Piecewise linear function ≈ Piecewise linear function
View article
Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks Open
We prove new upper and lower bounds on the VC-dimension of deep neural networks with the ReLU activation function. These bounds are tight for almost the entire range of parameters. Letting $W$ be the number of weights and $L$ be the number…
View article
Transformation and Linearization Techniques in Optimization: A State-of-the-Art Survey Open
To formulate a real-world optimization problem, it is sometimes necessary to adopt a set of non-linear terms in the mathematical formulation to capture specific operational characteristics of that decision problem. However, the use of non-…
View article
Research on convolutional neural network based on improved Relu piecewise activation function Open
With the continuous development of deep learning, convolution neural network with its excellent recognition performance obtains a series of major breakthrough results in target detection, image recognition and other fields. An improved ReL…
View article
Generating Multi-Scroll Chua’s Attractors via Simplified Piecewise-Linear Chua’s Diode Open
High implementation complexity of multi-scroll circuit is a bottleneck problem in real chaos-based communication. Especially, in multi-scroll Chua's circuit, the simplified implementation of piecewise-linear resistors with multiple segment…
View article
Multi-trip time-dependent vehicle routing problem with time windows Open
10.1016/j.ejor.2020.09.022
View article
Deep Learning with S-Shaped Rectified Linear Activation Units Open
Rectified linear activation units are important components for state-of-the-art deep convolutional networks. In this paper, we propose a novel S-shaped rectifiedlinear activation unit (SReLU) to learn both convexand non-convex functions, i…
View article
A Unified View of Piecewise Linear Neural Network Verification Open
The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. Despite the reputation of learned NN models to behave as black boxes and t…
View article
Narrowest-Over-Threshold Detection of Multiple Change-points and\n Change-point-like Features Open
We propose a new, generic and flexible methodology for nonparametric function\nestimation, in which we first estimate the number and locations of any features\nthat may be present in the function, and then estimate the function\nparametric…
View article
Nearly-tight VC-dimension bounds for piecewise linear neural networks Open
We prove new upper and lower bounds on the VC-dimension of deep neural networks with the ReLU activation function. These bounds are tight for almost the entire range of parameters. Letting $W$ be the number of weights and $L$ be the number…
View article
Fusion 2-categories and a state-sum invariant for 4-manifolds Open
We introduce semisimple 2-categories, fusion 2-categories, and spherical fusion 2-categories. For each spherical fusion 2-category, we construct a state-sum invariant of oriented singular piecewise-linear 4-manifolds.
View article
Benefits of depth in neural networks Open
For any positive integer $k$, there exist neural networks with $Θ(k^3)$ layers, $Θ(1)$ nodes per layer, and $Θ(1)$ distinct parameters which can not be approximated by networks with $\mathcal{O}(k)$ layers unless they are exponentially lar…
View article
Conditions for the Stability of Switched Systems Containing Unstable Subsystems Open
This brief studies the stability of switched systems in which all the subsystems may be unstable. In addition, some of the switching behaviors of the systems are destabilizing. By using the piecewise Lyapunov function method and taking a t…
View article
Learning Parameterized Skills Open
This dissertation research focuses on a high elevation Andean social-ecological system. It examines system linkages between climate, grazing pasture (wetlands), and agro-pastoralist livelihood strategies in an indigenous peasant community.…
View article
Adaptive Piecewise Equivalent Circuit Model With SOC/SOH Estimation Based on Extended Kalman Filter Open
Battery modelling plays a critical role in battery management tasks. A model that provides accurate estimations of state of charge and state of heath in varying operating conditions could significantly improve the performance of battery ma…
View article
Subdiffusion with a time-dependent coefficient: Analysis and numerical solution Open
In this work, a complete error analysis is presented for fully discrete solutions of the subdiffusion equation with a time-dependent diffusion coefficient, obtained by the Galerkin finite element method with conforming piecewise linear fin…
View article
