanding on average we construct explicitly the density functions of absolutely continuous T-invariant measures. In case the random system uses only expanding maps our…

This is paper for the smooth function approximation by neural networks (NN). Mathematical or physical functions can be replaced by NN models through regression. In this study, we get NNs that generate highly accurate and highly smooth…

Low-cost inertial measurement units (IMUs) are widely utilized in mobile robot localization due to their affordability and ease of integration. However, their complex, nonlinear, and time-varying noise characteristics often lead to…

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 effort, we derive a formula for the integral representation of a shallow neural network with the ReLU activation function. We assume that the outer weighs admit a finite $L_1$-norm with respect to Lebesgue measure on the sphere. For…

The paper introduces an interactive machine learning mechanism to process the measurements of an uncertain, nonlinear dynamic process and hence advise an actuation strategy in real-time. For concept demonstration, a trajectory-following…

74J30The maximal group of Lie point symmetries of a system of nonlinear equations used in geophysical fluid dynamics is presented. The Lie algebra of this group is infinite-dimensional and involves three arbitrary functions of time. The…

We present a generalization of Lie's method for finding the group invariant solutions to a system of partial differential equations. Our generalization relaxes the standard transversality assumption and encompasses the common situation…

The primary neural networks decision-making units are activation functions. Moreover, they evaluate the output of networks neural node; thus, they are essential for the performance of the whole network. Hence, it is critical to choose the…

A methodology is presented for the numerical solution of nonlinear elliptic systems in unbounded domains, consisting of three elements. First, the problem is posed on a finite domain by means of a proper nonlinear change of variables. The…

Most works on joint state and unknown input (UI) estimation require the assumption that the UIs are linear; this is potentially restrictive as it does not hold in many intelligent autonomous systems. To overcome this restriction and…

Selecting the most suitable activation function is a critical factor in the effectiveness of deep learning models, as it influences their learning capacity, stability, and computational efficiency. In recent years, the Gaussian Error Linear…

Macroscopic features of dynamical systems such as almost-invariant sets and coherent sets provide crucial high-level information on how the dynamics organises phase space. We introduce a method to identify time-parameterised families of…

In this paper, we investigate the relationship between deep neural networks (DNN) with rectified linear unit (ReLU) function as the activation function and continuous piecewise linear (CPWL) functions, especially CPWL functions from the…

This paper proposes a nonlinear stochastic complementary filter design for inertial navigation that takes advantage of a fusion of Ultra-wideband (UWB) and Inertial Measurement Unit (IMU) technology ensuring semi-global uniform ultimate…

We present an ideal mixed-integer programming (MIP) formulation for a rectified linear unit (ReLU) appearing in a trained neural network. Our formulation requires a single binary variable and no additional continuous variables beyond the…

Constraint admissible positively invariant (CAPI) sets play a pivotal role in ensuring safety in control and planning applications, such as the recursive feasibility guarantee of explicit reference governor and model predictive control.…

The paper briefy reviews several recent results on hierarchical architectures for learning from examples, that may formally explain the conditions under which Deep Convolutional Neural Networks perform much better in function approximation…

Deep ReLU neural networks admit nontrivial functional symmetries: vastly different architectures and parameters (weights and biases) can realize the same function. We address the complete identification problem -- given a function f,…

This paper investigates the ability of generative networks to convert their input noise distributions into other distributions. Firstly, we demonstrate a construction that allows ReLU networks to increase the dimensionality of their noise…