Related papers: Rectangular knot diagrams classification with deep…

In this paper we summarise the work discussed in Ref. [1] and [2] (q-alg/9505003), in which we introduced a method helpful in solving the problem of knot classification. We also present results obtained since then.

The presence of slipknots in configurations of proteins and DNA has been shown to affect their functionality, or alter it entirely. Historically, polymers are modeled as polygonal chains in space. As an alternative to space curves, we…

Networks are a powerful tool to model complex systems, and the definition of many Graph Neural Networks (GNN), Deep Learning algorithms that can handle networks, has opened a new way to approach many real-world problems that would be hardly…

The combinatorial approach to knot theory treats knots as diagrams modulo Reidemeister moves. Many constructions of knot invariants (e.g., index polynomials, quandle colorings, etc.) use elements of diagrams such as arcs and crossings by…

While neural networks are used for classification tasks across domains, a long-standing open problem in machine learning is determining whether neural networks trained using standard procedures are optimal for classification, i.e., whether…

A core challenge in the interpretation of deep neural networks is identifying commonalities between the underlying algorithms implemented by distinct networks trained for the same task. Motivated by this problem, we introduce DYNAMO, an…

Given a group endowed with a Z/2-valued morphism we associate a Gauss diagram theory, and show that for a particular choice of the group these diagrams encode faithfully virtual knots on a given arbitrary surface. This theory contains all…

Deep convolutional neural networks (CNNs) have achieved breakthrough performance in many pattern recognition tasks such as image classification. However, the development of high-quality deep models typically relies on a substantial amount…

Randomized Neural Networks explore the behavior of neural systems where the majority of connections are fixed, either in a stochastic or a deterministic fashion. Typical examples of such systems consist of multi-layered neural network…

Recent work in machine learning shows that deep neural networks can be used to solve a wide variety of inverse problems arising in computational imaging. We explore the central prevailing themes of this emerging area and present a taxonomy…

Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities.…

Despite the highest classification accuracy in wide varieties of application areas, artificial neural network has one disadvantage. The way this Network comes to a decision is not easily comprehensible. The lack of explanation ability…

Graph neural networks are deep neural networks designed for graphs with attributes attached to nodes or edges. The number of research papers in the literature concerning these models is growing rapidly due to their impressive performance on…

deepstruct connects deep learning models and graph theory such that different graph structures can be imposed on neural networks or graph structures can be extracted from trained neural network models. For this, deepstruct provides deep…

Neural networks are a prominent tool for identifying and modeling complex patterns, which are otherwise hard to detect and analyze. While machine learning and neural networks have been finding applications across many areas of science and…

Graph neural networks (GNNs) are among the most powerful tools in deep learning. They routinely solve complex problems on unstructured networks, such as node classification, graph classification, or link prediction, with high accuracy.…

We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unknotted, capable of being continuously deformed without self-intersection so that it lies in a plane. We show that this problem, {\sc…

Neural networks are known to be effective function approximators. Recently, deep neural networks have proven to be very effective in pattern recognition, classification tasks and human-level control to model highly nonlinear realworld…

Two geometric spaces are in the same topological class if they are related by certain geometric deformations. We propose machine learning methods that automate learning of topological invariance and apply it in the context of knot theory,…

A {\it stuck knot} is a knot diagram containing designated crossings, called {\it stuck crossings}, whose incident strands are required to remain locally non-separable. These rigidity constraints restrict the allowable ambient isotopies and…