arXiv research

Study local structure of knot group representations into SL(n,C).

Quantum representations of mapping class groups are locally rigid at prime levels.

This paper proposes a representational model for image pairs such as consecutive video frames that are related by local pixel displacements, in the hope that the model may shed light on motion perception in primary visual cortex (V1). The model couples the following two components: (1) the vector representations of loc…

Study local features of decorated representation spaces for spherical surfaces.

A framework compares image representations based on local geometry.

Minimal energy local systems on curves are compact components of character varieties.

The excellent performance of representation learning of autoencoders have attracted considerable interest in various applications. However, the structure and multi-local collaborative relationships of unlabeled data are ignored in their encoding procedure that limits the capability of feature extraction. This paper pre…

Let M be a non-compact hyperbolic 3-manifold that has a triangulation by positively oriented ideal tetraedra. We explain how to produce local coordinates for the variety defined by the gluing equations for PGL(3,C)-representations. In particular we prove local rigidity of the "geometric" representation in PGL(3,C), rec…

New parametrizations for minimal timelike surfaces discovered.

In an ego-network, an individual (ego) organizes its friends (alters) in different groups (social circles). This social network can be efficiently analyzed after learning representations of the ego and its alters in a low-dimensional, real vector space. These representations are then easily exploited via statistical mo…

LDReg addresses local dimensional collapse in self-supervised learning.

InstantEmbedding efficiently generates node representations with less computation and memory.

Federated learning is a method of training models on private data distributed over multiple devices. To keep device data private, the global model is trained by only communicating parameters and updates which poses scalability challenges for large models. To this end, we propose a new federated learning algorithm that …

Using the fact that any minimal strongly regular surface carries locally canonical principal parameters, we obtain a canonical representation of these surfaces, which makes more precise the Weierstrass representation in canonical principal parameters. This allows us to describe locally the solutions of the natural part…

Given a finite volume hyperbolic 3-manifold, we compose a lift of the holonomy in SL(2,C) with the n-dimensional irreducible representation of SL(2,C) in SL(n,C). In this paper we give local coordinates of the SL(n,C)-character variety around this representation. As a corollary, this representation is isolated among al…

Federated learning is a distributed, privacy-aware learning scenario which trains a single model on data belonging to several clients. Each client trains a local model on its data and the local models are then aggregated by a central party. Current federated learning methods struggle in cases with heterogeneous client-…

Proposes a new contrastive loss for semi-supervised medical image segmentation.

In this paper, we investigate the unsupervised deep representation learning issue and technically propose a novel framework called Deep Self-representative Concept Factorization Network (DSCF-Net), for clustering deep features. To improve the representation and clustering abilities, DSCF-Net explicitly considers discov…

We introduce a certain type of representations for the quantum Teichmuller space of a punctured surface, which we call local representations. We show that, up to finitely many choices, these purely algebraic representations are classified by classical geometric data. We also investigate the family of intertwining opera…

IsUMap improves data visualization of complex geometries.

This paper presents a preliminary study comparing different observation and action space representations for Deep Reinforcement Learning (DRL) in the context of Real-time Strategy (RTS) games. Specifically, we compare two representations: (1) a global representation where the observation represents the whole game state…

This paper improves a local-to-global principle for Morse quasigeodesics.

We list up all the possible local orbit types of hyperbolic or elliptic orbits for the isotropy representations of semisimple pseudo-Riemannian symmetric spaces. It is key to give a recipe to determine the local orbit types of hyperbolic principal orbits by using three kind of restricted root systems and Satake diagram…

Complete classification of Deligne-Mostow lattice representations into PGL(3,C).

LoCo learns local representations without end-to-end synchronization, improving performance on complex tasks.

We give an irreducible decomposition of the so-called local representations (see arXiv:0707.2151) of the quantum Teichmüller space $\mathcal{T}_q(Σ)$ where $Σ$ is a punctured surface of genus $g>0$ and $q$ is a primitive $N$-th root of unity with $N$ odd. As an application, we construct a family of representations of t…

We construct compactifications of Riemannian locally symmetric spaces arising as quotients by Anosov representations. These compactifications are modeled on generalized Satake compactifications and, in certain cases, on maximal Satake compactifications. We deduce that these Riemannian locally symmetric spaces are topol…

New framework assesses neural sensitivity to small perturbations.

Enhances knot Floer homology with algebraic representation theory.

New proof of Alesker's Irreducibility Theorem using localization techniques.

A new model decouples global and local image representations without supervision.

We prove that any minimal (maximal) strongly regular surface in the three-dimensional Minkowski space locally admits canonical principal parameters. Using this result, we find a canonical representation of minimal strongly regular time-like surfaces, which makes more precise the Weierstrass representation and shows mor…

Study kernels of mapping class group representations on surface configuration spaces.

Let Gamma be a cocompact lattice in SO(1,n). A representation rho: Gamma \to SO(2,n) is quasi-Fuchsian if it is faithfull, discrete, and preserves an acausal subset in the boundary of anti-de Sitter space - a particular case is the case of Fuchsian representations, ie. composition of the inclusions of Gamma in SO(1,n) …

Improved VAE representations lead to better image classification.

Personalized federated learning improves model accuracy and fairness by leveraging shared representations and local memorization.

Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant representations. Locality is achieved by defining a suitable probability distributi…

Study Heisenberg homology on surface configurations, revealing new representations of mapping class groups.

The notion of Anosov representations has been introduced by Labourie in his study of the Hitchin component for SL(n,R). Subsequently, Anosov representations have been studied mainly for surface groups, in particular in the context of higher Teichmueller spaces, and for lattices in SO(1,n). In this article we extend the…

New approach preserves privacy in high-dimensional data using representation learning.

New graph convolution captures local features on non-Euclidean grids.

The paper constructs TQFTs and Schrödinger representations for Heisenberg group.

FibeRed reduces complex data dimensions while preserving topology.

Meta-GLAR combines global deep representations with local adaptation for improved forecasting accuracy.

A new probabilistic polygonal curve representation using Gaussian Mixture Models.

We relate generalized Lebesgue decompositions of measures in terms of curve fragments (Alberti representations) and Weaver derivations. This correspondence leads to a geometric characterization of the local norm on the Weaver cotangent bundle of a metric measure space $(X,μ)$: the local norm of a form $df$ sees how fas…

Machine learning and geostatistics are powerful mathematical frameworks for modeling spatial data. Both approaches, however, suffer from poor scaling of the required computational resources for large data applications. We present the Stochastic Local Interaction (SLI) model, which employs a local representation to impr…

We introduce the notion of a local torus action modeled on the standard representation (for simplicity, we call it a local torus action). It is a generalization of a locally standard torus action and also an underlying structure of a locally toric Lagrangian fibration. For a local torus action, we define two invariants…