Improved optimal regularity for harmonic almost complex structures.
problem Establishing optimal regularity for harmonic almost complex structures.
method Quantitative stratification method and rectifiability of singular strata.
result Optimal regularity theory for energy minimizing harmonic almost complex structures.
Study shows how to balance memory and learning efficiency in continual learning.
problem Balancing memory and learning efficiency in continual learning.
method Structural regularization with Hessian-based regularization.
result Structural regularization improves statistical performance at the cost of increased memory complexity.
MARL algorithm uses regularization to avoid explicit structures, improving performance.
problem Lack of effective reinforcement learning methods for multi-agent systems.
method MARQ uses regularization to promote structured exploration without explicit centralized structures.
result MARQ outperforms existing methods in multi-agent environments.
New structures with symmetry found, contradicting previous assumptions.
problem Limitations of C1 regularity in almost-Grassmannian structures. method Constructing families of (2,n)-almost Grassmannian structures with C1 regularity and specific symmetry. result Theorem 1.3 of [9] is not valid under C1 regularity assumptions. We propose a novel data-dependent structured gradient regularizer to increase the robustness of neural networks vis-a-vis adversarial perturbations. Our regularizer can be derived as a controlled approximation from first principles, leveraging the fundamental link between training with noise and regularization. It adds…
Paper proposes ASR framework to improve image generation by incorporating human knowledge.
problem Deep generative models struggle to capture rich structures and relations in multi-object images.
method Introduces amortized structural regularization (ASR) framework using posterior regularization (PR) to embed human knowledge.
result Empirical results show ASR significantly outperforms DGM baselines in inference accuracy and sample quality.
Geometric deformations preserve post-Lie algebra structure in regularity structures.
problem Deriving geometric deformations of post-Lie algebras.
method Extending geometrical notions of torsion and curvature, deriving compatibility conditions.
result Derives a pre-Lie structure for regularity structures, isomorphic to a post-Lie algebra.
Novel regularization for Vision Transformers improves model generalization and sparsity.
problem Improving generalization and sparsity in Vision Transformers.
method Likelihood-guided variational Ising-based regularization.
result Improved generalization and sparsity in Vision Transformers.
A Jacobi structure J on a line bundle L→M is weakly regular if the sharp map J♯:J1L→DL has constant rank. A generalized contact bundle with regular Jacobi structure possess a transverse complex structure. Paralleling the work of Bailey in generalized complex geometry, we find condition on a pair …
Study Godbillon-Vey class for regular Jacobi foliations.
problem Characterizing foliations in Jacobi manifolds.
method Explicitly defined and computed Godbillon-Vey class for regular foliations.
result Expressed Godbillon-Vey class in terms of Jacobi structures.
Optimizes coordinate charts for smooth elliptic structures.
problem Achieving optimal regularity for coordinate charts of smooth elliptic structures.
method Generalizing Malgrange's proof of the Newlander-Nirenberg Theorem to this setting.
result Optimal regularity for coordinate charts of smooth elliptic structures.
New autoencoder learns structured representations without regularization.
problem Learning structured representations without relying on regularization.
method Proposes a novel autoencoder architecture that learns a hierarchy of latent variables.
result Improves results in generation, disentanglement, and extrapolation tasks.
In this paper we study the geometrical structures on the cotangent bundle using the notions of adapted tangent structure and regular vector fields. We prove that the dynamical covariant derivative on T∗M fix a nonlinear connection for a given J-regular vector field. Using the Legendre transformation in…
Fiedler regularization uses graph sparsity to improve neural network training.
problem Improving neural network training by respecting graph structure.
method Using the Fiedler value of the neural network's graph as a regularization tool.
result Fiedler regularization outperforms traditional methods like dropout and weight decay.
The paper proves smoothness of weakly biharmonic almost complex structures in dimension four.
problem Existence and regularity of weakly polyharmonic almost complex structures.
method Elliptic system analysis and critical growth nonlinearities.
result Weakly biharmonic almost complex structures are smooth in dimension four.
