arXiv research

Introduces Möbius structures and hyperbolic ends for $k$-surfaces in hyperbolic space.

This paper proves unique determination of certain non-quasi-Fuchsian manifolds by their end structure and bending lamination.

Study on projective orbifolds with ends and their deformation theory.

A real projective orbifold has a radial end if a neighborhood of the end is foliated by projective geodesics that develop into geodesics ending at a common point. It has a totally geodesic end if the end can be completed to have the totally geodesic boundary. The purpose of this paper is to announce some partial result…

Deep NLP models benefit from underlying structures in the data---e.g., parse trees---typically extracted using off-the-shelf parsers. Recent attempts to jointly learn the latent structure encounter a tradeoff: either make factorization assumptions that limit expressiveness, or sacrifice end-to-end differentiability. Us…

Structured Prediction Energy Networks (SPENs) are a simple, yet expressive family of structured prediction models (Belanger and McCallum, 2016). An energy function over candidate structured outputs is given by a deep network, and predictions are formed by gradient-based optimization. This paper presents end-to-end lear…

Infinite-genus surfaces have many isospectral hyperbolic structures.

Real projective structures on $n$-orbifolds are useful in understanding the space of representations of discrete groups into $\mathrm{SL}(n+1, \mathbb{R})$ or $\mathrm{PGL}(n+1, \mathbb{R})$. A recent work shows that many hyperbolic manifolds deform to manifolds with such structures not projectively equivalent to the o…

Real projective structures on $n$-orbifolds are useful in understanding the space of representations of discrete groups into $\mathrm{SL}(n+1, \mathbb{R})$ or $\mathrm{PGL}(n+1, \mathbb{R})$. A recent work shows that many hyperbolic manifolds deform to manifolds with such structures not projectively equivalent to the o…

Real projective structures on $n$-orbifolds are useful in understanding the space of representations of discrete groups into $\mathrm{SL}(n+1, \mathbb{R})$ or $\mathrm{PGL}(n+1, \mathbb{R})$. A recent work shows that many hyperbolic manifolds deform to manifolds with such structures not projectively equivalent to the o…

Real projective structures on $n$-orbifolds are useful in understanding the space of representations of discrete groups into $SL(n+1, \mathbb{R})$ or $PGL(n+1, \mathbb{R})$. A recent work shows that many hyperbolic manifolds deform to manifolds with such structures not projectively equivalent to the original ones. The …

The controlled end and h-cobrodism theorems (Ends of maps I, 1979) are used to give quick proofs of the Top/PL and PL/DIFF product structure theorems.

A real projective orbifold is an $n$-dimensional orbifold modeled on $\mathbb{RP}^n$ with the group $PGL(n+1, \mathbb{R})$. We concentrate on an orbifold that contains a compact codimension $0$ submanifold whose complement is a union of neighborhoods of ends, diffeomorphic to closed $(n-1)$-dimensional orbifolds times …

We present differentiable particle filters (DPFs): a differentiable implementation of the particle filter algorithm with learnable motion and measurement models. Since DPFs are end-to-end differentiable, we can efficiently train their models by optimizing end-to-end state estimation performance, rather than proxy objec…

End-to-end Text-to-speech (TTS) system can greatly improve the quality of synthesised speech. But it usually suffers form high time latency due to its auto-regressive structure. And the synthesised speech may also suffer from some error modes, e.g. repeated words, mispronunciations, and skipped words. In this paper, we…

We use Furuta's result, usually referred to as ``10/8-conjecture'', to show that for any compact 3-manifold $M$ the open manifold $M\times\r$ has infinitely many different smooth structures. Another consequence of Furuta's result is existence of infinitely many smooth structures on open topological 4-manifolds with a t…

Kaleidoscope matrices improve model quality and inference speed.

Study geometric structure of Ricci shrinker ends without global curvature assumptions.

This paper is devoted to introducing coarse structures in a very simple way, namely as an equivalence relation on the set of simple ends. As an application we show that Gromov boundary of every hyperbolic space is an example of a Higson corona and each Freundenthal compactification is an example of a Higson compactific…

This research studies end-periodic mapping tori and their hyperbolic structures.

Despite an explosion in the number of experimentally determined, atomically detailed structures of biomolecules, many critical tasks in structural biology remain data-limited. Whether performance in such tasks can be improved by using large repositories of tangentially related structural data remains an open question. …

Study circle patterns and polyhedral surfaces in hyperbolic ends, proving manifold properties.

A new model learns graph structures from data.

Researchers create a parametrix for resolvents on manifolds with ends.

The paper sets limits on the number of ends of certain geometric structures.

