arXiv research

New braid invariant derived from octagon solutions.

Octagon map accelerates diagonal changes algorithm.

This note provides an easy construction of fake octagons.

Normal and almost normal surfaces are essential tools for algorithmic 3-manifold topology, but to use them requires exponentially slow enumeration algorithms in a high-dimensional vector space. The quadrilateral coordinates of Tollefson alleviate this problem considerably for normal surfaces, by reducing the dimension …

We explicitly compute the limiting gap distribution for slopes of saddle connections on the flat surface associated to the regular octagon with opposite sides identified. This is the first such computation where the Veech group of the translation surface has multiple cusps. We also show how to parametrize a Poincaré se…

New algorithms compute points on generalized Bolza surfaces.

We define a 2-normal surface to be one which intersects every 3-simplex of a triangulated 3-manifold in normal triangles and quadrilaterals, with one or two exceptions. The possible exceptions are a pair of octagons, a pair of unknotted tubes, an octagon and a tube, or a 12-gon. In this paper we use the theory of criti…

A cluster variety of Fock and Goncharov is a scheme constructed by gluing split algebraic tori, called seed tori, via birational gluing maps called mutations. In quantum theory, the ring of functions on seed tori are deformed to non-commutative rings, represented as operators on Hilbert spaces. Mutations are quantized …

We propose a novel SPARsity and Clustering (SPARC) regularizer, which is a modified version of the previous octagonal shrinkage and clustering algorithm for regression (OSCAR), where, the proposed regularizer consists of a $K$-sparse constraint and a pair-wise $\ell_{\infty}$ norm restricted on the $K$ largest componen…

We prove an optimal systolic inequality for CAT(0) metrics on a genus~2 surface. We use a Voronoi cell technique, introduced by C.~Bavard in the hyperbolic context. The equality is saturated by a flat singular metric in the conformal class defined by the smooth completion of the curve y^2=x^5-x. Thus, among all CAT(0) …

Study on planar graphs in Poincare model of hyperbolic geometry.

We apply the OSCAR (octagonal selection and clustering algorithms for regression) in recovering group-sparse matrices (two-dimensional---2D---arrays) from compressive measurements. We propose a 2D version of OSCAR (2OSCAR) consisting of the $\ell_1$ norm and the pair-wise $\ell_{\infty}$ norm, which is convex but non-d…

Following Matveev, a k-normal surface in a triangulated 3-manifold is a generalization of both normal and (octagonal) almost normal surfaces. Using spines, complexity, and Turaev-Viro invariants of 3-manifolds, we prove the following results: 1) a minimal triangulation of a closed irreducible or a bounded hyperbolic 3-…

Efficient algorithms for clustered Lasso and OSCAR reduce computational costs.

Many state-of-the-art machine learning models such as deep neural networks have recently shown to be vulnerable to adversarial perturbations, especially in classification tasks. Motivated by adversarial machine learning, in this paper we investigate the robustness of sparse regression models with strongly correlated co…

Abstract Neural Networks (ANNs) improve DNN verification efficiency.

The OSCAR (octagonal selection and clustering algorithm for regression) regularizer consists of a L_1 norm plus a pair-wise L_inf norm (responsible for its grouping behavior) and was proposed to encourage group sparsity in scenarios where the groups are a priori unknown. The OSCAR regularizer has a non-trivial proximit…

Any two equivalent discrete curves must have the same invariants at the corresponding points under an affine transformation. In this paper, we construct the moving frame and invariants for the discrete centroaffine curves, which could be used to discriminate the same discrete curves from different graphics, and estimat…

Defines relations between Dirac structures and spinors using Courant algebroid relations.

Unsupervised relation discovery aims to discover new relations from a given text corpus without annotated data. However, it does not consider existing human annotated knowledge bases even when they are relevant to the relations to be discovered. In this paper, we study the problem of how to use out-of-relation knowledg…

Abstractor enhances Transformers for relational reasoning, improving sample efficiency and performance.