RMDA trains structured neural networks with regularization and variance reduction.
problem Training structured neural networks with desired properties.
method RMDA algorithm for structured NNs with regularization and variance reduction.
result RMDA achieves desired structures identical to regularizer's at stationary points.
We extend the Newlander-Nirenberg theorem to manifolds with almost complex structures that have somewhat less than Lipschitz regularity. We also discuss the regularity of local holomorphic coordinates in the integrable case, with particular attention to Lipschitz almost complex structures.
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.
Unified approach to structured prediction combining entropy regularization and neuro-symbolic logic.
problem Structured prediction challenges due to large output spaces and insufficient labeled data.
method Neuro-symbolic entropy regularization loss that restricts entropy regularization to valid structures.
result Models predict more accurately and are more likely to be valid.
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…
On an orientable manifold M, we consider a regular even dimensional foliation F which is globally defined by a set of k-independent 1-forms. We give necessary and sufficient conditions for the existence of a regular Poisson structure on M whose Characteristic foliation is precisely F. Moreover, introducing a special cl…
Proves existence of regular Lagrangians via Weinstein Lefschetz fibrations.
problem Existence of regular Lagrangians.
method Weinstein Lefschetz fibrations with a hypothesis.
result Existence of regular Lagrangians can be characterized by Lefschetz fibrations.
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design learning algorithms using a surrogate loss approach and regularization techniques. We p…
New constructions of Sasakian and K-contact structures on Smale-Barden manifolds.
problem Deciding when a Smale-Barden manifold admits a Sasakian or K-contact structure.
method Developing quasi-regular Seifert fibrations and applying them to constructions.
result Determined all Smale-Barden manifolds admitting null Sasakian structures and provided counterexamples to conjectures.
We look at Poisson geometry taking the viewpoint of singular foliations, understood as suitable submodules generated by Hamiltonian vector fields rather than partitions into (symplectic) leaves. The class of Poisson structures which behave best from this point of view, are those whose submodule generated by Hamiltonian…
The paper explores how regularization can improve multi-objective learning with high-dimensional data.
problem Improving multi-objective learning with high-dimensional and costly data.
method A two-stage MOL framework that leverages low-dimensional structure.
result Vanilla regularization approaches often fail in multi-objective learning, and a two-stage framework can successfully exploit low-dimensional structure.
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 prove h-principle for locally conformal symplectic foliations and contact foliations on open manifolds. We interpret the result on h principle of contact foliations in terms of the regular Jacobi structures.
The paper proves a regularity theorem for Brakke flows near triple junctions.
problem Understanding the structure of triple junctions in Brakke flows.
method Establishes the ε-regularity theorem for k-dimensional Brakke flows near static, multiplicity-one triple junctions.
result The regular structure of triple junctions persists under weak mean curvature flow.
Establishes 4D regularity for certain metric spaces.
problem Noncollapsed sequences of metrics with Ricci tensor bounds.
method A priori L2 curvature estimates.
result Diffeomorphism finiteness and rigidity theorems.
Regularization plays a crucial role in supervised learning. Most existing methods enforce a global regularization in a structure agnostic manner. In this paper, we initiate a new direction and propose to enforce the structural simplicity of the classification boundary by regularizing over its topological complexity. In…
Eta-Einstein and (κ,μ)-structures studied in dimension 3.
problem Characterizing and understanding Eta-Einstein and (κ,μ)-structures in 3D. method Analyzing closed manifolds and constructing examples.
result Almost regular Eta-Einstein structures not D-homothetic to Einstein structures exist.
Geometric structures on quaternionic unit ball for slice regular Möbius transformations.
problem No new problem introduced.
method Introducing Hermitian, Riemannian, and Kähler-like structures on quaternionic unit ball using regular Möbius transformations.
result Geometric structures are natural generalizations of complex setup and solve problems not achieved by other geometries.
