arXiv research

Novel algorithm for privacy-preserving distributed learning in analog domain.

SCL discovers compositional structures in analogical reasoning tasks.

There is an analogy between machine learning systems and economic entities in that they are both adaptive, and their behaviour is specified in a more-or-less explicit way. It appears that the area of AI that is most analogous to the behaviour of economic entities is that of morally good decision-making, but it is an op…

We study the curvature flow of planar nonconvex lens-shaped domains, considered as special symmetric networks with two triple junctions. We show that the evolving domain becomes convex in finite time; then it shrinks homothetically to a point. Our theorem is the analog of the result of Grayson for curvature flow of clo…

Building on a specific formalization of analogical relationships of the form "A relates to B as C relates to D", we establish a connection between two important subfields of artificial intelligence, namely analogical reasoning and kernel-based machine learning. More specifically, we show that so-called analogical propo…

Smooth analog of Gromov's dihedral rigidity for 3D weakly convex domains.

Paper formalizes analogy between data sets and models using Hoare logic.

Study Kähler-Ricci solitons on bounded domains, proving they are Kähler-Einstein.

Establishes a lower bound for Kähler-Einstein distance on certain domains.

Selects points from Jordan domains on Riemannian surfaces.

In this paper, it is shown that a Fuchsian group, acting on the upper half-plane model for $\mathbb{H}^2$, admits a Ford domain which is also a Dirichlet domain, for some center, if and only if it is an index 2 subgroup of a reflection group. This is used to exhibit an example of a maximal arithmetic hyperbolic reflect…

New rigidity found for 3D warped product domains.

The special linear groups, the mapping class groups of surfaces, the outer autormorphism groups of free groups appear in numerous domains. Their analogies, developped in particular in K. Vogtmann's work, have been written about a lot. In this report, we concentrate on the contractible spaces on which these groups act i…

We present a framework for translating unlabeled images from one domain into analog images in another domain. We employ a progressively growing skip-connected encoder-generator structure and train it with a GAN loss for realistic output, a cycle consistency loss for maintaining same-domain translation identity, and a s…

The index theorem connects anomalies on a domain wall to global integrals.

Our main result is that if a generic convex domain in $\R^n$ collapses to a domain in $\R^{n-1}$, then the difference between the first two Dirichlet eigenvalues of the Euclidean Laplacian, known as the fundamental gap, diverges. The boundary of the domain need not be smooth, merely Lipschitz continuous. To motivate th…

In this paper we consider discrete groups in ${\rm PGL}_d(\mathbb{R})$ acting convex co-compactly on a properly convex domain in real projective space. For such groups, we establish necessary and sufficient conditions for the group to be relatively hyperbolic in terms of the geometry of the convex domain. This answers …

Theory of packing diabolic domains in liquid crystals.

Analog deep learning shows promise but faces scalability challenges.

A scalable deep learning framework accelerates training of large neural networks for solving 3D Poisson equations.

The study sets lower bounds for eigenvalue sums of Laplacian on bounded domains and spheres.

ASE safely explores unknown MDPs with unknown dynamics, improving sample efficiency.

Proposes BN layers for neural networks on complex domains, improving training stability and accuracy.

In this paper, we provide a new neural-network based perspective on multi-task learning (MTL) and multi-domain learning (MDL). By introducing the concept of a semantic descriptor, this framework unifies MDL and MTL as well as encompassing various classic and recent MTL/MDL algorithms by interpreting them as different w…

New inequality controls domain volume for manifolds with large spectrum.

In this paper we prove that a flat free-boundary minimal $n$-disk, $n\geq3$, in the unit Euclidean ball $B^{n+1}$ is the unique compact free boundary minimal hypersurface in the unit Euclidean ball which the squared norm of the second fundamental form is less than either $\frac{n^2}{4}$ or $\frac{(n-2)^2}{4|x|^2}$. Mor…

The problem of domain generalization is to take knowledge acquired from a number of related domains where training data is available, and to then successfully apply it to previously unseen domains. We propose a new feature learning algorithm, Multi-Task Autoencoder (MTAE), that provides good generalization performance …

Study Gromov hyperbolic domains in Minkowski space, proving equivalence to boundary properties.

