Regular Lie groups are infinite dimensional Lie groups with the property that smooth curves in the Lie algebra integrate to smooth curves in the group in a smooth way (an `evolution operator' exists). Up to now all known smooth Lie groups are regular. We show in this paper that regular Lie groups allow to push surprisi…
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48 results for “group regularization”
The study connects group structure to smooth actions on one-manifolds.
problem Understanding how group actions affect the smoothness of manifolds.
method Analyzes the relationship between group algebraic structure and smoothness of group actions on one-dimensional manifolds.
result Uniform construction of groups acting on compact interval and circle with prescribed regularity.
Study intrinsic regular surfaces in Carnot groups, generalizing results from Heisenberg groups.
problem Equivalence of definitions of intrinsic regular surfaces in Carnot groups.
method Generalize results from Heisenberg groups to Carnot groups.
result Equivalence of definitions of intrinsic regular surfaces in Carnot groups.
We embed arbitrary groups into regular graphs with prescribed automorphisms.
problem Embedding arbitrary groups into regular graphs with specific automorphisms.
method Constructing regular graphs with strong embeddings and automorphism groups isomorphic to any given finite group.
result For every and every finite group , there exists a -regular graph with a strong embedding such that .
New theorem for generalized group sparsity improves consistency and convergence rates.
problem Improving statistical inference in high-dimensional data with element-wise and group-wise sparsity.
method Developed a generalized version of Sparse-Group Lasso and proved a universal theorem for consistency and convergence rates.
result Obtained results on consistency and convergence rates for different forms of double sparsity regularization.
Groups with specific curvature have a regular language of geodesics.
problem Understanding the language of geodesics in non-positively curved triangle groups.
method Proving finitely many cone types and regularity of geodesic languages.
result The language of lexicographically first geodesics is regular and satisfies the fellow traveller property.
Paper proposes a new sparse group k-max regularization for sparsity constraints.
problem Linear inverse problems with sparsity constraints are NP-hard.
method Sparse group k-max regularization, iterative soft thresholding algorithm.
result Approximates l0 norm more closely and enhances group-wise and in-group sparsity.
Paper describes invariants of slice regular functions' automorphism group.
problem Understanding invariants of slice regular functions' automorphism group.
method Analyzes automorphism group of slice regular functions over Clifford algebras.
result Describes invariants of the automorphism group of slice regular functions.
Regular languages describe contracting geodesics in groups.
problem Characterizing groups with infinite contracting geodesics.
method Analyzing geodesics in Cayley graphs with a contracting property.
result Groups with infinite contracting geodesics are either virtually Z or acylindrically hyperbolic.
Study shows critical exponents for tree-acting groups.
problem Understanding critical exponents of discrete groups on trees.
method Explicit construction of edge-indexed graphs.
result Proven existence of groups with specific critical exponents.
Let M be a real analytic manifold modeled on a locally convex space and K be a non-empty compact subset of M. We show that if an open neighborhood of K in M admits a complexification which is a regular topological space, then the germ of the latter (as a complex manifold) is uniquely determined. If M is regular and the…
New Lie group structure on vertical bisections of Lie groupoids.
problem Constructing Lie group structure on vertical bisections of Lie groupoids.
method Construct Lie group structure on the group of vertical bisections of a regular Lie groupoid, identify Lie algebra, discuss regularity properties.
result Established Lie theoretic properties of vertical bisections of Lie groupoids over non-compact bases.
Study slice-regular polynomial functions via twistor space group actions.
problem Characterize slice-regular functions and their polynomial subclasses.
method Employ the twistor construction and group actions of .
result Characterize slice-regular functions with planar twistor lifts and normal classes of polynomials.
New findings on mapping class group actions on the circle, improving critical regularity.
problem Improving understanding of mapping class group actions on the circle.
method Analyzing actions of non-solvable groups and finite index subgroups of mapping class groups.
result Critical regularity of mapping class groups is at most one for surfaces of complexity at least three.
Gradient descent implicitly favors group sparsity in neural networks.
problem Understanding implicit regularization in neural networks for structured sparsity.
method Novel neural reparameterization for diagonally grouped linear networks.
result Gradient descent without explicit regularization biases towards group sparsity.
Diffeomorphisms of convex polytopes form a Lie group.
problem Understanding transformations of convex polytopes.
method Forming a Lie group from diffeomorphisms of convex polytopes.
result The group of diffeomorphisms of a convex polytope is a regular Lie group.
Simple groups identified for contactomorphisms with high regularity.
problem Characterizing the structure of contactomorphism groups.
method Analyzing groups of contactomorphisms with compact support.
result Groups are simple for certain Hölder exponents.
