Related papers: Elementary properties of circle map sequences

We investigate the behavior of maps learned by machine translation methods. The maps translate words by projecting between word embedding spaces of different languages. We locally approximate these maps using linear maps, and find that they…

In this paper, we will investigate a harmonic cycle (discrete harmonic form). With a CW-complex, we can construct the combinatorial Laplacian operator. The kernel of the operator is the harmonic space, the set of harmonic cycles, and is…

We examine certain maps from root systems to vector spaces over finite fields. By choosing appropriate bases, the images of these maps can turn out to have nice combinatorial properties, which reflect the structure of the underlying root…

In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…

Embedding words in high-dimensional vector spaces has proven valuable in many natural language applications. In this work, we investigate whether similarly-trained embeddings of integers can capture concepts that are useful for mathematical…

We propose an architecture to jointly learn word and label embeddings for slot filling in spoken language understanding. The proposed approach encodes labels using a combination of word embeddings and straightforward word-label association…

Vector representations of graphs and relational structures, whether hand-crafted feature vectors or learned representations, enable us to apply standard data analysis and machine learning techniques to the structures. A wide range of…

Traces and their extension called combined traces (comtraces) are two formal models used in the analysis and verification of concurrent systems. Both models are based on concepts originating in the theory of formal languages, and they are…

Most of the time, the first step to learn word embeddings is to build a word co-occurrence matrix. As such matrices are equivalent to graphs, complex networks theory can naturally be used to deal with such data. In this paper, we consider…

In this article we consider combinatorial maps approach to graphs on surfaces, and how between them can be establish terminological uniformity in favor of combinatorial maps in way rotations are set as base structural elements and all other…

The focus of past machine learning research for Reading Comprehension tasks has been primarily on the design of novel deep learning architectures. Here we show that seemingly minor choices made on (1) the use of pre-trained word embeddings,…

The geometry of the moduli space of stable spin curves is studied, with emphasis on its combinatorial properties. In this context, the standard graph theoretic framework is not just a book-keeping device: some purely combinatorial results…

We consider countable linear orders and study the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results, and further extend our research to the case of…

A notion of heaps of modules as an affine version of modules over a ring or, more generally, over a truss, is introduced and studied. Basic properties of heaps of modules are derived. Examples arising from geometry (connections, affine…

We present a framework for characterizing injectivity of classes of maps (on cosets of a linear subspace) by injectivity of classes of matrices. Using our formalism, we characterize injectivity of several classes of maps, including…

We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…

Word embeddings are effective intermediate representations for capturing semantic regularities between words, when learning the representations of text sequences. We propose to view text classification as a label-word joint embedding…

We apply the method of spectral sequences to study classical problems in analysis. We illustrate the method by finding polynomial vector fields that commute with a given polynomial vector field and finding integrals of polynomial…

Sequence labeling architectures use word embeddings for capturing similarity, but suffer when handling previously unseen or rare words. We investigate character-level extensions to such models and propose a novel architecture for combining…

Geometric relational embeddings map relational data as geometric objects that combine vector information suitable for machine learning and structured/relational information for structured/relational reasoning, typically in low dimensions.…