Forecasting District Heating Demand using Machine Learning Algorithms Open
Short-term forecasting of thermal energy demand is critical to optimally manage on-site renewable energy generation and the charge and discharge of energy storage devices in district heating and cooling (DHC) systems. As part of a larger s…
View article
A cut finite element method with boundary value correction Open
In this contribution we develop a cut finite element method with boundary value correction of the type originally proposed by Bramble, Dupont, and Thomée in [Math. Comp. 26 (1972), 869–879]. The cut finite element method is a fictitious do…
View article
Parameterizations for ensemble Kalman inversion Open
The use of ensemble methods to solve inverse problems is attractive because\nit is a derivative-free methodology which is also well-adapted to\nparallelization. In its basic iterative form the method produces an ensemble of\nsolutions whic…
View article
Canards, Folded Nodes, and Mixed-Mode Oscillations in Piecewise-Linear Slow-Fast Systems Open
Canard-induced phenomena have been extensively studied in the last three decades, from both the mathematical and the application viewpoints. Canards in slow-fast systems with (at least) two slow variables, especially near folded-node singu…
View article
Optimal Proportional Cake Cutting with Connected Pieces Open
We consider the classic cake cutting problem where one allocates a divisible cake to n participating agents. Among all valid divisions, fairness and efficiency (a.k.a. ~social welfare) are the most critical criteria to satisfy and optimize…
View article
Complexity of Linear Regions in Deep Networks Open
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 activa…
View article
Nash Social Welfare for Indivisible Items under Separable, Piecewise-Linear Concave Utilities Open
Recently Cole and Gkatzelis [10] gave the first constant factor approximation algorithm for the problem of allocating indivisible items to agents, under additive valuations, so as to maximize the Nash social welfare (NSW). We give constant…
View article
Deep Learning with Low Precision by Half-wave Gaussian Quantization Open
The problem of quantizing the activations of a deep neural network is considered. An examination of the popular binary quantization approach shows that this consists of approximating a classical non-linearity, the hyperbolic tangent, by tw…
View article
Detecting Changes in Slope With an <i><i>L</i><sub>0</sub></i> Penalty Open
While there are many approaches to detecting changes in mean for a univariate time series, the problem of detecting multiple changes in slope has comparatively been ignored. Part of the reason for this is that detecting changes in slope is…
View article
Multi-stable nonlinear energy sink for rotor system Open
A multi-stable nonlinear energy sink (MNES) with piecewise linear stiffness and magnet negative stiffness is developed to suppress the vibration of unbalanced rotor system. The specific structure of the MNES is developed, and the working p…
View article
Log-Barrier Interior Point Methods Are Not Strongly Polynomial Open
We prove that primal-dual log-barrier interior point methods are not strongly\npolynomial, by constructing a family of linear programs with $3r+1$\ninequalities in dimension $2r$ for which the number of iterations performed is\nin $\\Omega…
View article
A novel energy sink with piecewise linear stiffness Open
In this paper, a nonlinear energy sink with piecewise linear stiffness spring is proposed, and the fundamental characteristics of the nonlinear energy sink are investigated. Firstly, the structure of the piecewise linear stiffness spring i…
View article
Energy Optimization of Robotic Cells Open
This study focuses on the energy optimization of industrial robotic cells,\nwhich is essential for sustainable production in the long term. A holistic\napproach that considers a robotic cell as a whole toward minimizing energy\nconsumption…
View article
Bifurcation analysis of wheel shimmy with non-smooth effects and time delay in the tyre–ground contact Open
The nonlinear dynamics of towed wheels is analysed with the help of the brush tyre model. The time delay in the tyre–ground contact and the non-smooth nature of the system caused by contact friction are considered simultaneously. Firstly, …
View article
High-Dimensional Quantile Regression: Convolution Smoothing and Concave Regularization Open
ℓ 1 -penalized quantile regression (QR) is widely used for analysing high-dimensional data with heterogeneity. It is now recognized that the ℓ1-penalty introduces non-negligible estimation bias, while a proper use of concave regularization…