We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called {\em weakly maximal} representations. We prove that weakly maximal representations are discrete and injective and we describe the structure of the Zariski closure of their image. Furthermore we prove that t…
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48 results for “weakly maximal representations”
We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called weakly maximal representations. They are defined in terms of invariants in bounded cohomology and extend considerably the scope of maximal representations. We prove that weakly maximal representations are d…
Introduces representations of surface groups into Lie groups preserving order.
problem Representations of surface groups into Lie groups that preserve the group order.
method Relates order preserving representations to weakly maximal representations and uses geometric and causal structure.
result Order preserving representations into Lie groups of Hermitian type are faithful with discrete image and form a closed set.
A deep learning framework learns meaningful representations for weakly supervised multiple instance learning.
problem Weakly supervised multiple instance learning with uncertainty in positive instance labels.
method Discriminative model regularized by variational autoencoders to learn latent representations.
result Improved performance on standard benchmark datasets compared to state-of-the-art approaches.
New method improves weakly-supervised action localization.
problem Locating action segments in videos with limited labels.
method Explicitly models key instance assignment as hidden variable using EM framework.
result Achieves state-of-the-art performance on THUMOS14 and ActivityNet1.2 benchmarks.
New algorithm improves weakly submodular maximization beyond cardinality constraints.
problem Maximizing weakly submodular functions under non-cardinality constraints.
method Randomized greedy algorithm for weakly submodular maximization under matroid constraints.
result Randomized greedy achieves an approximation ratio of for weakly submodular maximization under matroid constraints.
Paper proposes a framework to improve weakly supervised learning performance.
problem Weakly supervised data often lead to poor performance due to unreliable labels.
method Guides label quality optimization using a small validation set.
result Framework achieves impressive performance gains with minimal validation data.
Expanding FCCO to non-smooth weakly-convex problems, improving deep learning performance.
problem Addressing the limitations of current FCCO methods by tackling non-smooth weakly-convex problems.
method Developed a single-loop algorithm for non-smooth weakly-convex FCCO and extended it to tri-level problems.
result Established the complexity for finding ε-stationary points in the Moreau envelop of the objective function.
The article contains a survey of our results on weakly commensurable arithmetic and general Zariski-dense subgroups, length-commensurable and isospectral locally symmetric spaces and of related problems in the theory of semi-simple agebraic groups. We have included a discussion of very recent results and conjectures on…
On the normal holonomy representation of spacelike submanifolds in pseudo-Riemannian space formsmath.DG
In this paper we study weakly irreducible holonomy representations of the normal connection of a spacelike submanifold in a pseudo-Riemannian space from. We associate screen representations to weakly irreducible normal holonomy groups and classify the screen representations having the Borel-Lichnérowicz property. In pa…
Unitary Representations, Dolbeault Cohomology, and Weakly Symmetric Pseudo--Riemannian Nilmanifoldsmath.RT
New unitary representations constructed for complex nilmanifolds.
problem Constructing unitary representations on specific geometric spaces.
method Combining geometric methods with recent developments on pseudo-Riemannian nilmanifolds.
result Developed theory for square integrable representations on complex nilmanifolds.
We introduce the notion of a weakly reflective submanifold, which is an austere submanifold with a certain global condition, and study its fundamental properties. Using these, we determine weakly reflective orbits and austere orbits of s-representations.
The main goal of this paper is to reveal the geometric meaning of the maximal number of exceptional values of Gauss maps for several classes of immersed surfaces in space forms, for example, complete minimal surfaces in the Euclidean three-space, weakly complete improper affine spheres in the affine three-space and wea…
EM algorithm converges slowly for weakly identifiable Gaussian mixtures.
problem Slow convergence of EM algorithm for weakly identifiable Gaussian mixtures.
method Localized argument with two stages, each involving epoch-based arguments for surrogate EM operators at the population level.
result EM algorithm converges in $n^{ rac{3}{4}}$ steps with estimates at Euclidean distance of $n^{- rac{1}{8}}$ and $n^{- rac{1}{4}}$ from true parameters.
In this paper we construct an example of a weakly complete maximal surface in the Lorentz-Minkowski space L^3, which is bounded by a hyperboloid. Moreover, all the singularities of our example are of lightlike type.