New method improves graph neural networks by considering different types of relations in sampling.

Temporal networks are ubiquitous and evolve over time by the addition, deletion, and changing of links, nodes, and attributes. Although many relational datasets contain temporal information, the majority of existing techniques in relational learning focus on static snapshots and ignore the temporal dynamics. We propose…

Bayesian meta-learning on relation graphs improves few-shot relation extraction.

Proves one-relator groups with negative immersions are hyperbolic and virtually special.

HIRM models noisy, sparse, heterogeneous relational data using hierarchical clustering and Dirichlet processes.

Introduces Relational Privacy (RP) to control relation memorization in question answering models.

Proposes a new method for predicting missing relations in knowledge graphs.

Enhances social spam detection using multi-level dependency of relational sequences.

The paper explores the pentagon relation and its algebraic forms.

In this article, we extend the conventional framework of convolutional-Restricted-Boltzmann-Machine to learn highly abstract features among abitrary number of time related input maps by constructing a layer of multiplicative units, which capture the relations among inputs. In many cases, more than two maps are strongly…

This paper proposes an attention module augmented relational network called SARN(Sequential Attention Relational Network) that can carry out relational reasoning by extracting reference objects and making efficient pairing between objects. SARN greatly reduces the computational and memory requirements of the relational…

Identifying the underlying directional relations from observational time series with nonlinear interactions and complex relational structures is key to a wide range of applications, yet remains a hard problem. In this work, we introduce a novel minimum predictive information regularization method to infer directional r…

We consider the problem of learning causal relationships from relational data. Existing approaches rely on queries to a relational conditional independence (RCI) oracle to establish and orient causal relations in such a setting. In practice, queries to a RCI oracle have to be replaced by reliable tests for RCI against …

Existing relation classification methods that rely on distant supervision assume that a bag of sentences mentioning an entity pair are all describing a relation for the entity pair. Such methods, performing classification at the bag level, cannot identify the mapping between a relation and a sentence, and largely suffe…

Despite their impressive performance in many tasks, deep neural networks often struggle at relational reasoning. This has recently been remedied with the introduction of a plug-in relational module that considers relations between pairs of objects. Unfortunately, this is combinatorially expensive. In this extended abst…

This work proposes a method to compose visual relations more faithfully.

A new quantum relation connects exceptional Lie algebras and knots.

Traditional sequential multi-object attention models rely on a recurrent mechanism to infer object relations. We propose a relational extension (R-SQAIR) of one such attention model (SQAIR) by endowing it with a module with strong relational inductive bias that computes in parallel pairwise interactions between inferre…

Relation extraction aims to extract relational facts from sentences. Previous models mainly rely on manually labeled datasets, seed instances or human-crafted patterns, and distant supervision. However, the human annotation is expensive, while human-crafted patterns suffer from semantic drift and distant supervision sa…

We study a bordism relation for stable 3-forms on a 6-manifold, which is a binary relation on the set of closed $SL(3;\mathbb{C})$-structures on a 6-manifold via closed $G_2$-structures. Under $SO(3)$-symmetry and a co-associative condition the relation is reduced to a relation for geometric structures on a 3-manifold.…

RelEx explains relational models without gradient access.

Improves neural relational inference for dynamic multi-agent trajectories.

Study super cluster algebras from super Plücker and Ptolemy relations.

Proves a categorified relation in Khovanov homology.

Introduces new algebraic structures for relational groupoids and proves a reduction theorem.

We investigate Relational Graph Attention Networks, a class of models that extends non-relational graph attention mechanisms to incorporate relational information, opening up these methods to a wider variety of problems. A thorough evaluation of these models is performed, and comparisons are made against established be…

Relation extraction models suffer from limited qualified training data. Using human annotators to label sentences is too expensive and does not scale well especially when dealing with large datasets. In this paper, we use Auxiliary Classifier Generative Adversarial Networks (AC-GANs) to generate high-quality relational…