Generic Hitchin representations generate dense subgroups.
problem Understanding dense subgroups in SL_n(R) representations.
method Using a theorem by Rapinchuk, Benyash-Krivetz, and Chernousov.
result Generic Hitchin representations are strongly dense.
New representations of hyperbolic 3-manifold groups into larger groups.
problem Finding representations of hyperbolic 3-manifold groups into larger matrix groups.
method Holonomy representations from projective deformations of hyperbolic structures.
result First examples of strongly dense representations into SL(4,R) and SU(3,1). The paper studies volume classes and Borel classes for dense group representations.
problem Understanding volume and Borel classes for dense representations of discrete groups.
method Utilizes tools from Kleinian groups and properties of hyperbolic manifolds.
result Volume classes are linearly independent and have additional properties.
The paper finds dense subgroups in certain Lie groups.
problem Finding dense subgroups in Lie groups.
method Constructing dense surface subgroups in specific Lie groups.
result Uniform lattices contain infinitely many dense Hitchin representations.
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).
Deforms surface groups to be Zariski dense in SL(n,R)
problem Finding Zariski dense surface groups in SL(n,R)
method Deforming K-integral representations of surface groups result Generalizes Long and Thistlethwaite's method to SL(n,R)
DenseHMM improves HMMs by learning dense representations that enable gradient-based optimization.
problem Learning dense representations for hidden states and observables in HMMs.
method DenseHMM uses kernelized transition probabilities and two optimization schemes.
result DenseHMM achieves superior performance and expressiveness compared to standard HMMs.
Cataclysm deformations study Anosov representations and their convergence.
problem Understanding convergence of Anosov representations under deformation.
method Cataclysm deformation of Anosov representations using twisted transverse cocycles.
result Uniform convergence of cataclysm deformations on compact sets.
Cataclysm deformations study Anosov representations, leading to new formulas and non-open sets.
problem Understanding Anosov representations and their deformations.
method Cataclysm deformations based on twisted transverse cocycles.
result Uniform convergence of cataclysm deformations on compact sets.
Sparse representations improve network robustness and stability.
problem The benefits of sparse representations in artificial networks.
method Analysis of sparse networks with sparse weights and activations, simulations on MNIST and Google Speech Command Dataset.
result Sparse networks show significantly improved robustness and stability compared to dense networks.
ViCE uses superpixels to enhance self-supervised learning for better dense visual embeddings.
problem Lack of high-resolution feature maps from self-supervised models.
method Superpixels for dense representation learning, contrasting over regions.
result Improves unsupervised semantic segmentation on benchmarks like Cityscapes and COCO.
New domains of discontinuity found for Anosov representations.
problem Understanding Anosov representations acting on homogeneous spaces.
method Constructing open domains of discontinuity for Anosov representations acting on specific homogeneous spaces.
result Describes the largest possible open domains of discontinuity for Zariski dense Anosov representations.
Odd-dimensional SL(n,Q) contains dense surface subgroups.
problem Finding dense subgroups in SL(n,Q) for odd n.
method Constructing a continuous path of representations.
result Existence of dense surface subgroups in SL(n,Q) for odd n.
Generic Hitchin representations avoid hyperplanes in Lie algebras.
problem Properties of Hitchin representations in Lie algebras.
method Defined J(ρ) and used hyperplanes in Lie algebras to show J(ρ)∩H=∅. result Generic G-Hitchin representations avoid hyperplanes in the Lie algebra of G. The paper explores mapping class group quotients by Dehn twists and their representations.
problem Finite quotients and representations of mapping class groups by powers of Dehn twists.
method Construction of finite quotients using representations with Zariski dense images into semisimple Lie groups, and Long and Moody's method.
result The Fibonacci TQFT representation is a specialization of the Jones representation in genus 2.
We prove that a dense subgroup of Homeo+(I) is not elementary amenable. We also show that the topological group Homeo+(I) does not satisfy the Stability of the Generators Property, moreover, any finitely generated subgroup of Homeo+(I) admits a faithful discrete representation …
Study shows how to detect representation extendability using conformal measures.
problem Detecting extendability of representations using conformal measures.
method Using higher rank conformal measures and self-joinings of groups.
result Affirmative answer to detect extendability of representations.