GROOVE learns representations for weakly paired multimodal data.
problem Learning representations for high-content perturbation data with weakly paired samples.
method GroupCLIP contrastive loss integrated with an autoencoder framework.
result GROOVE performs on par with or outperforms existing approaches for cross-modal tasks.
Probabilistic model for weakly supervised analysis dictionary learning.
problem Discriminative analysis dictionary learning under weak supervision.
method Probabilistic modeling with EM algorithm and graph reformulation.
result Improved classification performance compared to synthesis dictionary learning.
We prove that M. Kramer's classification of list of spherical pairs coincides with that for weakly symmetric spaces by examining the linear isotropy representation of the corresponding homogeneous space associated to each pair.
Classifies semisimple weakly symmetric pseudo-Riemannian manifolds.
problem Classifying pseudo-Riemannian manifolds with specific properties.
method Developed from compact Lie group cases, analyzed isotropy representation and metric signature.
result Obtained classification of semisimple weakly symmetric manifolds of specific signatures.
Paper develops algorithms for solving non-convex non-concave problems with applications in GAN training.
problem Solving non-convex non-concave min-max saddle-point problems.
method Inexact proximal point method with strongly monotone mappings.
result First-order convergence to a nearly stationary solution of the original min-max problem.
Ricci flow shows PIC1 manifolds with maximal volume growth are like Euclidean space.
problem Characterizing complete PIC1 manifolds with maximal volume growth.
method Ricci flow with local curvature estimates.
result PIC1 manifolds with maximal volume growth are diffeomorphic to \(\mathbb{R}^n\).
A novel method learns representations from PU data without needing class-prior estimation.
problem Training classifiers from only positive and unlabeled data requires accurate class-prior probability estimation.
method Information-theoretic representation learning based on the information-maximization principle.
result Our method combined with deep neural networks achieves state-of-the-art PU classification performance.
Paper proposes MTL for weakly labelled SED, improving performance with 2-step attention.
problem Weakly labelled sound event detection.
method Multi-Task Learning framework with 2-step Attention Pooling.
result Improved SED performance with 22.3%, 12.8%, 5.9% gains at 0, 10, 20 dB SNR.
A derivative-free algorithm improves continuous submodular maximization.
problem Maximizing monotone DR-submodular continuous functions without gradient information.
method LDGM algorithm for continuous DR-submodular maximization, with and parameters.
result LDGM achieves -approximation guarantee with iterations.
Paper develops proper, lower-bounded losses for weakly supervised classification.
problem Weakly supervised classification with corrupted labels.
method Representation theorem for proper losses, derived condition for lower-boundedness, generalized logit squeezing.
result Proper and lower-bounded losses for weak-label learning.
Weak supervision enables learning causal representations from unstructured data.
problem Learning high-level causal representations from unstructured data like images.
method Weakly supervised setting with paired samples before and after interventions. Implicit latent causal models using variational autoencoders.
result Models can reliably identify causal structure and disentangle causal variables.
We consider the robust utility maximization using a static holding in derivatives and a dynamic holding in the stock. There is no fixed model for the price of the stock but we consider a set of probability measures (models) which are not necessarily dominated by a fixed probability measure. By assuming that the set of …
This paper introduces a general multi-class approach to weakly supervised classification. Inferring the labels and learning the parameters of the model is usually done jointly through a block-coordinate descent algorithm such as expectation-maximization (EM), which may lead to local minima. To avoid this problem, we pr…
New method learns useful disentangled representations from weakly labeled data.
problem Learning useful representations from weakly labeled data.
method Model pairs of non-i.i.d. images, learn disentangled representations without requiring annotation.
result Learn disentangled representations reliably from pairs of images without requiring group, individual factor, or number of changed factors annotation.
Model learns image-word associations from captions using contrastive learning.
problem Phrase grounding, associating image regions to caption words.
method Optimizing word-region attention to maximize mutual information, using language model guided word substitutions for negatives.
result Model achieves 76.7% accuracy on Flickr30K Entities benchmark, a 5.7% gain from weak supervision.
Subset selection improves weak supervision performance.
problem Optimizing the use of weakly-labeled data.
method Combining pretrained data representations with the cut statistic for subset selection.
result Subset selection improves weak supervision performance by up to 19%.
The study describes the geometry of surfaces and their representations in SL(3,R).
problem Understanding the geometry of surface group representations into SL(3,R).
method Proving asymptotic formulas and harmonic map convergence for equivariant maps.
result The geometry of the image is weakly convex and a (one-third) translation surface.
