Related papers: Learning to Unknot

We introduce a new combinatorial method to encode knots and links with applications to knot invariants. Clasp diagrams defined in this paper are combinatorial blueprints for building knot diagrams out of full twists on two strings rather…

We design and analyze a new paradigm for building supervised learning networks, driven only by local optimization rules without relying on a global error function. Traditional neural networks with a fixed topology are made up of identical…

The wiring of neurons in the brain is more flexible than the wiring of connections in contemporary artificial neural networks. It is possible that this extra flexibility is important for efficient problem solving and learning. This paper…

Twisted knot theory, introduced by M.O. Bourgoin, is a generalization of virtual knot theory. It naturally yields the notion of a twisted braid, which is closely related to the notion of a virtual braid due to Kauffman. In this paper, we…

We use deep neural networks to machine learn correlations between knot invariants in various dimensions. The three-dimensional invariant of interest is the Jones polynomial $J(q)$, and the four-dimensional invariants are the Khovanov…

Learning to Optimize is a recently proposed framework for learning optimization algorithms using reinforcement learning. In this paper, we explore learning an optimization algorithm for training shallow neural nets. Such high-dimensional…

Given a knot or link in the form of plat closure of a braid, we describe an algorithm to obtain a braid representing the same knot or link with the standard closure, and vice-versa. We analyze the three cases of knots and links: in…

Graph Neural Networks (GNNs) have achieved state-of-the-art performance for link prediction. However, GNNs suffer from poor interpretability, which limits their adoptions in critical scenarios that require knowing why certain links are…

There has been appreciable progress in unsupervised network representation learning (UNRL) approaches over graphs recently with flexible random-walk approaches, new optimization objectives and deep architectures. However, there is no common…

This paper studies a Markov network model for unbalanced data, aiming to solve the problems of classification bias and insufficient minority class recognition ability of traditional machine learning models in environments with uneven class…

In mathematics, a knot is a single strand of string crossed over itself any number of times, and connected at the ends. The Reidemeister Moves have been proven to be the three core moves necessary to fully untangle a knot. Some knots can be…

In this paper we investigate a neural network model in which weights between computational nodes are modified according to a local learning rule. To determine whether local learning rules are sufficient for learning, we encode the network…

Recently, strong results have been demonstrated by Deep Recurrent Neural Networks on natural language transduction problems. In this paper we explore the representational power of these models using synthetic grammars designed to exhibit…

Twisted Alexander invariants of knots are well-defined up to multiplication of units. We get rid of this multiplicative ambiguity via a combinatorial method and define normalized twisted Alexander invariants. We then show that the…

A transverse knot is a knot that is transverse to the planes of the standard contact structure on real 3-space. In this paper we prove the Markov Theorem for transverse braids, which states that two transverse closed braids that are…

Knowledge graph reasoning, which aims at predicting the missing facts through reasoning with the observed facts, is critical to many applications. Such a problem has been widely explored by traditional logic rule-based approaches and recent…

Pre-trained language models such as BERT have become a more common choice of natural language processing (NLP) tasks. Research in word representation shows that isotropic embeddings can significantly improve performance on downstream tasks.…

In the 1920's Artin defined the braid group in an attempt to understand knots in a more algebraic setting. A braid is a certain arrangement of strings in three-dimensional space. It is a celebrated theorem of Alexander that every knot is…

The contraction cost of a tensor network depends on the contraction order. However, the optimal contraction ordering problem is known to be NP-hard. We show that the linear contraction ordering problem for tree tensor networks admits a…

Inductive rule learning is arguably among the most traditional paradigms in machine learning. Although we have seen considerable progress over the years in learning rule-based theories, all state-of-the-art learners still learn descriptions…