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 show the set of faithful representations of a closed orientable hyperbolic surface group is dense in both irreducible components of the PSL(2,K) representation variety, where K is the field of real or complex numbers, answering a question of W. Goldman. We also prove the existence of faithful representations into PU…
New architecture improves decision-making in dense traffic.
problem Designing accurate and compact learning architectures for autonomous vehicles in crowded conditions.
method Attention-based architecture that accounts for interactions between vehicles.
result Significant performance gains and interpretable interaction patterns.
We prove analogues for Cartan geometries of Gromov's major theorems on automorphisms of rigid geometric structures. The starting point is a Frobenius theorem, which says that infinitesimal automorphisms of sufficiently high order integrate to local automorphisms. Consequences include a stratification theorem describing…
We show that for an odd prime r > 3 and an integer g > 1, in the projective representation given by the SO(3) Witten-Chern-Simons theory at an rth root of unity, the image of the mapping class group of a surface of genus g is dense.
This work proposes a method to learn sparse representations that are more efficient for large-scale data retrieval.
problem Efficient retrieval of high-dimensional representations from large databases is computationally challenging.
method The approach minimizes the number of floating-point operations (FLOPs) by learning sparse embeddings with uniform non-zero entries.
result The proposed method achieves a similar or better speed-vs-accuracy tradeoff compared to existing baselines.
We address feature interpretation and reproducibility issues in dense nets, proposing a modified loss function.
problem Feature interpretation and reproducibility issues in dense nets.
method Proposed a modified loss function to circumvent basis collapse.
result Substantially concise nets with 100x fewer parameters and lower MSE loss.
We use some Lie group theory and Budney's unitarization of the Lawrence-Krammer representation, to prove that for generic parameters of definite form the image of the representation (also on certain types of subgroups) is dense in the unitary group. This implies that, except possibly for closures of full-twist braids, …
Proposes a multi-level learning approach for 3D object recognition.
problem Improving 3D object recognition accuracy through multi-scale spatial features.
method End-to-end multi-level learning on a multi-level voxel grid.
result Comparable object recognition performance with lower memory usage.
New method speeds up sparse graph neural networks training on dense hardware.
problem Training sparse graph neural networks is slow on custom hardware.
method Inspired by sparse matrix optimization, developed techniques for dense hardware.
result Sparse graph neural networks trained in 13 minutes on 512-core TPUv2 Pod.
Minimal action of mapping class group on character variety.
problem Character variety of Deroin-Tholozan representations.
method Geometric perspective using symplectic structure.
result Infinite mapping class group orbits are dense.
New method learns robot actions from videos without explicit labels.
problem Training robots to perform tasks from few demonstrations.
method Uses images and text for task-agnostic and general representation, synthesizes hallucinated actions, and applies dense correspondences.
result Trains robot policies solely from RGB videos, achieving diverse tasks across different robots and environments.
Study non-semisimple TQFT for Burau representation density and unitarity.
problem Density and unitarity of the Burau representation from a non-semisimple TQFT perspective.
method TQFT construction of Squier's Hermitian form on the Burau representation.
result Density of the image of braid group in unitary representations.
Study mapping class group action on character varieties, proving Kronecker's Theorem.
problem Topological-dynamical action of mapping class group on character varieties.
method Analyzes Tn-character variety and dense orbit conditions. result Provides a dynamical proof of Kronecker's Theorem.
New properties established for SO(3) quantum representations, showing density and surjectivity.
problem Properties of SO(3) quantum representations of mapping class groups.
method Analyzing roots of unity and maximal ideals of Z[ζ_p] to establish properties.
result SO(3) quantum representations have dense image and are surjective modulo unramified maximal ideals.
NetSMF efficiently embeds large networks by sparse matrix factorization.
problem Learning latent representations for large-scale networks efficiently.
method NetSMF leverages spectral sparsification to efficiently sparsify and factorize a dense matrix.
result NetSMF achieves high efficiency and effectiveness on large-scale networks.