In this paper, we investigate the ergodic and rigidity properties of weakly hyperbolic group actions. Motivated by classical theorems describing Anosov diffeomorphisms, we obtain two main results: First, all C^2 volume preserving weakly hyperbolic actions on closed manifolds are ergodic. This result generalizes Anosov'…
Derives a family of hyperparameter scaling strategies for neural networks.
problem Optimizing hyperparameters for wide and deep neural networks.
method Introduces a one-parameter family of hyperparameter scaling strategies.
result Reveals proper scaling of depth with width for large-scale models.
Quaternionic analysis proves minimum of Willmore functional on Riemann surfaces.
problem Finding minimum of Willmore functional on Riemann surfaces.
method Extending quaternionic analysis to weakly conformal maps and using Darboux transformation.
result Minimum of Willmore functional on Riemann surfaces is achieved by weakly conformal maps.
Maximal and Borel Anosov representations in are proven to be Hitchin.
problem Characterizing representations of surface groups into that are Borel Anosov and maximal.
method Proving representations are Hitchin if they have maximal Toledo invariant and are Borel Anosov.
result Maximal and Borel Anosov representations in are Hitchin.
A new model learns from multiple types of data without needing complete information.
problem Learning from multiple types of data without complete information.
method Multimodal variational autoencoder (MVAE) with product-of-experts inference network and sub-sampled training.
result Matches state-of-the-art performance with fewer parameters and is robust to incomplete supervision.
Maximal representations in symplectic lattices proven for most cases.
problem Understanding maximal representations in symplectic lattices.
method Analyzing mapping class group orbits and continuous deformations of maximal diagonal representations.
result Proof of maximal representations in most lattices of Sp(2n,R).
New representations defined for groups and graphs, with applications to stable representations.
problem Defining and constructing new types of representations for groups and graphs.
method Introducing -directed Anosov representations and using Fock-Goncharov positivity to construct them.
result Constructs large families of primitive stable representations from to , including non-discrete and non-faithful examples.
Let be a real closed field. We define the notion of a maximal framing for a representation of the fundamental group of a surface with values in . We show that ultralimits of maximal representations in admit such a framing, and that all maximal framed represen…
Construct Schottky subgroups for maximal representations in symmetric spaces.
problem Maximal representations of surface groups into Sp(2n, R).
method Construction of Schottky type subgroups of automorphism groups.
result Schottky subgroups correspond to maximal representations of surface groups.
Gopal Prasad and A. S. Rapinchuk defined a notion of weakly commensurable lattices in a semisimple group, and gave a classification of weakly commensurable Zariski dense subgroups. A motivation was to classify pairs of locally symmetric spaces isospectral with respect to the Laplacian on functions. For this, in higher …
Weierstrass-type Representation of Weakly Regular Pseudospherical Surfaces in Euclidean Spacemath.DG
The paper presents a generalized Weierstrass representation for pseudospherical surfaces in terms of 3x3 matrices, using moving frames and loop group decompositions. The construction of all such surfaces, starting from a given representation, constitutes the subject of a separate, ulterior report. The appendix of the p…
The paper provides a framework for weakly supervised disentanglement guarantees.
problem Learning disentangled representations in real-world data.
method Theoretical framework for analyzing disentanglement guarantees with weak supervision.
result Empirical verification of weak supervision methods' predictive power and usefulness.
Maximal representations in infinite dimensional Hermitian spaces are studied with boundary maps.
problem Characterizing maximal representations in infinite dimensional Hermitian symmetric spaces.
method Definition of Toledo number, study of boundary maps, geometric constructions.
result Existence and non-existence conditions for maximal representations.
We generalize arc coordinates for maximal representations on a pair of pants.
problem Maximal representations of reflection groups on hyperbolic surfaces.
method Introducing geometric parameters and reflections in Siegel space.
result Natural parametrization of maximal representations into PSp(4, R).
Study fibrations of projective spaces for maximal representations.
problem Characterize maximal representations of surface groups.
method Analyze fibrations of projective spaces and use geometric structures.
result Maximal representations correspond to fibrations with specific properties.
Maximal representations into have bounded volume.
problem Bounding the volume of maximal representations into .
method Uniform upper and lower bounds on the volume for different surface groups.
result Volume is bounded from above and below for maximal representations into .