The paper proves that the support norm of tight contact structures adds up.
problem Understanding the support norm of contact structures.
method Analyzing open books supporting contact structures.
result Additivity of the support norm for tight contact structures.
Proposes GTTN for discovering all low-rank structures in deep multi-task learning.
problem Discovering all low-rank structures among tasks in deep multi-task models.
method Introduces GTTN, a convex combination of matrix trace norms of all tensor flattenings, to automatically determine the importance of components.
result Demonstrates the effectiveness of GTTN on real-world datasets.
The paper studies the metric and algebraic structures on section rings of projective manifolds.
problem Understanding the relationship between metric and algebraic structures on section rings.
method Analyzes the section ring of projective manifolds and ample line bundles, proving approximate isometry properties under various norms.
result Characterizes L2-norms associated with continuous plurisubharmonic metrics and refines the theorem of Phong-Sturm. Differential calculus on metric spaces is contained in the algebraic study of normed groupoids with δ-structures. Algebraic study of normed groups endowed with dilatation structures is contained in the differential calculus on metric spaces. Thus all algebraic properties of the small world of normed groups with dilat…
The Euler class conjecture links geometric structures to integral points on the Thurston norm ball.
problem Determining if integral points on the Thurston norm dual ball correspond to geometric structures.
method Examining various geometric, topological, and dynamical structures on 3-manifolds.
result Integral points on the Thurston norm dual ball correspond to the Euler class of taut foliations and other structures.
New evidence supports the Euler class one conjecture for tight contact structures.
problem Euler class one conjecture for taut foliations and tight contact structures.
method Analysis of tight contact structures and counterexamples to the conjecture.
result Counterexamples to the Euler class one conjecture for taut foliations are also Euler classes of tight contact structures.
We discuss structured Schatten norms for tensor decomposition that includes two recently proposed norms ("overlapped" and "latent") for convex-optimization-based tensor decomposition, and connect tensor decomposition with wider literature on structured sparsity. Based on the properties of the structured Schatten norms,…
We consider the empirical risk minimization problem for linear supervised learning, with regularization by structured sparsity-inducing norms. These are defined as sums of Euclidean norms on certain subsets of variables, extending the usual ℓ1-norm and the group ℓ1-norm by allowing the subsets to overlap. T…
Any Sasakian structure can be closely mimicked by embeddings into weighted spheres.
problem Approximating Sasakian structures on closed manifolds.
method Using CR embeddings into weighted Sasakian spheres and strengthening previous approximation results.
result Sasakian structures can be approximated in the Cq-norm by embeddings into weighted Sasakian spheres. Study the stable norm on irrational slopes of 2-torus.
problem Understanding the stable norm on irrational slopes of 2-torus.
method Analyzing Finsler metrics and geodesic flow.
result Stable norm detects KAM-tori and hyperbolicity.
The paper extends von Neumann's theory to normed modules and shows how they can be represented.
problem Understanding the structure of normed modules and their representability.
method Combining von Neumann's theory of liftings with Gigli's differential structure.
result Every separable normed module can be represented as sections of a measurable Banach bundle.
Proposes a new sparse graph-regularized SVD for biclustering.
problem Learning blocking structure in high-dimensional data.
method Imposes graph-regularized norm and L0-norm penalties on singular vectors.
result Efficiently captures natural blocking structures in real and simulated data.
Bounds projective structure norms by bending lamination lengths.
problem Bounding the L2-norm of projective structures. method Using the Thurston parameterization and Krasnov-Schlenker's W-volume theory. result Upper bounds on L2-norm of holomorphic quadratic differential by the length of bending lamination. Study shows various pixel p-norm measures do not match human perception of adversarial attacks.
problem Understanding human perception of adversarial attacks on image classification systems.
method Performed a behavioral study comparing different p-norm measures and alternative metrics.
result Human perception of adversarial attacks does not align with pixel p-norm measures and other metrics.
In this note we observe that the no two of the three invariants defined for contact structures by Etnyre and Ozbagci -- that is, the support genus, binding number and support norm -- determine the third.
Estimates VAR models with correlated data using structured norms.
problem Estimating VAR models with dependent data and structured norms.
method Structured VAR models with various norms, using Lasso-type techniques.
result Error bounds for structured VAR parameters are comparable to independent data settings.
