Related papers: Geometrical morphology
Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…
Large language models (LLMs) work by manipulating the geometry of input embedding vectors over multiple layers. Here, we ask: how are the input vocabulary representations of language models structured, and how and when does this structure…
Morphisms are homomorphisms under the concatenation operation of the set of words over a finite set. Changing the elements of the finite set does not essentially change the morphism. We propose a way to select a unique representing member…
Hierarchies allow feature sharing between objects at multiple levels of representation, can code exponential variability in a very compact way and enable fast inference. This makes them potentially suitable for learning and recognizing a…
A general definition of mathematical morphology has been defined within the algebraic framework of complete lattice theory. In this framework, dealing with deterministic and increasing operators, a dilation (respectively an erosion) is an…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
Mathematical morphology is a part of image processing that uses a window that moves across the image to change certain pixels according to certain operations. The concepts of supremum and infimum play a crucial role here, but it proves…
This thesis investigates how the sub-structure of words can be accounted for in probabilistic models of language. Such models play an important role in natural language processing tasks such as translation or speech recognition, but often…
The concept of a morphism determined by an object provides a method to construct or classify morphisms in a fixed category. We show that this works particularly well for triangulated categories having Serre duality. Another application of…
Neural sequence-to-sequence models are currently the predominant choice for language generation tasks. Yet, on word-level tasks, exact inference of these models reveals the empty string is often the global optimum. Prior works have…
This paper describes in details the first version of Morphonette, a new French morphological resource and a new radically lexeme-based method of morphological analysis. This research is grounded in a paradigmatic conception of derivational…
Critical to natural language generation is the production of correctly inflected text. In this paper, we isolate the task of predicting a fully inflected sentence from its partially lemmatized version. Unlike traditional morphological…
In this article, we present a fresh perspective on language, combining ideas from various sources, but mixed in a new synthesis. As in the minimalist program, the question is whether we can formulate an elegant formalism, a universal…
We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…
In this paper we present an introduction to morphological calculus in which geometrical objects play the rule of generalised natural numbers.
Prior studies in multilingual language modeling (e.g., Cotterell et al., 2018; Mielke et al., 2019) disagree on whether or not inflectional morphology makes languages harder to model. We attempt to resolve the disagreement and extend those…
We introduce a topological approach to words. Words are approximated by Gauss words and then studied up to natural modifications inspired by homotopy transformations of curves on the plane.
One often sees a sharp distinction in mathematics between descriptions from the outside and from the inside. Think of defining a set in the plane through an algebraic equation, or dynamically as the closure of the orbit of some point under…
In this work, we focus on the task of learning and representing dense correspondences in deformable object categories. While this problem has been considered before, solutions so far have been rather ad-hoc for specific object types (i.e.,…
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.…