Related papers: Applying language models to algebraic topology: ge…

Homogeneous generative meta-programming (HGMP) enables the generation of program fragments at compile-time or run-time. We present the first foundational calculus which can model powerful HGMP languages such as Template Haskell. The…

Mirkovic and Vilonen discovered a canonical basis of algebraic cycles for the intersection homology of (the closures of the strata of) the loop Grassmannian. The moment map images of these varieties are a collection of polytopes, and they…

We establish model category structures on algebras and modules over operads in symmetric spectra, and study when a morphism of operads induces a Quillen equivalence between corresponding categories of algebras (resp. modules) over operads.

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast…

We define a class of probability distributions that we call simplicial mixture models, inspired by simplicial complexes from algebraic topology. The parameters of these distributions represent their topology and we show that it is possible…

We establish a unified group-theoretic framework bridging the arithmetic homotopy exact sequence of a variety and the Birman exact sequence of a surface. Within this framework, we reinterpret classical arithmetic notions - such as the…

Lexical semantic typology has identified important cross-linguistic generalizations about the variation and commonalities in polysemy patterns---how languages package up meanings into words. Recent computational research has enabled…

The BERTopic framework leverages transformer embeddings and hierarchical clustering to extract latent topics from unstructured text corpora. While effective, it often struggles with social media data, which tends to be noisy and sparse,…

The goal of this thesis is to prove that $\pi_4(S^3) \simeq \mathbb{Z}/2\mathbb{Z}$ in homotopy type theory. In particular it is a constructive and purely homotopy-theoretic proof. We first recall the basic concepts of homotopy type theory,…

We study classical spin networks with group SU(2). In the first part, using gaussian integrals, we compute their generating series in the case where the networks are equipped with holonomies; this generalizes Westbury's formula. In the…

Similarity-based method gives rise to a new class of methods for multi-label learning and also achieves promising performance. In this paper, we generalize this method, resulting in a new framework for classification task. Specifically, we…

The spaces of flattenings of a simplicial sphere played a key role in the study of existence and uniqueness of differentiable structures on a simplicial sphere. In this paper, we will establish that the spaces of flattenings of some…

In this paper, we propose three methods for generating synthetic samples to train and evaluate multimodal large language models capable of processing both text and speech inputs. Addressing the scarcity of samples containing both…

Sigma models effectively describe ordered phases of systems with spontaneously broken symmetries. At low energies, field configurations fall into solitonic sectors, which are homotopically distinct classes of maps. Depending on context,…

This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins. It is intended to be accessible to…

In a previous article, we have introduced the problem of local generation of languages, where the communication underlying the generation procedure is captured by a simplicial complex. We study in details this problem for the language of…

To exploit the Web Ontology Language OWL as an answer set programming (ASP) language, we introduce the notion of bounded model semantics, as an intuitive and computationally advantageous alternative to its classical semantics. We show that…

Training in machine learning generally consists in finding one model, whose parameters minimize a data-dependent loss. Yet, empirical work shows that ensemble learning, an approach in which multiple models are sampled, can improve…

In this paper we study the problem of determining the homology groups of a quotient of a topological space by an action of a group. The method is to represent the original topological space as a homotopy limit of a diagram, and then act…

Theoretical development and applications of graph signal processing (GSP) have attracted much attention. In classical GSP, the underlying structures are restricted in terms of dimensionality. A graph is a combinatorial object that models…