Related papers: Lexicographic Generation of Projective Spaces
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
Numerous methods have been proposed for probabilistic generative modelling of 3D objects. However, none of these is able to produce textured objects, which renders them of limited use for practical tasks. In this work, we present the first…
We construct natural symbolic representations of intrinsically ergodic, but not necessarily expansive, principal algebraic actions of countably infinite amenable groups and use these representations to find explicit generating partitions…
This work has been motivated by two long term goals: to understand how humans learn language and to build programs that can understand language. Using a representation that makes the relevant features explicit is a prerequisite for…
Lexical ambiguity presents a profound and enduring challenge to the language sciences. Researchers for decades have grappled with the problem of how language users learn, represent and process words with more than one meaning. Our work…
This paper seeks to develop a deeper understanding of the fundamental properties of neural text generations models. The study of artifacts that emerge in machine generated text as a result of modeling choices is a nascent research area.…
In semialgebraic geometry, projections play a prominent role. A definable choice is a semialgebraic selection of one point in every fiber of a projection. Definable choices exist by semialgebraic triviality, but their complexity depends…
We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order…
We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. In a previous paper we have shown that the inclusion of the first space into the second one is a homotopy…
Large Language Models achieve next-token prediction by transporting a vectorized piece of text (prompt) across an accompanying embedding space under the action of successive transformer layers. The resulting high-dimensional trajectories…
This communication describes a representation of images as a set of edges characterized by their position and orientation. This representation allows the comparison of two images and the computation of their similarity. The first step in…
With the widespread use of large language models (LLMs), many researchers have turned their attention to detecting text generated by them. However, there is no consistent or precise definition of their target, namely "LLM-generated text".…
Recent works on language identification and generation have established tight statistical rates at which these tasks can be achieved. These works typically operate under a strong realizability assumption: that the input data is drawn from…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
A new construction of naturally reductive spaces is presented. This construction gives a large amount of new families of naturally reductive spaces. First the infinitesimal models of the new naturally reductive spaces are constructed. A…
In this work, we consider the typography generation task that aims at producing diverse typographic styling for the given graphic document. We formulate typography generation as a fine-grained attribute generation for multiple text elements…
When automatically generating programming exercise tasks one often also needs to automatically generate programs. At the very least when providing sample solutions is part of automated feedback. But programs can also be used as part of the…
We introduce an asymptotic notion of positivity in algebraic geometry that turns out to be related to some high-dimensional convex sets. The dimension of the convex sets grows with the number of birational operations. In the case of complex…
Starting from the hypothesis that knowledge in semantic space is organized along structured manifolds, we argue that this geometric structure renders the space explorable. By traversing it and using the resulting continuous representations…
For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the…