arXiv research

Paper tackles cold-start domain adaptation with language descriptions.

Sharp estimates for heat flow on nonconvex domains.

Researchers prove hot spots conjecture for Gaussian spaces.

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

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.

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…

In this article we dwell into the class of so called ill posed Linear Inverse Problems (LIP) in machine learning, which has become almost a classic in recent times. The fundamental task in an LIP is to recover the entire signal / data from its relatively few random linear measurements. Such problems arise in variety of…

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…

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 …

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 …

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 $C^0$-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…

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…

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.

Speech-driven visual speech synthesis involves mapping features extracted from acoustic speech to the corresponding lip animation controls for a face model. This mapping can take many forms, but a powerful approach is to use deep neural networks (DNNs). However, a limitation is the lack of synchronized audio, video, an…

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…

Recent work shows unequal performance of commercial face classification services in the gender classification task across intersectional groups defined by skin type and gender. Accuracy on dark-skinned females is significantly worse than on any other group. In this paper, we conduct several analyses to try to uncover t…

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…

Interpretability and fairness are critical in computer vision and machine learning applications, in particular when dealing with human outcomes, e.g. inviting or not inviting for a job interview based on application materials that may include photographs. One promising direction to achieve fairness is by learning data …

Visual Speech Recognition (VSR) is the process of recognizing or interpreting speech by watching the lip movements of the speaker. Recent machine learning based approaches model VSR as a classification problem; however, the scarcity of training data leads to error-prone systems with very low accuracies in predicting un…

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…

In recent years, there have been numerous developments towards solving multimodal tasks, aiming to learn a stronger representation than through a single modality. Certain aspects of the data can be particularly useful in this case - for example, correlations in the space or time domain across modalities - but should be…

Correntropy is a local similarity measure defined in kernel space and the maximum correntropy criterion (MCC) has been successfully applied in many areas of signal processing and machine learning in recent years. The kernel function in correntropy is usually restricted to the Gaussian function with center located at ze…

Aggregated hold-out (Agghoo) is a method which averages learning rules selected by hold-out (that is, cross-validation with a single split). We provide the first theoretical guarantees on Agghoo, ensuring that it can be used safely: Agghoo performs at worst like the hold-out when the risk is convex. The same holds true…

This is first of series papers on new two-side Gaussian bounds for the heat kernel $H(x,y,t)$ on a complete manifold $(M,g)$. In this paper, on a complete manifold $M$ with $Ric(M)\geq 0$, we obtain new two-side Gaussian bounds for the heat kernel $H(x,y,t)$, which improve the well-known Li-Yau's two-side bounds. As ap…

We solve the differentiability problem for the evolution map in Milnor's infinite dimensional setting. We first show that the evolution map of each $C^k$-semiregular Lie group $G$ (for $k\in \mathbb{N}\sqcup\{\mathrm{lip},\infty\}$) admits a particular kind of sequentially continuity $-$ called Mackey k-continuity. We …

Automatic speech recognition can potentially benefit from the lip motion patterns, complementing acoustic speech to improve the overall recognition performance, particularly in noise. In this paper we propose an audio-visual fusion strategy that goes beyond simple feature concatenation and learns to automatically align…

An open question in systems and computational neuroscience is how neural circuits accumulate evidence towards a decision. Fitting models of decision-making theory to neural activity helps answer this question, but current approaches limit the number of these models that we can fit to neural data. Here we propose a unif…

Horseshoe priors improve small area estimation by borrowing strength globally but locally.

Let $C$ be a subset of $\mathbb{R}^n$ (not necessarily convex), $f:C\to\mathbb{R}$ be a function, and $G:C\to\mathbb{R}^n$ be a uniformly continuous function, with modulus of continuity $ω$. We provide a necessary and sufficient condition on $f$, $G$ for the existence of a convex function $F\in C^{1, ω}(\mathbb{R}^n)$ …

In this work we present an adversarial training algorithm that exploits correlations in video to learn --without supervision-- an image generator model with a disentangled latent space. The proposed methodology requires only a few modifications to the standard algorithm of Generative Adversarial Networks (GAN) and invo…

We will study metric measure spaces $(X,d,m)$ beyond the scope of spaces with synthetic lower Ricci bounds. In particular, we introduce distribution-valued lower Ricci bounds BE$_1(κ,\infty)$ $\bullet$ for which we prove the equivalence with sharp gradient estimates, $\bullet$ the class of which will be preserved under…

We present a systematic analysis on the performance of a phonetic recogniser when the window of input features is not symmetric with respect to the current frame. The recogniser is based on Context Dependent Deep Neural Networks (CD-DNNs) and Hidden Markov Models (HMMs). The objective is to reduce the latency of the sy…

Harmonic maps between specific metric spaces are studied with Lipschitz estimates and variational principles.

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…