New nonconvex regularizers improve low-rank matrix recovery efficiency and accuracy.
problem Efficiently recover low-rank matrices from incomplete data.
method Factor group-sparse regularization, related to Schatten-p norms.
result Improved generalization error bounds for Schatten-p norms as p decreases.
New bounds on geodesic dimension and curvature exponent in Carnot groups.
problem Characterizing geodesic dimension and curvature exponent in Carnot groups.
method Characterization and lower bound calculation for geodesic dimension and curvature exponent.
result Found an example where curvature exponent is greater than geodesic dimension.
Anosov groups limit sets are Ahlfors regular, with applications in Teichmüller spaces.
problem Understanding Ahlfors regularity of limit sets for Anosov groups.
method Proving Ahlfors regularity for limit sets and Patterson-Sullivan measures.
result Patterson-Sullivan measures are Ahlfors regular if and only if associated linear forms are symmetric.
In this paper, we construct new examples of Veech groups by extending Schmithusen's method for calculating Veech groups of origamis to Veech groups of unramified finite coverings of regular 2n-gons. We calculate the Veech groups of certain Abelian coverings of regular 2n-gons by using an algebraic method.
DNN nodes selection improved using gLasso regularization.
problem Selecting important nodes in DNN hidden layers.
method Applied gLasso regularization to DNN weights, compared with L2 regularization.
result gLasso successfully selected necessary and sufficient hidden layer nodes.
A fast method for discrete OT with group-sparse regularization for class label preservation.
problem Efficiently measuring the distance between two discrete distributions with class labels.
method Fast discrete OT with group-sparse regularizers using gradient-based algorithms.
result Up to 8.6 times faster than original method without degrading accuracy.
It is shown that every abelian regular Lie group is a quotient of its Lie algebra via the exponential mapping.
New groups found in anti-de Sitter space that are not quasi-isometric to hyperbolic space.
problem Finding strictly GHC-regular groups in anti-de Sitter space that are not quasi-isometric to hyperbolic space.
method Using the Tits representation of well-chosen Coxeter groups.
result Examples of strictly GHC-regular groups in anti-de Sitter space that are not quasi-isometric to hyperbolic space.
The OSCAR (octagonal selection and clustering algorithm for regression) regularizer consists of a L_1 norm plus a pair-wise L_inf norm (responsible for its grouping behavior) and was proposed to encourage group sparsity in scenarios where the groups are a priori unknown. The OSCAR regularizer has a non-trivial proximit…
Regular Reduction of Controlled Magnetic Hamiltonian System with Symmetry of the Heisenberg Groupmath.SG
A controlled magnetic Hamiltonian (CMH) system is a regular controlled Hamiltonian (RCH) system with magnetic symplectic form, it is an important special case of RCH system. Note that there is a magnetic term on the cotangent bundle of the Heisenberg group, such that we can define a CMH system with symmetry of the Heis…
Improved neural networks by combining group DRO with regularization.
problem Overparameterized neural networks can fail on atypical groups due to spurious correlations.
method Coupling distributionally robust optimization (DRO) with increased regularization.
result Significant improvements in worst-case group accuracy, maintaining high average accuracy.
The paper defines -orientability for surfaces in the Heisenberg group and finds non--orientable surfaces.
problem Defining orientability in the Heisenberg group for surfaces.
method Defined -orientability for -regular 1-codimensional surfaces in .
result Existence of non--orientable -regular surfaces in .
New method uses feature grouping to improve model generalization in high-dimensional data.
problem Overfitting in high-dimensional, expensive data.
method Feature grouping with stochastic regularizer applied to complex models.
result Improves model generalization and convergence speed.
The paper shows how data augmentation and regularization can enforce group equivariance in machine learning models.
problem Improving model performance by leveraging known symmetries in machine learning tasks.
method Training with data augmentation and regularization to enforce group equivariance.
result Equivariance of the trained model can be achieved through training on augmented data in tandem with regularization.
Solves regularity problem for Lie groups with asymptotic estimate Lie algebras.
problem Regularity problem for Milnor's infinite dimensional Lie groups.
method Analyzes Lie groups with asymptotic estimate Lie algebras and their evolution maps.
result Shows -continuity of evolution map on specific domains.
Trouvé group connects image analysis flows to diffeomorphisms.
problem Understanding the relationship between image analysis flows and diffeomorphisms.
method Proving the equality of the Trouvé group and the connected component of diffeomorphisms for various regularity classes.
result The Trouvé group has a natural regular Lie group structure.