The paper examines convergence of distances in Lipschitz structures on manifolds.
problem Convergence of distances in Lipschitz vector fields and norms on manifolds.
method Analysis of convergence of distances associated to converging structures of Lipschitz vector fields and norms.
result Under mild controllability assumption, distances converge locally uniformly to the limit Carnot-Carathéodory distance.
New method selects variables in groups with few nonzeros, improving support recovery.
problem Structured variable selection with sparse patterns across groups.
method Composite norm and proximal algorithm for exclusive group sparsity.
result Asymptotic consistency in signed support recovery under conventional assumptions.
Unified analysis of matrix completion with structural constraints.
problem Matrix completion under general structural constraints.
method Unified analysis using generic chaining and characterizations of Gaussian widths.
result Unified upper bounds on sample complexity and estimation error.
Generalizes Sobolev IPM for graph-based measures using Orlicz geometric structure.
problem Limitation of Le et al. (2025) framework to Lp geometry. method Generalizes Sobolev IPM through Orlicz geometric structure, employing convex functions to capture nuanced geometric relationships.
result GSI-M reduces to a simple univariate optimization problem, achieving remarkable computational efficiency.
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the regularization by the ℓ1-norm. In this paper, we consider situations where we…
Unified approach for error bounds in group sparse compressed sensing.
problem Error bounds for group sparse vectors in compressed sensing.
method Unified approach using decomposable and γ-decomposable norms.
result Bounds for various group sparse norms derived.
Small Nijenhuis tensor found on compact manifolds.
problem Finding compact manifolds with small Nijenhuis tensor.
method Provided explicit examples of manifolds with small Nijenhuis tensor.
result Examples of manifolds with small Nijenhuis tensor in various dimensions.
Paper introduces structured sparsity estimators for Generalized Linear Models.
problem Estimating structured sparsity in GLMs with debiased estimators.
method Extends Stucky and van de Geer's results to GLMs with structured sparsity.
result Proves oracle inequalities for structured sparsity estimators in GLMs.
Paper analyzes structured matrix recovery using generalized Dantzig selector.
problem Structured matrix recovery for applications like recommender systems and computer vision.
method Non-asymptotic analysis of generalized Dantzig selector for estimation of generally structured matrices.
result Estimation error can be expressed in terms of geometric measures of suitable sets.
Study normal curves in sub-Finsler Lie groups with specific norms, focusing on branching and face stability.
problem Analyzing normal curves in sub-Finsler Lie groups with different norms.
method Using tools from convex analysis, the Pontryagin Maximum Principle is revisited to express the normal equation as a differential inclusion involving the subdifferential of the dual norm.
result Normal curves in polyhedral norms have controls that locally take values in a single face of a sphere with respect to the norm.
Sparse methods for supervised learning aim at finding good linear predictors from as few variables as possible, i.e., with small cardinality of their supports. This combinatorial selection problem is often turned into a convex optimization problem by replacing the cardinality function by its convex envelope (tightest c…
CNNs use a bottleneck structure to focus on a few frequencies, affecting function representation.
problem Understanding how CNNs focus on specific frequencies in their feature learning.
method Defined Convolution Bottleneck (CBN) structure, measured CBN rank, and analyzed parameter norms.
result Parameter norm scales with depth and CBN rank, and networks with optimal parameters exhibit this structure.
Analyzes normed modules over metric measure spaces.
problem Understanding the structure of normed modules over metric measure spaces.
method Examines conditions for L0-normed modules to be sections of measurable Banach bundles. result Establishes an equivalence of categories between L0-normed modules and measurable Banach bundles. New adversarial examples with structured distortion sets improve robustness and perceptibility.
problem Improving adversarial robustness and perceptibility of images.
method Exploring and constraining adversarial search with trace-norms and other norms.
result Structured adversarial perturbations allow larger distortions and control over generation.
New method solves graph-structured sparsity problems efficiently.
problem Graph-structured sparsity optimization in complex models.
method Stochastic gradient-based approach for non-convex graph-structured sparsity.
result Linear convergence up to a constant error.
Geodesics of contactomorphisms on a specific manifold are characterized by Hamiltonian functions.
problem Characterizing geodesics of contactomorphisms on a manifold with a standard contact structure.
method Analyzing geodesics defined by different norms on the identity component of the group of contactomorphisms.
result The norm of a geodesic contactomorphism can be expressed in terms of the maximum of the Hamiltonian function.