Survey of word embedding techniques for NLP.
problem Creating effective word representations for natural language processing.
method Describes recent strategies for fixed-length, dense word embeddings.
result Word embeddings encode syntactic and semantic information and improve NLP tasks.
Study TQFT representations for surfaces with boundary, showing irreducibility at prime roots of unity and Zariski density for transcendental parameters.
problem Understanding TQFT representations of mapping class groups with boundary.
method Examined TQFT representations for surfaces with boundary associated with SU(2) gauge group or $U_q(\Sl(2))$ quantum group. result At prime roots of unity, representations are irreducible; for transcendental parameters, the image of mapping class groups is Zariski dense.
Study shows Transformer and Neural GPU are Turing complete without external memory.
problem Exploring computational power of modern neural network architectures.
method Analyzing computational properties of Transformer and Neural GPU.
result Transformer and Neural GPU are Turing complete without external memory.
Anosov representations of surface groups are complex manifolds.
problem Characterizing the geometry of Anosov representations of surface groups.
method Analyzing the character varieties of Anosov representations into $\SL(n , \C)$.
result Character varieties of Anosov representations are complex manifolds of specific dimension.
Detects anomalous behavior in social media users by analyzing content and connections.
problem Identifying disruptive patterns in user behavior on social media platforms.
method Joint representation learning of content and connection to detect anomalous behavior.
result Observed densely connected users engaging in local politics and exhibiting troll-like behavior.
DNAS disentangles neural architecture search for better interpretability and performance.
problem Lack of interpretability in existing neural architecture search methods.
method DNAS disentangles the hidden representation of the controller into semantically meaningful concepts.
result DNAS achieves state-of-the-art performance and competitive architectures.
New examples of embeddings defy Anosov representation limits.
problem Examples of robust quasi-isometric embeddings not approximated by Anosov representations.
method Exhibited non-locally rigid, Zariski dense embeddings in SLm(K). result Higher rank Anosov representation theorems fail for m≥30. Paper proposes efficient inner product approximation for hybrid sparse and dense vectors.
problem Efficient search in hybrid spaces with both sparse and dense components is challenging.
method Proposes a technique to approximate inner product computation in hybrid vectors.
result Achieves over 10x speedup and higher accuracy in search compared to baselines.
Chromatic Learning reduces feature dimensions for sparse datasets.
problem Sparse, high-dimensional data challenges traditional learning methods.
method Graph coloring over co-occurrence graph to create dense feature representation.
result Compresses sparse datasets significantly while maintaining model accuracy.
New meta-learning method outperforms human-designed architectures in dense image prediction tasks.
problem Designing efficient neural network architectures for dense image prediction.
method Recursive search space construction for multi-scale visual information.
result Meta-learning method achieves state-of-the-art performance on scene parsing, person-part segmentation, and semantic image segmentation.
We consider the question: can the isotropy representation of an irreducible pseudo-Riemannian symmetric space be realized as a conformal holonomy group? Using recent results of Cap, Gover and Hammerl, we study the representations of SO(2,1), PSU(2,1) and PSp(2,1) as isotropy groups of irreducible symmetric spaces of si…
Minimal variations guide unsupervised learning for better downstream tasks.
problem Efficiently describing raw data for various future tasks.
method Minimal variations as a guiding principle for unsupervised representation learning.
result Unveiling minimal variations as a principle behind unsupervised learning.
New brain atlas method improves classification accuracy.
problem Creating accurate brain atlases from connectomes.
method Connectivity-based hierarchical clustering and consensus aggregation.
result Consensus parcellation outperforms existing atlases in classification tasks.
The abstract discusses rational approximations for Hitchin representations on surfaces.
problem Density of Hitchin representations in the Hitchin component for surfaces of genus g≥2. method Dynamical proof for g≥3; extension to other Q-groups. result Density of Hitchin representations for various Q-groups. Extends DAMs to Gaussian distributions for efficient pattern storage and retrieval.
problem Limited storage capacity and retrieval methods for non-vector pattern representations.
method Introduces a log-sum-exp energy function over Gaussian distributions, using optimal transport maps for retrieval dynamics.
result Proves exponential storage capacity and provides quantitative retrieval guarantees.