Related papers: Learning to Unknot
Quantum Computing (QC) stands to revolutionize computing, but is currently still limited. To develop and test quantum algorithms today, quantum circuits are often simulated on classical computers. Simulating a complex quantum circuit…
The unknotting number $u$ and the genus $g$ of braid positive knots are equal, as shown by Rudolph. We prove the stronger statement that any positive braid diagram of a genus $g$ knot contains $g$ crossings, such that changing them produces…
In recent years some researchers have explored the use of reinforcement learning (RL) algorithms as key components in the solution of various natural language processing tasks. For instance, some of these algorithms leveraging deep neural…
Recent advances in reasoning domains with neural networks have primarily been enabled by a training recipe that optimizes Large Language Models, previously trained to predict the next-token in a sequence, with reinforcement learning…
A well-known algorithm for unknotting knots involves traversing a knot diagram and changing each crossing that is first encountered from below. The minimal number of crossings changed in this way across all diagrams for a knot is called the…
Deep learning has shown that learned functions can dramatically outperform hand-designed functions on perceptual tasks. Analogously, this suggests that learned optimizers may similarly outperform current hand-designed optimizers, especially…
How much can pruning algorithms teach us about the fundamentals of learning representations in neural networks? And how much can these fundamentals help while devising new pruning techniques? A lot, it turns out. Neural network pruning has…
Knotted ribbons form an important topic in knot theory. They have applications in natural sciences, such as cyclic duplex DNA modeling. A flat knotted ribbon can be obtained by gently pulling a knotted ribbon tight so that it becomes flat…
Developing link prediction models to automatically complete knowledge graphs has recently been the focus of significant research interest. The current methods for the link prediction taskhavetwonaturalproblems:1)the relation distributions…
We point out the connection between mathematical knot theory and spin glass/search problem. In particular, we present a statistical mechanical formulation of the problem of computing a knot invariant; p-colorability problem, which provides…
We study whether a Large Language Model can learn the deterministic sequence of trees generated by the iterated prime factorization of the natural numbers. Each integer is mapped into a rooted planar tree and the resulting sequence $…
Expressive text encoders such as RNNs and Transformer Networks have been at the center of NLP models in recent work. Most of the effort has focused on sentence-level tasks, capturing the dependencies between words in a single sentence, or…
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…
We make use of the 3D nature of knots and links to find savings in computational complexity when computing knot invariants such as the linking number and, in general, most finite type invariants. These savings are achieved in comparison…
This paper gives new and elementary combinatorial topological proofs of the classification of unoriented and oriented rational knots and links. These proofs are based on the known classification of alternating knots through flyping, and the…
Structured pruning is a popular method for compressing a neural network: given a large trained network, one alternates between removing channel connections and fine-tuning; reducing the overall width of the network. However, the efficacy of…
Recurrent neural networks have been the dominant models for many speech and language processing tasks. However, we understand little about the behavior and the class of functions recurrent networks can realize. Moreover, the heuristics used…
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…
A powerful way to study groups is via their actions on suitable spaces. Classifying spaces for families of subgroups are a type of these spaces, obtained by imposing some strict conditions on the fixed-point sets. We show how in the…
We introduce tensor network contraction algorithms for the evaluation of the Jones polynomial of arbitrary knots. The value of the Jones polynomial of a knot maps to the partition function of a $q$-state Potts model defined as a planar…