arXiv research

MaskGAN fills in text blanks more flexibly and effectively.

Let $F_g$ denote a closed oriented surface of genus $g$. A set of simple closed curves is called a filling of $F_g$ if its complement is a disjoint union of discs. The mapping class group $\text{Mod}(F_g)$ of genus $g$ acts on the set of fillings of $F_g$. The union of the curves in a filling forms a graph on the surfa…

Recent years have seen remarkable progress of text generation in different contexts, such as the most common setting of generating text from scratch, and the emerging paradigm of retrieval-and-rewriting. Text infilling, which fills missing text portions of a sentence or paragraph, is also of numerous use in real life, …

The study finds knots with specific surgeries that don't allow weak symplectic fillings.

Estimates the degree of trace fields of hyperbolic Dehn fillings.

New filling functions for groups with coefficients show different asymptotic behavior.

Neural text generation models are often autoregressive language models or seq2seq models. These models generate text by sampling words sequentially, with each word conditioned on the previous word, and are state-of-the-art for several machine translation and summarization benchmarks. These benchmarks are often defined …

In this paper, we develop a method for constructing left-orders on the fundamental groups of rational homology 3-spheres. We begin by constructing the holonomy extension locus of a rational homology solid torus $M$, which encodes the information about peripherally hyperbolic $\widetilde{\text{PSL}_2\mathbb{R}}$ represe…

Let $F_g$ be a closed orientable surface of genus $g$. A set $Ω= \{ γ_1, \dots, γ_s\}$ of pairwise non-homotopic simple closed curves on $F_g$ is called a \emph{filling system} or simply a \emph{filling} of $F_g$, if $F_g\setminus Ω$ is a union of $b$ topological discs for some $b\geq 1$. A filling system is called \em…

In this paper we show that for a generalized Berger metric $\hat{g}$ on $S^3$ close to the round metric, the conformally compact Einstein (CCE) manifold $(M, g)$ with $(S^3, [\hat{g}])$ as its conformal infinity is unique up to isometries. For the high-dimensional case, we show that if $\hat{g}$ is an $\text{SU}(k+1)$-…

The paper studies properties of optimal metrics associated to curves on surfaces.

Computed linking number of modular knots and Lorenz links.

Computes minimal dilatation for Thurston maps on surfaces.

Pruning is one of the most effective model reduction techniques. Deep networks require massive computation and such models need to be compressed to bring them on edge devices. Most existing pruning techniques are focused on vision-based models like convolutional networks, while text-based models are still evolving. The…

Paper improves text-to-SQL models with schema-aware denoising.

Paper debiases text embeddings using context injection.

As a result of social network popularity, in recent years, hate speech phenomenon has significantly increased. Due to its harmful effect on minority groups as well as on large communities, there is a pressing need for hate speech detection and filtering. However, automatic approaches shall not jeopardize free speech, s…

We present BART, a denoising autoencoder for pretraining sequence-to-sequence models. BART is trained by (1) corrupting text with an arbitrary noising function, and (2) learning a model to reconstruct the original text. It uses a standard Tranformer-based neural machine translation architecture which, despite its simpl…

The paper connects hyperbolic Dehn surgery and Higgs bundles to construct model objects in representation varieties.

Automatic understanding of domain specific texts in order to extract useful relationships for later use is a non-trivial task. One such relationship would be between railroad accidents' causes and their correspondent descriptions in reports. From 2001 to 2016 rail accidents in the U.S. cost more than $4.6B. Railroads i…

Tensor networks improve sequence modeling with efficient sampling and parallelism.

As deep neural networks continue to revolutionize various application domains, there is increasing interest in making these powerful models more understandable and interpretable, and narrowing down the causes of good and bad predictions. We focus on recurrent neural networks, state of the art models in speech recogniti…

Study Stein and Milnor fillings of links from surface singularities.

Proves upper bound on systolic ratio for circle fillings.

The paper explores the geometry and dynamics of free splitting and free factor complexes for groups.

The paper constructs minimal coherent filling pairs on surfaces.

The paper classifies symplectic fillings of lens spaces and constructs cobordisms.

Computes A-polynomials of knots from Whitehead sister link fillings.

If a simple 3-manifold M admits a reducible and a toroidal Dehn filling, the distance between the filling slopes is known to be bounded by three. In this paper, we classify all manifolds which admit a reducible Dehn filling and a toroidal Dehn filling with distance 3.

We give three infinite families of examples of nonhyperbolic Dehn fillings on hyperbolic manifolds. A manifold in the first family admits two Dehn fillings of distance two apart, one of which is toroidal and annular, and the other is reducible and $\partial$-reducible. A manifold in the second family has boundary consi…

Study negative definite spin fillings of knot covers.

The paper proves finiteness of cosmetic fillings on a specific type of 3-manifold.

Study generalizes Lebesgue curves to new space-filling and fractal sets.

We use Menke's JSJ-type decomposition theorem for symplectic fillings to reduce the classification of strong and exact symplectic fillings of virtually overtwisted torus bundles to the same problem for tight lens spaces. For virtually overtwisted structures on elliptic or parabolic torus bundles, this gives a complete …

Let M be a simple 3-manifold with a toral boundary component partial_0 M. If Dehn filling M along partial_0 M one way produces a toroidal manifold and Dehn filling M along partial_0 M another way produces a boundary-reducible manifold, then we show that the absolute value of the intersection number on partial_0 M of th…

If a hyperbolic 3-manifold M admits a reducible and a finite Dehn filling, the distance between the filling slopes is known to be 1. This has been proved recently by Boyer, Gordon and Zhang. The first example of a manifold with two such fillings was given by Boyer and Zhang. In this paper, we give examples of hyperboli…

Affirmative proof that rank 3 3-manifolds have filling links.

Study filling links in 3-manifolds to understand their topological properties.

New method fills cluster seeds with exact Lagrangian structures.

Study shows connectedness of Bowditch boundary persists in long Dehn fillings.

Positive braids have endless filling possibilities.

This paper classifies and determines the length of the shortest filling pairs on a specific type of surface.

Let $M$ be an irreducible, compact, connected, orientable 3-manifold whose boundary is a torus. We show that if $M$ is hyperbolic, then it admits at most six finite/cyclic fillings of maximal distance 5. Further, the distance of a finite/cyclic filling to a cyclic filling is at most 2. If $M$ has a non-boundary-paralle…

Four-dimensional Einstein Dehn filling is impossible.

Study Stein fillings of planar contact 3-manifolds with relative trisection genus 2.

Study on Legendrian knots and their non-orientable Lagrangian fillings.

Study shows no large mean curvature fill-ins for nonnegative scalar curvature.

We extend Thurston's metric to projective filling currents, embedding Teichmüller space into the larger space.