Related papers: Linear Classifiers in Product Space Forms

Pre-trained word embeddings are widely used for transfer learning in natural language processing. The embeddings are continuous and distributed representations of the words that preserve their similarities in compact Euclidean spaces.…

A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices…

Recognition of grocery products in store shelves poses peculiar challenges. Firstly, the task mandates the recognition of an extremely high number of different items, in the order of several thousands for medium-small shops, with many of…

Image retrieval methods rely on metric learning to train backbone feature extraction models that can extract discriminant queries and reference (gallery) feature representations for similarity matching. Although state-of-the-art accuracy…

An algebraic investigation on bicomplex numbers is carried out here. Particularly matrices and linear maps defined on them are discussed. A new kind of cartesian product, referred to as an idempotent product, is introduced and studied. The…

The need for efficiently comparing and representing datasets with unknown alignment spans various fields, from model analysis and comparison in machine learning to trend discovery in collections of medical datasets. We use manifold learning…

Understanding how linguistic structures are encoded in contextualized embedding could help explain their impressive performance across NLP@. Existing approaches for probing them usually call for training classifiers and use the accuracy,…

In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…

Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…

Learning good image representations that are beneficial to downstream tasks is a challenging task in computer vision. As such, a wide variety of self-supervised learning approaches have been proposed. Among them, contrastive learning has…

In many data science applications, the objective is to extract appropriately-ordered smooth low-dimensional data patterns from high-dimensional data sets. This is challenging since common sorting algorithms are primarily aiming at finding…

Semantic segmentation in hyperbolic space enables compact modeling of hierarchical structure while providing inherent uncertainty quantification. Prior approaches predominantly rely on the Poincar\'e ball model, which suffers from numerical…

Tabular data learning has extensive applications in deep learning but its existing embedding techniques are limited in numerical and categorical features such as the inability to capture complex relationships and engineering. This paper…

Low-dimensional embeddings are essential for machine learning tasks involving graphs, such as node classification, link prediction, community detection, network visualization, and network compression. Although recent studies have identified…

Node embedding methods find latent lower-dimensional representations which are used as features in machine learning models. In the last few years, these methods have become extremely popular as a replacement for manual feature engineering.…

Given multi-category point sets from different place-types, our goal is to develop a spatially-lucid classifier that can distinguish between two classes based on the arrangements of their points. This problem is important for many…

Despite advances in representation learning, high-dimensional classification remains challenging in low-sample-size regimes, where the dominant signal may vary across applications and labeled data are often limited. We propose a…

This article proposes and studies warped-linear models for time series classification. The proposed models are time-warp invariant analogues of linear models. Their construction is in line with time series averaging and extensions of…

Recent works have demonstrated reasonable success of representation learning in hypercomplex space. Specifically, "fully-connected layers with Quaternions" (4D hypercomplex numbers), which replace real-valued matrix multiplications in…

One of the main methods for computational interpretation of a text is mapping it into a vector in some embedding space. Such vectors can then be used for a variety of textual processing tasks. Recently, most embedding spaces are a product…