Related papers: Variational autoencoders understand knot topology

A polynomial is presented that models a topological knot in a unique manner. It distinguishes all types of knots including the orientation and has a group theory interpretation. The topologies may be labeled via a number, which upon a base…

Generative thermal design for complex geometries is fundamental in many areas of engineering, yet it faces two main challenges: the high computational cost of high-fidelity simulations and the limitations of conventional generative models.…

The area of Machine learning (ML) has seen exceptional growth in recent years. Successful implementation of ML methods in various branches of physics has led to new insights. These methods have been shown to classify phases in condensed…

Variational Auto-Encoders (VAEs) have emerged as powerful probabilistic models for generative tasks. However, their convergence properties have not been rigorously proven. The challenge of proving convergence is inherently difficult due to…

Unsupervised representation learning holds the promise of exploiting large amounts of unlabeled data to learn general representations. A promising technique for unsupervised learning is the framework of Variational Auto-encoders (VAEs).…

Autoencoders are unsupervised machine learning circuits whose learning goal is to minimize a distortion measure between inputs and outputs. Linear autoencoders can be defined over any field and only real-valued linear autoencoder have been…

Using machine learning (ML) to recognize different phases of matter and to infer the entire phase diagram has proven to be an effective tool given a large dataset. In our previous proposals, we have successfully explored phase transitions…

Clustering is among the most fundamental tasks in computer vision and machine learning. In this paper, we propose Variational Deep Embedding (VaDE), a novel unsupervised generative clustering approach within the framework of Variational…

We show that a topological quantum computer based on the evaluation of a Witten-Reshetikhin-Turaev TQFT invariant of knots can always be arranged so that the knot diagrams with which one computes are diagrams of hyperbolic knots. The…

Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…

Variational autoencoders (VAEs) are widely used deep generative models capable of learning unsupervised latent representations of data. Such representations are often difficult to interpret or control. We consider the problem of…

Like fingerprints, cortical folding patterns are unique to each brain even though they follow a general species-specific organization. Some folding patterns have been linked with neurodevelopmental disorders. However, due to the high…

We use machine learning to classify examples of braids (or flat braids) as trivial or non-trivial. Our ML takes form of supervised learning using neural networks (multilayer perceptrons). When they achieve good results in classification, we…

Variational autoencoders (VAEs) are latent variable models that can generate complex objects and provide meaningful latent representations. Moreover, they could be further used in downstream tasks such as classification. As previous work…

The varying coefficient model has received broad attention from researchers as it is a powerful dimension reduction tool for non-parametric modeling. Most existing varying coefficient models fitted with polynomial spline assume equidistant…

Anomalies are by definition rare, thus labeled examples are very limited or nonexistent, and likely do not cover unforeseen scenarios. Unsupervised learning methods that don't necessarily encounter anomalies in training would be immensely…

High-dimensional data, particularly in the form of high-order tensors, presents a major challenge in self-supervised learning. While MLP-based autoencoders (AE) are commonly employed, their dependence on flattening operations exacerbates…

Layout design with complex constraints is a challenging problem to solve due to the non-uniqueness of the solution and the difficulties in incorporating the constraints into the conventional optimization-based methods. In this paper, we…

Classical metric and non-metric multidimensional scaling (MDS) variants are widely known manifold learning (ML) methods which enable construction of low dimensional representation (projections) of high dimensional data inputs. However,…

This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in…