Related papers: Enumeration of max-pooling responses with generali…
Convolutional layers in graph neural networks are a fundamental type of layer which output a representation or embedding of each graph vertex. The representation typically encodes information about the vertex in question and its…
Global pooling layers are an essential part of Convolutional Neural Networks (CNN). They are used to aggregate activations of spatial locations to produce a fixed-size vector in several state-of-the-art CNNs. Global average pooling or…
Deep neural networks with alternating convolutional, max-pooling and decimation layers are widely used in state of the art architectures for computer vision. Max-pooling purposefully discards precise spatial information in order to create…
Pooling operations, which can be calculated at low cost and serve as a linear or nonlinear transfer function for data reduction, are found in almost every modern neural network. Countless modern approaches have already tackled replacing the…
Convolutional networks almost always incorporate some form of spatial pooling, and very often it is alpha times alpha max-pooling with alpha=2. Max-pooling act on the hidden layers of the network, reducing their size by an integer…
Nowadays, Deep Neural Networks are among the main tools used in various sciences. Convolutional Neural Network is a special type of DNN consisting of several convolution layers, each followed by an activation function and a pooling layer.…
We present results on the number of linear regions of the functions that can be represented by artificial feedforward neural networks with maxout units. A rank-k maxout unit is a function computing the maximum of $k$ linear functions. For…
In convolutional neural networks (CNNs), pooling operations play important roles such as dimensionality reduction and deformation compensation. In general, max pooling, which is the most widely used operation for local pooling, is performed…
The goal of this paper is to introduce pooling strategies for simplicial convolutional neural networks. Inspired by graph pooling methods, we introduce a general formulation for a simplicial pooling layer that performs: i) local aggregation…
We seek to improve deep neural networks by generalizing the pooling operations that play a central role in current architectures. We pursue a careful exploration of approaches to allow pooling to learn and to adapt to complex and variable…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis problem described in…
We derive tight expressions for the maximum number of $k$-faces, $0\le{}k\le{}d-1$, of the Minkowski sum, $P_1\oplus{}P_2$, of two $d$-dimensional convex polytopes $P_1$ and $P_2$, as a function of the number of vertices of the polytopes.…
We present generalized versions of the commonly used maximum pooling operation: $k$th maximum and sorted pooling operations which selects the $k$th largest response in each pooling region, selecting locally consistent features of the input…
Inspired by the Hardy-Littlewood maximal function, we propose a novel pooling strategy which is called maxfun pooling. It is presented both as a viable alternative to some of the most popular pooling functions, such as max pooling and…
Pooling is essentially an operation from the field of Mathematical Morphology, with max pooling as a limited special case. The more general setting of MorphPooling greatly extends the tool set for building neural networks. In addition to…
The article deals with operations defined on convex polyhedra or polyhedral convex functions. Given two convex polyhedra, operations like Minkowski sum, intersection and closed convex hull of the union are considered. Basic operations for…
Multiplication layers are a key component in various influential neural network modules, including self-attention and hypernetwork layers. In this paper, we investigate the approximation capabilities of deep neural networks with…
Image classification is considered, and a hierarchical max-pooling model with additional local pooling is introduced. Here the additional local pooling enables the hierachical model to combine parts of the image which have a variable…
Max-Pooling operations are a core component of deep learning architectures. In particular, they are part of most convolutional architectures used in machine vision, since pooling is a natural approach to pattern detection problems. However,…