We describe Milnor open books and Legendrian surgery diagrams for canonical contact structures of links of some rational surface singularities. We also describe an infinite family of Milnor fillable contact 3-manifolds so that the Milnor genus (resp. Milnor norm) is strictly greater than the support genus (resp. suppor…
S-MTGPR improves normative modeling of neuroimaging data.
problem Normative modeling of neuroimaging data without spatial covariance structure.
method Scalable multi-task Gaussian process regression (S-MTGPR) with low-rank approximation and Kronecker product.
result S-MTGPR provides higher sensitivity in novelty detection scenarios.
Develops a new OT framework for class-based data with improved robustness.
problem Understand and recover class structure in optimal transport schemes.
method Proposes a convex OT program with sum-of-norms regularization and an accelerated proximal algorithm.
result The new regularizer preserves class structure better and is more robust to data geometry.
We consider a class of learning problems that involve a structured sparsity-inducing norm defined as the sum of ℓ∞-norms over groups of variables. Whereas a lot of effort has been put in developing fast optimization methods when the groups are disjoint or embedded in a specific hierarchical structure, we add…
Algorithm leverages low-rank relations between surrogate tasks for structured prediction.
problem Structured prediction with large or infinite-dimensional surrogate spaces.
method Trace norm regularization to leverage relationships between surrogate outputs without explicit coding/decoding functions.
result Our algorithm can improve generalization performance over previous methods.
Exact partitioning of high-order planted models achieved through convex optimization.
problem Efficiently partitioning hypergraphs generated by high-order planted models.
method Solving a computationally efficient convex optimization problem with a tensor nuclear norm constraint.
result Exact recovery of true underlying cluster structures with high probability.
Study of unitary and groupoid orbits of normal operators, focusing on manifold structures and spectral conditions.
problem Understanding the manifold structures of orbits of normal operators under different norm topologies.
method Unified treatment of unitary and groupoid orbits, using moment maps and conditional expectations.
result Differentiable structures for orbits and necessary spectral conditions for norm closure and submanifold properties.
HBR improves normative modeling of neuroimaging data across multiple sites.
problem Dealing with nuisance variation in neuroimaging data across different sites.
method Hierarchical Bayesian regression (HBR) for multi-site normative modeling.
result HBR provides more accurate normative ranges compared to existing methods.
Deep neural networks with adversarial training achieve sup-norm convergence for nonparametric regression.
problem Achieving sup-norm convergence for deep neural network estimators in nonparametric regression.
method Developed an adversarial training scheme to address the sup-norm convergence issue.
result Deep neural network estimators achieve optimal sup-norm convergence with the proposed adversarial training.
We consider a class of sparse learning problems in high dimensional feature space regularized by a structured sparsity-inducing norm which incorporates prior knowledge of the group structure of the features. Such problems often pose a considerable challenge to optimization algorithms due to the non-smoothness and non-s…
The paper studies how norms of random vectors are preserved by random projections.
problem Understanding how random matrix affects norms of random vectors.
method Proved the distribution of the norm of random vector is preserved by random projection.
result Random matrix preserves the distribution of the norm of random vectors with i.i.d. entries.
Deep normative modeling of clinical neuroimaging data improves diagnostic performance.
problem Modeling variation of neuroimaging measures across individuals for psychiatric disorders.
method Proposes a deep normative modeling framework based on neural processes (NPs) for spatially structured mixed-effect modeling of neuroimaging data.
result Substantial improvements in novelty detection performance for certain diagnostic problems.
New method for tensor recovery with fewer samples.
problem Recovering low-TT-rank tensors from few samples.
method Minimizing a weighted sum of nuclear norms of unfoldings.
result Significantly fewer samples required for recovery.
We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS…
New bounds for CNNs show better generalization than previous models.
problem Improving understanding of CNNs' generalization ability.
method Proposed tighter generalization bounds for CNNs by exploiting the sparse and permutation structure of weight matrices and spectral norms of convolution operations.
result Theoretical and experimental results show tighter bounds for CNNs than existing bounds.
This work improves trace norm regularization for multi-task learning with limited data.
problem Learning from few samples across multiple tasks.
method Trace norm regularization for a linear shared representation model.
result First estimation error bound for trace norm regularized estimator with scarce data.