Two Kähler structures are PCR equivalent in the Siegel domain.
problem Equivalence of two Kähler structures in the Siegel domain.
method Construction of complex hyperbolic and Kähler structures from Sasakian structure.
result PCR Kähler equivalent structures in Siegel domain.
Dual-structured method improves cross-domain imitation learning.
problem Learning policies in a target domain from source domain expert demonstrations.
method Extracts domain and policy expertness features, synthesizes new features.
result Superior performance compared to other algorithms in MuJoCo tasks.
This paper proposes a new method to improve domain adaptation by distinguishing between marginal and dependence structure differences.
problem Existing domain adaptation methods fail to differentiate between marginal and dependence structure differences, leading to suboptimal transferability.
method The paper introduces a new approach that measures and optimizes the differences in internal dependence structure separately from marginals.
result The new method significantly improves transferability and robustness compared to existing benchmarks on real-world datasets.
The paper explores how to make machine learning models robust to domain shifts.
problem Machine learning models are unreliable in domains different from training.
method Introducing a broad formal notion of invariance and causal structures.
result The true underlying causal structure of the data plays a critical role in robustness.
Graph-Relational Domain Adaptation (GRDA) adapts domains based on their graph structure.
problem Uniform alignment of domains ignores topological structures.
method Uses a domain graph to encode adjacency and a novel graph discriminator.
result Empirically shows improved generalization and domain information incorporation.
New minimal surfaces found with Cantor ends in convex domains.
problem Finding complex structures for minimal surfaces with Cantor ends.
method Proving existence of complete minimal surfaces with Cantor ends in minimally convex domains.
result Existence of a Cantor set whose complement forms a complete minimal surface.
A novel unsupervised domain adaptation method using hierarchical optimal transport.
problem Unsupervised domain adaptation between source and target domains.
method Hierarchical optimal transport, leveraging class labels for structure formation in the source domain and learning probability measures in the target domain.
result The proposed HOT-DA method outperforms state-of-the-art approaches on various datasets.
A new method uncovers intrinsic data structures for unsupervised domain adaptation.
problem Learning domain-aligned features can damage intrinsic target discrimination.
method Structurally Regularized Deep Clustering (H-SRDC) integrating structural source regularization.
result H-SRDC outperforms existing methods in image classification and semantic segmentation.
Learn to automatically plug domain-specific modules into a common network.
problem Learning inflexibility and computational intensiveness in multi-domain learning.
method Neural Architecture Search (NAS) for data-driven adapter plugging and structure design.
result NAS-driven MDL model achieves comparable performance to existing approaches.
Develops a logifold structure for understanding datasets.
problem Understanding and classifying complex datasets.
method Local-to-global approach using measure-theoretical models.
result Improves accuracy in data classification problems.
In 1998, Gompf described a Stein domain structure on the disk cotangent bundle of any closed surface S, by a Legendrian handlebody diagram. We prove that Gompf's Stein domain is symplectomorphic to the disk cotangent bundle equipped with its canonical symplectic structure and the boundary of this domain is contactomorp…
Unsupervised domain adaptation aims to address the problem of classifying unlabeled samples from the target domain whilst labeled samples are only available from the source domain and the data distributions are different in these two domains. As a result, classifiers trained from labeled samples in the source domain su…
New algorithm improves model generalization in structured biomedical domains.
problem Improving model generalization in structured biomedical domains.
method Proposes a new regret minimization (RGM) algorithm and its structured extension for better performance in diverse environments.
result Significantly outperforms previous state-of-the-art baselines on molecular property prediction, protein homology, and stability prediction.
Adversarial training is a useful approach to promote the learning of transferable representations across the source and target domains, which has been widely applied for domain adaptation (DA) tasks based on deep neural networks. Until very recently, existing adversarial domain adaptation (ADA) methods ignore the usefu…
Adaptive transfer learning model for varying mechanisms across domains.
problem Improving inference in a target domain by leveraging related source domains with varying mechanisms.
method Semi-parametric domain-varying coefficient model (DVCM) for structured transfer learning.
result Minimax rate-optimal adaptive transfer learning estimator with provable negative transfer safeguards.
Sheng and Zuo's characteristic forms are invariants of a variation of Hodge structure. We show that they characterize Gross's canonical variations of Hodge structure of Calabi-Yau type over (Hermitian symmetric) tube domains.
Method learns domain-specific representations without supervision.
problem Domain generalization without labeled data.
method Hierarchical variational autoencoder approach.
result Model generalizes to unseen domains without domain supervision.
PDSketch enables flexible robot planning by learning from domain structures.
problem Building general robots with flexible planning.
method Exploiting locality and sparsity in environmental models, PDSketch defines high-level structures for trainable neural networks.
result PDSketch automatically generates planning heuristics without additional training.
