arXiv research

In recent years, deep metric learning has achieved promising results in learning high dimensional semantic feature embeddings where the spatial relationships of the feature vectors match the visual similarities of the images. Similarity search for images is performed by determining the vectors with the smallest distanc…

This paper proposes novel algorithms for speaker embedding using subjective inter-speaker similarity based on deep neural networks (DNNs). Although conventional DNN-based speaker embedding such as a $d$-vector can be applied to multi-speaker modeling in speech synthesis, it does not correlate with the subjective inter-…

Explains differences and similarities of strictly nef and ample vector bundles.

In this work we present STEVE - Soccer TEam VEctors, a principled approach for learning real valued vectors for soccer teams where similar teams are close to each other in the resulting vector space. STEVE only relies on freely available information about the matches teams played in the past. These vectors can serve as…

Similarity metrics are a core component of many information retrieval and machine learning systems. In this work we propose a method capable of learning a similarity metric from data equipped with a binary relation. By considering only the similarity constraints, and initially ignoring the features, we are able to lear…

Proposes a method to compare neural networks using feature and gradient vectors.

A large body of research into semantic textual similarity has focused on constructing state-of-the-art embeddings using sophisticated modelling, careful choice of learning signals and many clever tricks. By contrast, little attention has been devoted to similarity measures between these embeddings, with cosine similari…

I classify spacelike self-similar shrinking solutions of the mean curvature flow in pseudo-euclidean space in arbitrary codimension, if the mean curvature vector is not a null vector and the principal normal vector is parallel in the normal bundle. Moreover, I exclude the existence of such self-shrinkers in several cas…

Automatic measurement of semantic text similarity is an important task in natural language processing. In this paper, we evaluate the performance of different vector space models to perform this task. We address the real-world problem of modeling patent-to-patent similarity and compare TFIDF (and related extensions), t…

We consider the problem of learning a measure of distance among vectors in a feature space and propose a hybrid method that simultaneously learns from similarity ratings assigned to pairs of vectors and class labels assigned to individual vectors. Our method is based on a generative model in which class labels can prov…

Two private algorithms estimate Jaccard similarity efficiently.

This paper addresses the nearest neighbor search problem under inner product similarity and introduces a compact code-based approach. The idea is to approximate a vector using the composition of several elements selected from a source dictionary and to represent this vector by a short code composed of the indices of th…

New compression schemes save communication in distributed mean estimation.

ICQ improves high-dimensional similarity search without sacrificing precision.

We present a new trace estimator of the matrix whose explicit form is not given but its matrix multiplication to a vector is available. The form of the estimator is similar to the Hutchison stochastic trace estimator, but instead of the random noise vectors in Hutchison estimator, we use small number of probing vectors…

Eliciting semantic similarity between concepts in the biomedical domain remains a challenging task. Recent approaches founded on embedding vectors have gained in popularity as they risen to efficiently capture semantic relationships The underlying idea is that two words that have close meaning gather similar contexts. …

One of the ubiquitous representation of long DNA sequence is dividing it into shorter k-mer components. Unfortunately, the straightforward vector encoding of k-mer as a one-hot vector is vulnerable to the curse of dimensionality. Worse yet, the distance between any pair of one-hot vectors is equidistant. This is partic…

In this paper we explore the "vector semantics" problem from the perspective of "almost orthogonal" property of high-dimensional random vectors. We show that this intriguing property can be used to "memorize" random vectors by simply adding them, and we provide an efficient probabilistic solution to the set membership …

Geospatial analysis lacks methods like the word vector representations and pre-trained networks that significantly boost performance across a wide range of natural language and computer vision tasks. To fill this gap, we introduce Tile2Vec, an unsupervised representation learning algorithm that extends the distribution…

We investigate three-dimensional surfaces where the normal vector forms a constant angle with the radius vector. These surfaces naturally extend equiangular (logarithmic) spirals in the plane.

New method for estimating firm linkages using CVLs and QCML.

Estimates mean of distributed vectors with sparsification and spatial/temporal correlations.

Feed-forward networks are widely used in cross-modal applications to bridge modalities by mapping distributed vectors of one modality to the other, or to a shared space. The predicted vectors are then used to perform e.g., retrieval or labeling. Thus, the success of the whole system relies on the ability of the mapping…

In this review paper, we present several results on central extensions of the Lie algebra of symplectic (Hamiltonian) vector fields, and compare them to similar results for the Lie algebra of (exact) divergence free vector fields. In particular, we comment on universal central extensions and integrability to the group …

The Global Vectors for word representation (GloVe), introduced by Jeffrey Pennington et al. is reported to be an efficient and effective method for learning vector representations of words. State-of-the-art performance is also provided by skip-gram with negative-sampling (SGNS) implemented in the word2vec tool. In this…

Curvature flow and inverse curvature flow solutions on 2D light cone identified.

