arXiv research

Improved speech recognition with audio-visual fusion.

The goal of this project is to develop a limited lip reading algorithm for a subset of the English language. We consider a scenario in which no audio information is available. The raw video is processed and the position of the lips in each frame is extracted. We then prepare the lip data for processing and classify the…

Researchers compare two GAN models for lip-synchronization tasks.

We reformulate LIPs as min-max problems for easier solution.

Lips and swallow-tails are generic local moves of singularities of a smooth map to a 2-manifold. We prove that these moves of singularities of the product map of two functions on a 3-manifold can be realized by isotopies of the functions.

New algorithm disentangles latent space in GANs using video sequences.

We show that at generic points blow-ups/tangents of differentiability spaces are still differentiability spaces; this implies that an analytic condition introduced by Keith as an inequality (and later proved to actually be an equality) passes to tangents. As an application, we characterize the $p$-weak gradient on iter…

The paper explores how close two Lipschitz functions can be without their difference exceeding a certain bound.

We provide a sufficient condition for the nontriviality of the Lipschitz homotopy group of the Heisenberg group, $π_m^{Lip}(H_n)$, in terms of properties of the classical homotopy group of the sphere, $π_m(S^n)$. As an application we provide a new simplified proof of the fact that $π_n^{Lip}(H_n)\neq 0$, $n=1,2,...$, a…

Paper tackles cold-start domain adaptation with language descriptions.

Unified framework models neural decision-making, improving accuracy.

Solves signal recovery from few linear measurements using convex duality.

A new estimator reduces variance in slate bandit OPE.

Let us consider a Riemannian manifold $M$ (either separable or non-separable). We prove that, for every $ε>0$, every Lipschitz function $f:M\rightarrow\mathbb R$ can be uniformly approximated by a Lipschitz, $C^1$-smooth function $g$ with $\Lip(g)\le \Lip(f)+ε$. As a consequence, every Riemannian manifold is uniformly …

Sharp estimates for heat flow on nonconvex domains.

We construct a smooth compact n-dimensional manifold Y with one point singularity such that all its Lipschitz homotopy groups are trivial, but Lipschitz mappings Lip(S^n,Y) are not dense in the Sobolev space W^{1,n}(S^n,Y). On the other hand we show that if a metric space Y is Lipschitz (n-1)-connected, then Lipschitz …

We show that for every Lipschitz function $f$ defined on a separable Riemannian manifold $M$ (possibly of infinite dimension), for every continuous $ε:M\to (0,+\infty)$, and for every positive number $r>0$, there exists a $C^\infty$ smooth Lipschitz function $g:M\to\mathbb{R}$ such that $|f(p)-g(p)|\leqε(p)$ for every …

Paper finds gender classification accuracy varies by skin type, not ethnicity.

We prove that the groups of orientation preserving quasiconformal or bilipschitz homeomorphisms of S^n are simple in dimensions 2 and higher.

We relate generalized Lebesgue decompositions of measures in terms of curve fragments (Alberti representations) and Weaver derivations. This correspondence leads to a geometric characterization of the local norm on the Weaver cotangent bundle of a metric measure space $(X,μ)$: the local norm of a form $df$ sees how fas…

This paper determines the flexible exponent for non-geometric 3-manifolds.

We solve the regularity problem for Milnor's infinite dimensional Lie groups in the asymptotic estimate context. Specifically, let $G$ be a Lie group with asymptotic estimate Lie algebra $\mathfrak{g}$, and denote its evolution map by $\mathrm{evol}\colon \mathrm{D}\equiv \mathrm{dom}[\mathrm{evol}]\rightarrow G$, i.e.…

Let M be a PL 2-manifold and X be a compact subpolyhedron of M and let E(X, M) denote the space of embeddings of X into M with the compact-open topology. In this paper we study an extension property of embeddings of X into M and show that the restriction map from the homeomorphism group of M to E(X, M) is a principal b…

Researchers prove hot spots conjecture for Gaussian spaces.