On regularity of profinite isomorphisms between cusped hyperbolic 3-manifolds and the -polynomialmath.GT
Proves regularity of isomorphisms between hyperbolic 3-manifolds.
problem Regularity of isomorphisms between cusped hyperbolic 3-manifolds.
method Proves regularity of profinite completions of fundamental groups.
result Proves -polynomial is a profinite invariant.
Examples of area-minimizing graphs with low regularity in a specific group.
problem Finding area-minimizing graphs with low regularity in a sub-Finsler Heisenberg group.
method Providing examples of entire area-minimizing horizontal graphs with prescribed singular sets.
result Examples of area-minimizing graphs that are locally Lipschitz but not necessarily smoother.
Study shows exact dimensionality and regularity of manifolds for specific groups.
problem Exact dimensionality and regularity of manifolds for relatively Anosov groups.
method Dynamical methods, including finite and mixing of Bowen–Margulis–Sullivan measures.
result Manifolds are -regular and growth indicator is strictly concave.
OMP improves text classification accuracy with sparse models.
problem Overfitting in text classification due to high dimensionality.
method Greedy variable selection algorithm (OMP) and overlapping Group OMP.
result OMP and overlapping GOMP produce effective and very sparse models.
Since learning is typically very slow in Boltzmann machines, there is a need to restrict connections within hidden layers. However, the resulting states of hidden units exhibit statistical dependencies. Based on this observation, we propose using regularization upon the activation possibilities of hidden unit…
We describe a class (called regular) of invariant generalized complex structures on a real semisimple Lie group G. The problem reduces to the description of admissible pairs (\gk, ω), where \gk is an appropriate regular subalgebra of the complex Lie algebra \gg^{C} associated to G and ωis a closed 2-form on \gk, such t…
Completeness of the Model Space Does Not Force Regularity for Infinite-Dimensional Lie Groupsmath.DG
Counterexample disproves completeness of model space forcing regularity in infinite-dimensional Lie groups.
problem Whether every Lie group modeled on a complete locally convex space is regular.
method Constructing a specific contractible complex analytic BCH-Lie group with unique properties.
result The group is not even -semiregular, and smooth controls have no evolution.
A theorem simplifies mass-minimizing flat chains' regularity.
problem Understanding the regularity of mass-minimizing flat chains.
method Simple condition for fundamental regularity principle.
result Fundamental regularity principle holds for mass-minimizing chains.
Researchers compute determinants and torsions of Rumin complex in specific Lie group representations.
problem Computing determinants and torsions of Rumin complex in specific Lie group representations.
method Analyzing Schrodinger and generic representations of the (2,3,5) nilpotent Lie group.
result Computed the spectrum and zeta regularized determinant of Rumin differentials in Schrodinger representations and evaluated their alternating product in generic representations.
Classifies isotopy classes of links from Thompson's group F and its subgroup.
problem Classify isotopy classes of links from Thompson's group F and its subgroup.
method Introduced a method to produce links from elements of Thompson's group F and its subgroup.
result Classified isotopy classes of links from Thompson's group F and its subgroup.
We find canonical decompositions for finitely presented groups which specialize to the classical JSJ-decomposition when restricted to the fundamental groups of Haken manifolds. The decompositions that we obtain are invariant under automorphisms of the group. A crucial new ingredient is the concept of a regular neighbou…
Optimally regularizes boundaries in the Heisenberg group with prescribed curvature.
problem Optimizing boundaries with prescribed sub-Finsler mean curvature in the Heisenberg group.
method Analyzes critical sets of the prescribed mean curvature functional in the Heisenberg group.
result Characteristic curves of critical sets are -regular, optimal in the Heisenberg group.
New fairness approach removes direct effects of unprivileged groups through causal regularization.
problem Ensuring fairness in machine learning models for unprivileged groups.
method Proposes a new fairness definition based on causal effects and develops regularizations to remove the impact of unprivileged groups on model outcomes.
result Demonstrates effectiveness of the approach on various datasets, reducing unfairness with minimal performance loss.
New theoretical framework improves error rates for sparse learning with convex regularization.
problem Improving error rates for sparse learning with convex regularization.
method Proposed a new theoretical framework using common assumptions to derive high-dimensional estimation bounds.
result Improved error rates for L1, Slope, and Group L1-L2 regularizations, matching or exceeding existing results.
Study learns convolution operators on compact Abelian groups using regularization.
problem Learning convolution operators on compact Abelian groups.
method Regularization-based approach with ridge regression estimator.
result Characterizes the accuracy of the estimator in terms of finite sample bounds.