arXiv research

A new framework for fair representation learning using correction vectors.

In this paper, we introduce a study of prolongations of homogeneous vector bundles. We give an alternative approach for the prolongation. For a given homogeneous vector bundle E, we obtain a new homogeneous vector bundle. The homogeneous structure and its corresponding representation are derived. The prolongation of in…

Latent representations are the essence of deep generative models and determine their usefulness and power. For latent representations to be useful as generative concept representations, their latent space must support latent space interpolation, attribute vectors and concept vectors, among other things. We investigate …

SL(n) covariant valuations on Orlicz spaces are represented and characterized.

Dictionaries are collections of vectors used for representations of random vectors in Euclidean spaces. Recent research on optimal dictionaries is focused on constructing dictionaries that offer sparse representations, i.e., $\ell_0$-optimal representations. Here we consider the problem of finding optimal dictionaries …

The paper explores theories behind graph and relational data vector embeddings.

Constructs 2-representations and 2-vector bundles for Lie 2-groups.

Constructs a representation of the string 2-group on a von Neumann algebra.

This paper considers the Pontryagin characters of graded vector bundles of finite rank, in the cohomology vector spaces of a Lie algebroid over the same base. These Pontryagin characters vanish if the graded vector bundle carries a representation up to homotopy of the Lie algebroid. As a consequence, this gives a stron…

Geometric models for representations up to homotopy using simplicial vector bundles.

Extends adjoint representation concept to higher Lie groupoids.

This paper proposes a representational model for grid cells. In this model, the 2D self-position of the agent is represented by a high-dimensional vector, and the 2D self-motion or displacement of the agent is represented by a matrix that transforms the vector. Each component of the vector is a unit or a cell. The mode…

We demonstrate that the notions of derivative representation of a Lie algebra on a vector bundle, of semi-linear representations of a Lie group on a vector bundle, and related concepts, may be understood in terms of representations of Lie algebroids and Lie groupoids, and we indicate how these notions extend to derivat…

Dictionaries are collections of vectors used for representations of elements in Euclidean spaces. While recent research on optimal dictionaries is focussed on providing sparse (i.e., $\ell_0$-optimal,) representations, here we consider the problem of finding optimal dictionaries such that representations of samples of …

Learning representations of data is an important problem in statistics and machine learning. While the origin of learning representations can be traced back to factor analysis and multidimensional scaling in statistics, it has become a central theme in deep learning with important applications in computer vision and co…

Proofs Lie's classification of certain vector field subalgebras.

In representation learning (RL), how to make the learned representations easy to interpret and less overfitted to training data are two important but challenging issues. To address these problems, we study a new type of regulariza- tion approach that encourages the supports of weight vectors in RL models to have small …

Investigates set-valued risk measures for processes and vectors, proving equivalence and providing new dual representations.

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…

The paper proves a quadratic formality for Sasakian manifolds' representation varieties.

Semantic representations of words have been successfully extracted from unlabeled corpuses using neural network models like word2vec. These representations are generally high quality and are computationally inexpensive to train, making them popular. However, these approaches generally fail to approximate out of vocabul…

Model predicts travel time under rare conditions using a vector-space model.

Computes the decomposition of rank-three bundles over the projective line with three marked points.

This paper proposes a representational model for image pairs such as consecutive video frames that are related by local pixel displacements, in the hope that the model may shed light on motion perception in primary visual cortex (V1). The model couples the following two components: (1) the vector representations of loc…

VecMol generates 3D molecules as continuous vector fields, overcoming modality and geometry constraints.

Top2Vec finds topic vectors from documents and words without needing stop words or custom settings.

An important part of many machine learning workflows on graphs is vertex representation learning, i.e., learning a low-dimensional vector representation for each vertex in the graph. Recently, several powerful techniques for unsupervised representation learning have been demonstrated to give the state-of-the-art perfor…

Enhances multi-tag classification using low-dimensional vector representations and virtual data.

VB-groupoids are vector bundles in the category of Lie groupoids. They encompass several classical objects, including Lie group representations and 2-vector spaces. Moreover, they provide geometric pictures for 2-term representations up to homotopy of Lie groupoids. We attach to every VB-groupoid a cochain complex cont…

The recently introduced continuous Skip-gram model is an efficient method for learning high-quality distributed vector representations that capture a large number of precise syntactic and semantic word relationships. In this paper we present several extensions that improve both the quality of the vectors and the traini…

A new method learns discrete representations for images and videos, improving upon previous models.

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 define Lie algebroids over infinite jet spaces and establish their equivalent representation through homological evolutionary vector fields.

New method preserves topology in Hodge decomposition for scalar and vector fields.

Transformers infer tasks from context via two modes, geometrically shaped task vectors explain their behavior.

Given vector representations for individual words, it is necessary to compute vector representations of sentences for many applications in a compositional manner, often using artificial neural networks. Relatively little work has explored the internal structure and properties of such sentence vectors. In this paper, we…

Explores tensor products in hyperdimensional computing.

This paper shows that deep learning (DL) representations of data produced by generative adversarial nets (GANs) are random vectors which fall within the class of so-called \textit{concentrated} random vectors. Further exploiting the fact that Gram matrices, of the type $G = X^T X$ with $X=[x_1,\ldots,x_n]\in \mathbb{R}…

Vector representations of words have heralded a transformational approach to classical problems in NLP; the most popular example is word2vec. However, a single vector does not suffice to model the polysemous nature of many (frequent) words, i.e., words with multiple meanings. In this paper, we propose a three-fold appr…

Representation learning is an essential problem in a wide range of applications and it is important for performing downstream tasks successfully. In this paper, we propose a new model that learns coupled representations of domains, intents, and slots by taking advantage of their hierarchical dependency in a Spoken Lang…

Study partially hyperbolic flows on flat bundles, proving equivalence for complete affine manifolds.

Into this note we collect topics related to homogeneous vector bundles, elliptic adjoint orbits and so forth.

Real-valued word representations have transformed NLP applications; popular examples are word2vec and GloVe, recognized for their ability to capture linguistic regularities. In this paper, we demonstrate a {\em very simple}, and yet counter-intuitive, postprocessing technique -- eliminate the common mean vector and a f…

Paper introduces vector-valued variation spaces for multi-output neural networks.

Most of the information is stored as text, so text mining is regarded as having high commercial potential. Aiming at the semantic constraint problem of classification methods based on sparse representation, we propose a weighted recurrent neural network (W-RNN), which can fully extract text serialization semantic infor…

We examine the relationship between nonabelian Hodge theory for Riemann surfaces and the theory of vector valued modular forms. In particular, we explain how one might use this relationship to prove a conjectural three-term inequality on the weights of free bases of vector valued modular forms associated to complex, fi…

Recurrent neural networks (RNNs) are an effective representation of control policies for a wide range of reinforcement and imitation learning problems. RNN policies, however, are particularly difficult to explain, understand, and analyze due to their use of continuous-valued memory vectors and observation features. In …

Automated sentiment analysis and opinion mining is a complex process concerning the extraction of useful subjective information from text. The explosion of user generated content on the Web, especially the fact that millions of users, on a daily basis, express their opinions on products and services to blogs, wikis, so…