We shall give useful criteria of lips, beaks and swallowtail singularities of smooth map from the plane into the plane. As an application of criteria, we will discuss the singularities of Cauchy problem of single conservation law.

The paper proves conditions for infinite lifetime of Brownian motion and regularity of heat flow.

One means of fitting functions to high-dimensional data is by providing smoothness constraints. Recently, the following smooth function approximation problem was proposed: given a finite set $E \subset \mathbb{R}^d$ and a function $f: E \rightarrow \mathbb{R}$, interpolate the given information with a function $\wideha…

We investigate singularities of all parallel surfaces to a given regular surface. In generic context, the types of singularities of parallel surfaces are cuspidal edge, swallowtail, cuspidal lips, cuspidal beaks, cuspidal butterfly and 3-dimensional $D_4^\pm$ singularities. We give criteria for these singularities type…

In this paper we introduce a synthetic notion of Riemannian Ricci bounds from below for metric measure spaces (X,d,m) which is stable under measured Gromov-Hausdorff convergence and rules out Finsler geometries. It can be given in terms of an enforcement of the Lott, Sturm and Villani geodesic convexity condition for t…

A new VAD method uses respiration patterns from video to detect speech.

New bounds on mapping degrees for geometric 3-manifolds.

A metric space $(X,d)$ has the de Groot property $GP_n$ if for any points $x_0,x_1,...,x_{n+2}\in X$ there are positive indices $i,j,k\le n+2$ such that $i\ne j$ and $d(x_i,x_j)\le d(x_0,x_k)$. If, in addition, $k\in\{i,j\}$ then $X$ is said to have the Nagata property $NP_n$. It is known that a compact metrizable spac…

Let $E$ be an arbitrary subset of $\mathbb{R}^n$ (not necessarily bounded), and $f:E\to\mathbb{R}$, $G:E\to\mathbb{R}^n$ be functions. We provide necessary and sufficient conditions for the $1$-jet $(f,G)$ to have an extension $(F, \nabla F)$ with $F:\mathbb{R}^n\to\mathbb{R}$ convex and of class $C^{1}$. Besides, if $…

Verifying the robustness property of a general Rectified Linear Unit (ReLU) network is an NP-complete problem [Katz, Barrett, Dill, Julian and Kochenderfer CAV17]. Although finding the exact minimum adversarial distortion is hard, giving a certified lower bound of the minimum distortion is possible. Current available m…

In classical differential geometry, the problem of the determination of the position vector of an arbitrary space curve according to the intrinsic equations $κ=κ(s)$ and $τ=τ(s)$ (where $κ$ and $τ$ are the curvature and torsion of the space curve $ψ$, respectively) is still open \cite{eisenh, lips}. However, in the cas…

MT-VAE learns motion transitions for generating diverse future motions.

We solve the regularity problem for Milnor's infinite dimensional Lie groups in the $C^0$-topological context, and provide necessary and sufficient regularity conditions for the (standard) $C^k$-topological setting. We prove that the evolution map is $C^0$-continuous on its domain $\textit{iff}\hspace{1pt}$ the Lie gro…

Introduces Motion Programs for better video analysis of human motion.

Study motion planning for points avoiding obstacles in a plane.

Paper introduces new motion synthesis model using normalizing flows.

Programmatic Motion Concepts learn human actions from paired videos.

Unified framework for human motion generation on Riemannian manifolds.

Study on determinants of unitary Brownian motion and their asymptotic laws.

New framework predicts diverse, contextually plausible 3D human motions.

Study refracted skew Brownian motion, find densities and asymptotics.

Neural network predicts vessel motions with high accuracy.

Study fractal dimension for motion without crossing a subset.

Let $E$ be a closed set in the Riemann sphere $\widehat{\mathbb{C}}$. We consider a holomorphic motion $φ$ of $E$ over a complex manifold $M$, that is, a holomorphic family of injections on $E$ parametrized by $M$. It is known that if $M$ is the unit disk $Δ$ in the complex plane, then any holomorphic motion of $E$ ove…