Related papers: Terminal Embeddings in Sublinear Time
We present a finite-temperature extension of density matrix embedding theory (FT-DMET) for realistic crystalline systems. We describe a practical framework for constructing extended bath orbitals, solving the embedding problem, and…
Wasserstein distances form a family of metrics on spaces of probability measures that have recently seen many applications. However, statistical analysis in these spaces is complex due to the nonlinearity of Wasserstein spaces. One…
Probabilistic metric embedding into trees is a powerful technique for designing online algorithms. The standard approach is to embed the entire underlying metric into a tree metric and then solve the problem on the latter. The overhead in…
Randomized dimensionality reduction has been recognized as one of the fundamental techniques in handling high-dimensional data. Starting with the celebrated Johnson-Lindenstrauss Lemma, such reductions have been studied in depth for the…
The main goal of this paper is to develop a new embedding method which we use to show that some finite metric spaces admit low-distortion embeddings into all non-superreflexive spaces. This method is based on the theory of…
An outstanding open question posed by Guha and Indyk in 2006 asks to characterize metric spaces in which distances can be estimated using efficient sketches. Specifically, we say that a sketching algorithm is efficient if it achieves…
In machine learning or statistics, it is often desirable to reduce the dimensionality of a sample of data points in a high dimensional space $\mathbb{R}^d$. This paper introduces a dimensionality reduction method where the embedding…
We study symmetric tensor decompositions, i.e., decompositions of the form $T = \sum_{i=1}^r u_i^{\otimes 3}$ where $T$ is a symmetric tensor of order 3 and $u_i \in \mathbb{C}^n$.In order to obtain efficient decomposition algorithms, it is…
Good approximations have been attained for the sparsest cut problem by rounding solutions to convex relaxations via low-distortion metric embeddings. Recently, Bryant and Tupper showed that this approach extends to the hypergraph setting by…
We consider the vector embedding problem. We are given a finite set of items, with the goal of assigning a representative vector to each one, possibly under some constraints (such as the collection of vectors being standardized, i.e.,…
Given a set of well-formed terminal pairs on the external face of an undirected planar graph with unit edge weights, we give a linear-time algorithm for computing the union of non-crossing shortest paths joining each terminal pair, where…
Many real-world problems can be formulated as geometric optimization problems in high dimensions, especially in the fields of machine learning and data mining. Moreover, we often need to take into account of outliers when optimizing the…
A plethora of sentence embedding models makes it challenging to choose one, especially for technical domains rich with specialized vocabulary. In this work, we domain adapt embeddings using telecom data for question answering. We evaluate…
Most mathematical distortions used in ML are fundamentally integral in nature: $f$-divergences, Bregman divergences, (regularized) optimal transport distances, integral probability metrics, geodesic distances, etc. In this paper, we unveil…
We explore the effectiveness of an LLM-guided query refinement paradigm for extending the usability of embedding models to challenging zero-shot search and classification tasks. Our approach refines the embedding representation of a user…
Learning the embedding space, where semantically similar objects are located close together and dissimilar objects far apart, is a cornerstone of many computer vision applications. Existing approaches usually learn a single metric in the…
Frechet's classical isometric embedding argument has evolved to become a major tool in the study of metric spaces. An important example of a Frechet embedding is Bourgain's embedding. The authors have recently shown that for every e>0 any…
Under which conditions and with which distortions can we preserve the pairwise-distances of low-complexity vectors, e.g., for structured sets such as the set of sparse vectors or the one of low-rank matrices, when these are mapped in a…
The modern ability to collect vast quantities of data poses a challenge for parameter estimation problems. When posed as a nonlinear least squares problem fitting a model to data, the cost of each iteration grows linearly with the amount of…
Macro embedding is a popular approach to defining extensible shallow embeddings of object languages in Scheme like host languages. While macro embedding has even been shown to enable implementing extensible typed languages in systems like…