Related papers: Enumerative Encoding in the Grassmannian Space
Humans are believed to perceive numbers on a logarithmic mental number line, where smaller values are represented with greater resolution than larger ones. This cognitive bias, supported by neuroscience and behavioral studies, suggests that…
We present the first empirical evaluation of techniques for encoding distributions of quantitative edge values within adjacency matrices. In many real-world networks, edges represent not a single value but a set of measurements. While…
We propose a method to compare and visualise sentence encoders at scale by creating a map of encoders where each sentence encoder is represented in relation to the other sentence encoders. Specifically, we first represent a sentence encoder…
A central topic in mathematical logic is the classification of theorems from mathematics in hierarchies according to their logical strength. Ideally, the place of a theorem in a hierarchy does not depend on the representation (aka coding)…
Unary coding is useful but it is redundant in its standard form. Unary coding can also be seen as spatial coding where the value of the number is determined by its place in an array. Motivated by biological finding that several neurons in…
Learning representations of geographical space is vital for any machine learning model that integrates geolocated data, spanning application domains such as remote sensing, ecology, or epidemiology. Recent work embeds coordinates using sine…
Over the past few decades, there has been extensive research on scattered subspaces, partly because of their link to MRD codes. These subspaces can be characterized using linearized polynomials over finite fields. Within this context,…
In this article, three types of joins are introduced for subspaces of a vector space. Decompositions of the Gra{\ss}mannian into joins are discussed. This framework admits a generalization of large set recursion methods for block designs to…
Systems that employ network coding for content distribution convey to the receivers linear combinations of the source packets. If we assume randomized network coding, during this process the network nodes collect random subspaces of the…
The objective of knowledge graph embedding is to encode both entities and relations of knowledge graphs into continuous low-dimensional vector spaces. Previously, most works focused on symbolic representation of knowledge graph with…
In this paper, we generalize the well-known index coding problem to exploit the structure in the source-data to improve system throughput. In many applications, the data to be transmitted may lie (or can be well approximated) in a…
An equiangular tight frame (ETF) is a sequence of vectors in a Hilbert space that achieves equality in the Welch bound and so has minimal coherence. More generally, an equichordal tight fusion frame (ECTFF) is a sequence of equi-dimensional…
In this paper we introduce and study line Hermitian Grassmann codes as those subcodes of the Grassmann codes associated to the $2$-Grassmannian of a Hermitian polar space defined over a finite field of square order. In particular, we…
Sequence-to-sequence models are widely used to train Abstract Meaning Representation (Banarescu et al., 2013, AMR) parsers. To train such models, AMR graphs have to be linearized into a one-line text format. While Penman encoding is…
Modern machine learning algorithms have been adopted in a range of signal-processing applications spanning computer vision, natural language processing, and artificial intelligence. Many relevant problems involve subspace-structured…
Limited feedback is a paradigm for the feedback of channel state information in wireless systems. In multiple antenna wireless systems, limited feedback usually entails quantizing a source that lives on the Grassmann manifold. Most work on…
Euclidean representations distort data with intrinsic non-Euclidean structure. While Riemannian representation learning offers a solution by embedding data onto matching manifolds, it typically relies on an encoder to estimate densities on…
Combining Generative Adversarial Networks (GANs) with encoders that learn to encode data points has shown promising results in learning data representations in an unsupervised way. We propose a framework that combines an encoder and a…
The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…
The success of machine learning methods heavily relies on having an appropriate representation for data at hand. Traditionally, machine learning approaches relied on user-defined heuristics to extract features encoding structural…