Negative curvature restricts the gap between the first and second eigenvalues of convex domains.

Few-shot visual reasoning model learns analogical relationships from small data.

We study actions of discrete subgroups $Γ$ of semi-simple Lie groups $G$ on associated oriented flag manifolds. These are quotients $G/P$, where the subgroup $P$ lies between a parabolic subgroup and its identity component. For Anosov subgroups $Γ\subset G$, we identify domains in oriented flag manifolds by removing a …

We study the problem of formally verifying the robustness to adversarial examples of support vector machines (SVMs), a major machine learning model for classification and regression tasks. Following a recent stream of works on formal robustness verification of (deep) neural networks, our approach relies on a sound abst…

Theorem shows generic metrics yield non-degenerate geodesic nets.

Investigates properties of a pseudometric on domains in Euclidean space, linking it to hyperbolic geometry.

We study the problem of inviscid slightly compressible fluids in a bounded domain. We find a unique solution to the initial-boundary value problem and show that it is near the analogous solution for an incompressible fluid provided the initial conditions for the two problems are close. In particular, the divergence of …

The Einstein equations (EE) are certain conditions on the Riemann tensor on the real Minkowski space M. In the twistor picture, after complexification and compactification M becomes the Grassmannian $Gr_{2}^{4}$ of 2-dimensional subspaces in the 4-dimensional complex one. Here we answer for which of the classical domai…

Study of knotted defects in smectic liquid crystals using topological knot theory.

In this note, we investigate upper bounds of the Neumann eigenvalue problem for the Laplacian of a bounded domain (with smooth boundary) in a given complete (not compact a priori) Riemannian manifold with Ricci bounded below . For this, we use test functions for the Rayleigh quotient subordinated to a family of open se…

A new definition for vector fields extends the Jacobi set concept.

The expression (-1/u) times the Hessian of u transforms as a symmetric (0,2) tensor under projective coordinate transformations, so long as u transforms as a section of a certain line bundle. On a locally projectively flat manifold M, the section u can be regarded as a metric potential analogous to the local potential …

We are interested in comparing properties of symplectic mapping class groups of symplectic manifolds of dimension four or higher with properties of classical mapping class groups of surfaces. For $n \geq 2$, consider a configuration of Lagrangian $S^n$s in a Weinstein domain $M^{2n}$. If it is analogous, in some sense …

The paper resolves a problem about metric inequivalence and characterizes proper holomorphic maps.

Harmonic maps from $\BR^2$ or one-connected domain $Ø\subset \BR^2$ into $GL(m, \BC)$ and $U(m)$ are treated. The GBDT version of the Bäcklund-Darboux transformation is applied to the case of the harmonic maps. A new general formula on the GBDT transformations of the Sym-Tafel immersions is derived. A class of the harm…

Parallel sentences are a relatively scarce but extremely useful resource for many applications including cross-lingual retrieval and statistical machine translation. This research explores our new methodologies for mining such data from previously obtained comparable corpora. The task is highly practical since non-para…

As in the case of irreducible holomorphic symplectic manifolds, the period domain $Compl$ of compact complex tori of even dimension $2n$ contains twistor lines. These are special $2$-spheres parametrizing complex tori whose complex structures arise from a given quaternionic structure. In analogy with the case of irredu…

In this paper, we present Russian language datasets in the digital humanities domain for the evaluation of word embedding techniques or similar language modeling and feature learning algorithms. The datasets are split into two task types, word intrusion and word analogy, and contain 31362 task units in total. The chara…

The paper studies the First Order BSPDEs (Backward Stochastic Partial Differential Equations) suggested earlier for a case of multidimensional state domain with a boundary. These equations represent analogs of Hamilton-Jacobi-Bellman equations and allow to construct the value function for stochastic optimal control pro…

Object ranking or "learning to rank" is an important problem in the realm of preference learning. On the basis of training data in the form of a set of rankings of objects represented as feature vectors, the goal is to learn a ranking function that predicts a linear order of any new set of objects. In this paper, we pr…