Related papers: Revealing the canalizing structure of Boolean func…

There are several examples of spaces of univariate functions for which we have a characterization of all sets of knots which are poised for the interpolation problem. For the standard spaces of univariate polynomials, or spline functions…

Pooling is a simple but essential layer in modern deep CNN architectures for feature aggregation and extraction. Typical CNN design focuses on the conv layers and activation functions, while leaving the pooling layers with fewer options. We…

In this paper, we give a number of new exact algorithms and heuristics to compute linear boolean decompositions, and experimentally evaluate these algorithms. The experimental evaluation shows that significant improvements can be made with…

In convolutional neural network-based character recognition, pooling layers play an important role in dimensionality reduction and deformation compensation. However, their kernel shapes and pooling operations are empirically predetermined;…

Holonomic functions play an essential role in Computer Algebra since they allow the application of many symbolic algorithms. Among all algorithmic attempts to find formulas for power series, the holonomic property remains the most important…

A knowledge compilation map analyzes tractable operations in Boolean function representations and compares their succinctness. This enables the selection of appropriate representations for different applications. In the knowledge…

Boolean functions are mathematical objects used in diverse domains and have been actively researched for several decades already. One domain where Boolean functions play an important role is cryptography. There, the plethora of settings one…

Bilinear pooling has been recently proposed as a feature encoding layer, which can be used after the convolutional layers of a deep network, to improve performance in multiple vision tasks. Different from conventional global average pooling…

Computed tomography is widely used as an imaging tool to visualize three-dimensional structures with expressive bone-soft tissue contrast. However, CT resolution and radiation dose are tightly entangled, highlighting the importance of…

We consider the scenario in which a set of sources generate messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can…

Boolean functions have very nice applications in cryptography and coding theory, which have led to a lot of research focusing on their applications. The objective of this paper is to construct binary linear codes with few weights from the…

Polynomial functions have plenty of useful analytical properties, but they are rarely used as learning models because their function class is considered to be restricted. This work shows that when trained properly polynomial functions can…

In this paper, we investigate the problem of finding tight linear lower bounding functions for multivariate polynomials over boxes. These functions are obtained by the expansion of polynomials into Bernstein form and using the linear least…

We study critical random Boolean networks with two inputs per node that contain only canalyzing functions. We present a phenomenological theory that explains how a frozen core of nodes that are frozen on all attractors arises. This theory…

This paper continues a systematic and comprehensive study on the structural properties of CFL functions, which are in general multi-valued partial functions computed by one-way one-head nondeterministic pushdown automata equipped with…

One of the biggest challenges for deep learning algorithms in medical image analysis is the indiscriminate mixing of image properties, e.g. artifacts and anatomy. These entangled image properties lead to a semantically redundant feature…

Our formal understanding of the inductive bias that drives the success of convolutional networks on computer vision tasks is limited. In particular, it is unclear what makes hypotheses spaces born from convolution and pooling operations so…

This paper revisits the problem of learning a k-CNF Boolean function from examples in the context of online learning under the logarithmic loss. In doing so, we give a Bayesian interpretation to one of Valiant's celebrated PAC learning…

Four terminal switching network is an alternative structure to realize the logic functions in electronic circuit modeling. This network can be used to implement a Boolean function with less number of switches than the two terminal based…

We present algorithms for computation and visualization of amoebas, their contours, compactified amoebas and sections of three-dimensional amoebas by two-dimensional planes. We also provide method and an algorithm for the computation…