We show that Out(G) is residually finite if G is a one-ended group that is hyperbolic relative to virtually polycyclic subgroups. More generally, if G is one-ended and hyperbolic relative to proper residually finite subgroups, the group of outer automorphisms preserving the peripheral structure is residually finite. We…

The affine sphere construction gives, on any oriented surface, a one-to-one correspondence between convex $\mathbb{RP}^2$-structures and holomorphic cubic differentials. Generalizing results of Benoist-Hulin, Loftin and Dumas-Wolf, we show that poles of order less than $3$ of cubic differentials correspond to finite vo…

This paper develops new tools for understanding surfaces with more than one end (and usually, of infinite topology) which properly minimally embed into Euclidean three-space. On such a surface, the set of ends forms a compact Hausdorff space, naturally ordered by the relative heights of the ends in space. One of our ma…

This note revisits recent results regarding the geometry and moduli of solutions of the heterotic string on manifolds $Y$ with a $G_2$ structure. In particular, such heterotic $G_2$ systems can be rephrased in terms of a differential $\check {\cal D}$ acting on a complex $\checkΩ^*(Y , {\cal Q})$, where ${\cal Q}=T^*Y\…

It is important to learn various types of classifiers given training data with noisy labels. Noisy labels, in the most popular noise model hitherto, are corrupted from ground-truth labels by an unknown noise transition matrix. Thus, by estimating this matrix, classifiers can escape from overfitting those noisy labels. …

New Hilbert bundles with ends defined from indexed bases.

We survey the interactions between foliations and contact structures in dimension three, with an emphasis on sutured manifolds and invariants of sutured contact manifolds. This paper contains two original results: the fact that a closed orientable irreducible 3-manifold M with nonzero second homol-ogy carries a hyperti…

Complex environments and tasks pose a difficult problem for holistic end-to-end learning approaches. Decomposition of an environment into interacting controllable and non-controllable objects allows supervised learning for non-controllable objects and universal value function approximator learning for controllable obje…

End-to-end algorithm for controlling bilinear systems with probabilistic noise.

In this paper it is shown that for any network there is a uniquely determined network based on a structure tree that provides a convenient way of determining a minimal cut separating a pair $s, t$ where each of $s, t$ is either a vertex or an end in the original network. A Max-Flow Min-Cut Theorem is proved for any net…

Consider the following variational problem: among all curves in $\mathbb{R}^n$ of fixed length with prescribed end points and prescribed tangents at the end points, minimise the $L^\infty$-norm of the curvature. We show that the solutions of this problem, and of a generalised version, are characterised by a system of d…

In this paper, we propose an end-to-end deep learning model, called E2Efold, for RNA secondary structure prediction which can effectively take into account the inherent constraints in the problem. The key idea of E2Efold is to directly predict the RNA base-pairing matrix, and use an unrolled algorithm for constrained p…

Study examines $L^p$-boundedness of Hodge projection on manifolds with ends.

Automated multi-task learning algorithm that optimizes network topology.

Consider a one-ended word-hyperbolic group. If it is the fundamental group of a graph of free groups with cyclic edge groups then either it is the fundamental group of a surface or it contains a finitely generated one-ended subgroup of infinite index. As a corollary, the same holds for limit groups. We also obtain a ch…

These revised lecture notes are an expository account of part of the proof of Thurston's Ending Lamination Conjecture for Kleinian surface groups, which states that such groups are uniquely determined by invariants that describe the asymptotic structure of the ends of their quotient manifolds.

This paper introduces the Differentiable Algorithm Network (DAN), a composable architecture for robot learning systems. A DAN is composed of neural network modules, each encoding a differentiable robot algorithm and an associated model; and it is trained end-to-end from data. DAN combines the strengths of model-driven …

Study of minimal surfaces in 4D with specific ends.

In this paper we describe the notion of an annular end of a Riemann surface being of finite type with respect to some harmonic function and prove some theoretical results relating the conformal structure of such an annular end to the level sets of the harmonic function. We then apply these results to understand and cha…

A key goal of computer vision is to recover the underlying 3D structure from 2D observations of the world. In this paper we learn strong deep generative models of 3D structures, and recover these structures from 3D and 2D images via probabilistic inference. We demonstrate high-quality samples and report log-likelihoods…

This paper presents a comparison of a traditional hybrid speech recognition system (kaldi using WFST and TDNN with lattice-free MMI) and a lexicon-free end-to-end (TensorFlow implementation of multi-layer LSTM with CTC training) models for German syllable recognition on the Verbmobil corpus. The results show that expli…

New minimal surfaces found with Cantor ends in convex domains.

We introduce efficient algorithms which achieve nearly optimal regrets for the problem of stochastic online shortest path routing with end-to-end feedback. The setting is a natural application of the combinatorial stochastic bandits problem, a special case of the linear stochastic bandits problem. We show how the diffi…