SU(3)-structures found on quotients of 3-Sasakian manifolds.
problem Exploring SU(3)-structures on specific quotients of 3-Sasakian manifolds.
method Analyzing quasi-regular 3-Sasakian orbifolds and their quotients, computing torsion and providing nearly Kähler structures.
result SU(3)-structures and nearly Kähler structures found on quotients of 3-Sasakian manifolds.
Develops structure theory for RCD spaces with upper curvature bounds.
problem Understanding the structure of RCD spaces with curvature bounds.
method Structure theory development for RCD spaces with upper curvature bounds in Alexandrov sense.
result RCD spaces with curvature bounds are topological manifolds with boundary, and the interior is a smooth manifold.
In a recent work (arXiv:0910.2517), for nonlinear models with sparse underlying linear structures, we studied the error bounds of ℓ0-regularized estimation. In this note, we show that ℓ1-regularized estimation in some important cases can achieve the same order of error bounds as those in the aforementioned …
SymCircuit learns PC structure via entropy-regularized RL, improving inference efficiency and accuracy.
problem Greedy algorithms in PC structure learning lead to suboptimal solutions.
method Entropy-regularized reinforcement learning to train a learned generative policy for PC structure inference.
result SymCircuit learns the optimal policy as a tempered Bayesian posterior, improving inference efficiency and accuracy.
SinSim improves self-supervised learning by integrating optimal transport into contrastive learning.
problem Lack of explicit regularization in contrastive learning methods leads to suboptimal generalization.
method Integrates Sinkhorn regularization from optimal transport theory into SimCLR.
result SinSim outperforms SimCLR and other self-supervised methods on various datasets.
Structured regularizers enable faster optimization on SPD manifolds with constraints.
problem Optimizing SPD matrices with additional constraints.
method Structured regularizers based on symmetric gauge functions.
result Structured regularizers can preserve or induce desirable structure like convexity.
We prove the C1 regularity for a class of abnormal length-minimizers in rank 2 sub-Riemannian structures. As a consequence of our result, all length-minimizers for rank 2 sub-Riemannian structures of step up to 4 are of class C1.
A regular Poisson manifold can be described as a foliated space carrying a tangentially symplectic form. Examples of foliations are produced here that are not induced by any Poisson structure although all the basic obstructions vanish.
The paper explores optimal regularizers for data sources, linking them to star bodies.
problem Understanding optimal regularizers for data sources.
method Investigates optimal regularizers for data distributions using star bodies and dual Brunn-Minkowski theory.
result Identifies optimal regularizers and assesses amenability to convex regularization.
Improved prediction of hierarchical time series using structured regularization.
problem Making coherent forecasts for hierarchical time series.
method Structured regularization method for bottom-level time series predictions.
result Superior prediction accuracy and computational efficiency compared to previous methods.
The paper proves existence and multiplicity of affine connections on regular manifolds.
problem Existence and multiplicity of affine connections on regular manifolds.
method Regularity theory and properties of the structural presheaf.
result The space of regular affine connections is an affine space of the space of regular End(TM)-valued 1-forms. An f-structure on a manifold M is an endomorphism field φ satisfying φ3+φ=0. We call an f-structure {\em regular} if the distribution T=kerφ is involutive and regular, in the sense of Palais. We show that when a regular f-structure on a compact manifold M is an almost §-structure, as defined by Dugg…
A new method learns robust policies from offline data with latent structures.
problem Conservative policies under unrealistic dynamics shifts.
method d-RRMDP framework with f-divergence regularization and R2PVI algorithm. result R2PVI learns robust policies with superior computational efficiency.
Based on the notion of dilatation structure arXiv:math/0608536, we give an intrinsic treatment to sub-riemannian geometry, started in the paper arXiv:0706.3644 . Here we prove that regular sub-riemannian manifolds admit dilatation structures. From the existence of normal frames proved by Bellaiche we deduce the rest of…
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.