Related papers: Variations on the Chebyshev-Lagrange Activation Fu…
We characterize the complexity of the lattice decoding problem from a neural network perspective. The notion of Voronoi-reduced basis is introduced to restrict the space of solutions to a binary set. On the one hand, this problem is shown…
To compress deep convolutional neural networks (CNNs) with large memory footprint and long inference time, this paper proposes a novel pruning criterion using layer-wised Ln-norm of feature maps. Different from existing pruning criteria,…
A wide range of numerical methods exists for computing polynomial approximations of solutions of ordinary differential equations based on Chebyshev series expansions or Chebyshev interpolation polynomials. We consider the application of…
We propose CoNSAL (Combining Neural networks and Symbolic regression for Analytical Lyapunov function) to construct analytical Lyapunov functions for nonlinear dynamic systems. This framework contains a neural Lyapunov function and a…
Spectral graph convolutional networks (GCNs) are particular deep models which aim at extending neural networks to arbitrary irregular domains. The principle of these networks consists in projecting graph signals using the…
We propose an active learning method for discovering low-dimensional structure in high-dimensional Gaussian process (GP) tasks. Such problems are increasingly frequent and important, but have hitherto presented severe practical…
Convolutional neural networks (CNNs) have become the state-of-the-art tool for dealing with unsolved problems in computer vision and image processing. Since the convolution operator is a linear operator, several generalizations have been…
We extend the necessity part of Lucas Lehmer iteration for testing Mersenne prime to all base and uniformly for both generalized Mersenne and Wagstaff numbers(the later correspond to negative base). The role of the quadratic iteration $x…
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…
Deep neural networks yield the state-of-the-art results in many computer vision and human machine interface applications such as object detection, speech recognition etc. Since, these networks are computationally expensive, customized…
Motivated by polynomial approximations of differential forms, we study analytical and numerical properties of a polynomial interpolation problem that relies on function averages over interval segments. The usage of segment data gives rise…
Deep neural networks have been successful in many predictive modeling tasks, such as image and language recognition, where large neural networks are often used to obtain good accuracy. Consequently, it is challenging to deploy these…
Efficient and stable algorithms for the calculation of spectral quantities and correlation functions are some of the key tools in computational condensed matter physics. In this article we review basic properties and recent developments of…
We study the family of functions that are represented by a linear convolutional neural network (LCN). These functions form a semi-algebraic subset of the set of linear maps from input space to output space. In contrast, the families of…
Deep neural networks paved the way for significant improvements in image visual categorization during the last years. However, even though the tasks are highly varying, differing in complexity and difficulty, existing solutions mostly build…
Deep neural network models have a complex architecture and are overparameterized. The number of parameters is more than the whole dataset, which is highly resource-consuming. This complicates their application and limits its usage on…
After training complex deep learning models, a common task is to compress the model to reduce compute and storage demands. When compressing, it is desirable to preserve the original model's per-example decisions (e.g., to go beyond top-1…
Deep feedforward neural networks with piecewise linear activations are currently producing the state-of-the-art results in several public datasets. The combination of deep learning models and piecewise linear activation functions allows for…
The combination of linear transformations and non-linear activation functions forms the foundation of most modern deep neural networks, enabling them to approximate highly complex functions. This paper explores the introduction of quadratic…
In this paper, we explore the concept of adding learn-able slope and mean shift parameters to an activation function to improve the total response region. The characteristics of an activation function depend highly on the value of…