We prove a theorem which asserts that the Lie algebra of all holomorphic vector fields on a compact Kähler manifold with a perturbed extremal metric has the structure similar to the case of an unperturbed extremal Kähler metric proved by Calabi.

New self-similarity for Einstein vacuum equations identified.

Generative autoencoders offer a promising approach for controllable text generation by leveraging their latent sentence representations. However, current models struggle to maintain coherent latent spaces required to perform meaningful text manipulations via latent vector operations. Specifically, we demonstrate by exa…

The following paper presents a method of comparing two sets of vectors. The method can be applied in all tasks, where it is necessary to measure the closeness of two objects presented as sets of vectors. It may be applicable when we compare the meanings of two sentences as part of the problem of paraphrasing. This is t…

Matrix factorization is at the heart of many machine learning algorithms, for example, dimensionality reduction (e.g. kernel PCA) or recommender systems relying on collaborative filtering. Understanding a singular value decomposition (SVD) of a matrix as a neural network optimization problem enables us to decompose lar…

Optimized fuzzy entropy framework improves feature selection and classification performance.

In this paper, we define a new family of curves and call it a {\it family of similar curves with variable transformation} or briefly {\it SA-curves}. Also we introduce some characterizations of this family and we give some theorems. This definition introduces a new classification of a space curve. Also, we use this def…

In this paper we introduce and study a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its various properties, prove the global existence of the solution of this flow, discuss its convergence and possible applications, and its relation to the …

New method reduces clustering time and improves accuracy.

Vector embedding is a foundational building block of many deep learning models, especially in natural language processing. In this paper, we present a theoretical framework for understanding the effect of dimensionality on vector embeddings. We observe that the distributional hypothesis, a governing principle of statis…

The paper characterizes vector bundles and differential operators using Lie algebras and their symbols.

Given a discrete subgroup $Γ$ of finite co-volume of $\mathrm{PGL}(2,\mathbb{R})$, we define and study parabolic vector bundles on the quotient $Σ$ of the (extended) hyperbolic plane by $Γ$. If $Γ$ contains an orientation-reversing isometry, then the above is equivalent to studying real and quaternionic parabolic vecto…

For statistical learning, categorical variables in a table are usually considered as discrete entities and encoded separately to feature vectors, e.g., with one-hot encoding. "Dirty" non-curated data gives rise to categorical variables with a very high cardinality but redundancy: several categories reflect the same ent…

We propose a family of near-metrics based on local graph diffusion to capture similarity for a wide class of data sets. These quasi-metametrics, as their names suggest, dispense with one or two standard axioms of metric spaces, specifically distinguishability and symmetry, so that similarity between data points of arbi…

We consider the problem of developing suitable learning representations (embeddings) for library packages that capture semantic similarity among libraries. Such representations are known to improve the performance of downstream learning tasks (e.g. classification) or applications such as contextual search and analogica…

Let $X$ be a smooth projective variety over $\mathbb C$. We prove that a twisted Higgs vector bundle $(\calE\, ,θ)$ on $X$ admits an Einstein--Hermitian connection if and only if $(\calE\, ,θ)$ is polystable. A similar result for twisted vector bundles (no Higgs fields) was proved by S. Wang in \cite{Wa}. Our approach …

Text classification has become indispensable due to the rapid increase of text in digital form. Over the past three decades, efforts have been made to approach this task using various learning algorithms and statistical models based on bag-of-words (BOW) features. Despite its simple implementation, BOW features lack se…

We present a neural model for representing snippets of code as continuous distributed vectors ("code embeddings"). The main idea is to represent a code snippet as a single fixed-length $\textit{code vector}$, which can be used to predict semantic properties of the snippet. This is performed by decomposing code to a col…

Traditionally, multi-layer neural networks use dot product between the output vector of previous layer and the incoming weight vector as the input to activation function. The result of dot product is unbounded, thus increases the risk of large variance. Large variance of neuron makes the model sensitive to the change o…

Identification of high affinity drug-target interactions is a major research question in drug discovery. Proteins are generally represented by their structures or sequences. However, structures are available only for a small subset of biomolecules and sequence similarity is not always correlated with functional similar…

A collection of $U \: (\in \mathbb{N})$ data vectors is called a $U$-tuple, and the association strength among the vectors of a tuple is termed as the \emph{hyperlink weight}, that is assumed to be symmetric with respect to permutation of the entries in the index. We herein propose Bregman hyperlink regression (BHLR), …

Gaussian random vectors exhibit the loss of dimension phenomena, which relate to their joint survival tail behaviour. Besides, the fact that the components of such vectors are light-tailed complicates the approximations of various multivariate risk measures significantly. In this contribution we derive precise approxim…