相关论文: Translation-Equivariant Matchings of Coin-Flips on…
Consider Bernoulli(1/2) percolation on $\Z^d$, and define a perfect matching between open and closed vertices in a way that is a deterministic equivariant function of the configuration. We want to find such matching rules that make the…
Consider a point process in Euclidean space obtained by perturbing the integer lattice with independent and identically distributed random vectors. Under mild assumptions on the law of the perturbations, we construct a translation-invariant…
The many-to-many multilingual neural machine translation can translate between language pairs unseen during training, i.e., zero-shot translation. Improving zero-shot translation requires the model to learn universal representations and…
We study the problem of covering R^d by overlapping translates of a convex body P, such that almost every point of R^d is covered exactly k times. Such a covering of Euclidean space by translations is called a k-tiling. The investigation of…
Continuous word representations learned separately on distinct languages can be aligned so that their words become comparable in a common space. Existing works typically solve a least-square regression problem to learn a rotation aligning a…
Our goal is to compare two planar point sets by finding subsets of a given size such that a minimum-weight matching between them has the smallest weight. This can be done by a translation of one set that minimizes the weight of the…
Spin models are widely studied in the natural sciences, from investigating magnetic materials in condensed matter physics to studying neural networks. Previous work has demonstrated that there exist simple classical spin models that are…
Consider Bernoulli(1/2) percolation on $\mathbb{Z}^d$, and define a perfect matching between open and closed vertices in a way that is a deterministic equivariant function of the configuration. We want to find such matching rules that make…
This paper proposes a mechanism for learning pattern correspondences between two languages from a corpus of translated sentence pairs. The proposed mechanism uses analogical reasoning between two translations. Given a pair of translations,…
In this paper, we propose an Optimal Transport objective for learning one-dimensional translation-equivariant systems and demonstrate its applicability to single pitch estimation. Our method provides a theoretically grounded, more…
For the basic case of $L_2$ optimal transport between two probability measures on a Euclidean space, the regularity of the coupling measure and the transport map in the tail regions of these measures is studied. For this purpose, Robert…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
This paper is concerned with a pairs trading rule. The idea is to monitor two historically correlated securities. When divergence is underway, i.e., one stock moves up while the other moves down, a pairs trade is entered which consists of a…
We prove the existence of a finitely dependent proper colouring of the integer lattice Z^d that is fully isometry-invariant in law, for all dimensions d. Previously this was known only for d=1, while only translation-invariant examples were…
The Earth Mover's Distance is a popular similarity measure in several branches of computer science. It measures the minimum total edge length of a perfect matching between two point sets. The Earth Mover's Distance under Translation…
We characterize the polytopes in $\mathbb{R}^d$ (not necessarily convex or connected ones) which multi-tile the space by translations along a given lattice. We also give a necessary and sufficient condition for two polytopes in…
For a game with positive profit, the optimal proportion of investment required to continue investing without borrowing is uniquely determined by an integral equation for each price. For a game with parallel translated profit, the ratio of…
Suppose that the vertices of ${\mathbb Z}^d$ are assigned random colors via a finitary factor of independent identically distributed (iid) vertex-labels. That is, the color of vertex $v$ is determined by a rule that examines the labels…
Objects' rigid motions in 3D space are described by rotations and translations of a highly-correlated set of points, each with associated $x,y,z$ coordinates that real-valued networks consider as separate entities, losing information.…
Many multilingual NLP applications need to translate words between different languages, but cannot afford the computational expense of inducing or applying a full translation model. For these applications, we have designed a fast algorithm…