The paper classifies fiber structures of discontinuity domains for Anosov representations.
problem Understanding the topology of discontinuity domains for Anosov representations.
method Explicitly working out a smooth version of Fintushel's classification theorem for S1-actions on 4-manifolds. result The action on the fiber is equivalent to a circle action on a Hirzebruch surface.
We focus on explicitly learning disentangled representation for natural image generation, where the underlying spatial structure and the rendering on the structure can be independently controlled respectively, yet using no tuple supervision. The setting is significant since tuple supervision is costly and sometimes eve…
Proposes MD-LiNA for multi-domain latent factor causal discovery.
problem Discovering causal structures among latent factors from multi-domain data.
method Multi-Domain Linear Non-Gaussian Acyclic Models (MD-LiNA) with an integrated two-phase algorithm.
result Locally consistent estimators of causal structure among shared latent factors.
Inter-domain Deep Gaussian Processes improve inference for non-stationary data.
problem Inference limitations in Gaussian processes for non-stationary data.
method Combines inter-domain and deep Gaussian processes for scalable approximate inference.
result Outperforms inter-domain shallow GPs and conventional DGPs on non-stationary data.
Paper tackles robust domain adaptation without target domain data.
problem Learning domain invariant representations without target domain data.
method Integrates deep autoencoder and causal structure learning into a unified model.
result CAE learns causal representations using only source domain data.
Two semi-supervised manifold alignment methods improve cross-domain classification.
problem Aligning data from multiple sources for better analysis.
method SPUD and MASH methods using graph integration and diffusion.
result SPUD and MASH methods outperform existing methods in cross-domain classification.
CDSPP learns domain-specific projections for heterogeneous domain adaptation.
problem Heterogeneous domain adaptation problems where source and target domains have different modalities or feature dimensions.
method Cross-Domain Structure Preserving Projection (CDSPP) algorithm that learns domain-specific projections to map features into a common subspace.
result CDSPP achieves superior performance in both supervised and semi-supervised HDA compared to state-of-the-art methods.
Proposes CTSDG model for better vehicle intention prediction across domains.
problem Domain generalization for vehicle intention prediction in dynamic environments.
method Structural causal model with recurrent latent variable integration.
result Consistent improvement in prediction accuracy compared to state-of-the-art methods.
The Masur domain is a subset of the space of projective measured geodesic laminations on the boundary of a 3-manifold M. This domain plays an important role in the study of the hyperbolic structures on the interior of M. In this paper, we define an extension of the Masur domain and explain that it shares a lot of prope…
MuVI models multi-view data with structured sparsity, integrating domain knowledge.
problem Disentangling variation across multiple data views in complex systems.
method Multi-view latent variable model with structured sparsity using a modified horseshoe prior.
result MuVI outperforms state-of-the-art methods in structured sparsity modeling and integrates noisy domain expertise.
DMRL improves UDA by mixing source and target samples and enriching latent space structures.
problem Lack of class-aware information and insufficient samples for domain-invariant feature extraction.
method Dual Mixup Regularized Learning (DMRL) that conducts category and domain mixup regularizations.
result DMRL achieves state-of-the-art performance on domain adaptation benchmarks.
Paper develops a model for verifying facts in tables without pre-retrieved evidence.
problem Verification of factual claims in structured data, especially in open-domain settings.
method Joint reranking-and-verification model that fuses evidence documents.
result Model achieves comparable performance to closed-domain state-of-the-art on TabFact dataset.
Let Ξ be the crown domain associated with a non-compact irreducible hermitian symmetric space G/K. We give an explicit description of the unique G-invariant adapted hyper-Kähler structure on Ξ, i.e. compatible with the adapted complex structure Jad and with the G-invariant Kähle…
Empirical Bayes improves causal representation learning across multiple domains.
problem Estimating causal representations from data across multiple domains.
method Developed an EB f-modeling algorithm for linearly-mixed causal representations. result Our method achieves more accurate estimation of causal variables than other methods.
Surveying joint Gaussian graphical models to identify shared structures across domains.
problem Estimating shared structures across different data sources.
method Statistical inference of joint Gaussian graphical models.
result Improved estimation power for high-dimensional data.
The paper extends Newlander-Nirenberg theorem to domains with C2 boundary.
problem Extending Newlander-Nirenberg theorem to domains with C2 boundary. method Analyzing formally integrable complex structures on domains with C2 boundary. result Existence of global holomorphic coordinate systems on the closure of a bounded strictly pseudoconvex domain.
Study equi-affine invariants for convex domains with asymptotes.
problem Understanding geometric properties of convex domains with specific asymptotes.
method Introducing equi-affine invariants by averaging tropical structures.
result Proving a limiting description of level sets for unbounded domains with two non-parallel asymptotes.
We discuss general notions of metrics and of Finsler structures which we call weak metrics and weak Finsler structures. Any convex domain carries a canonical weak Finsler structure, which we call its tautological weak Finsler structure. We compute distances in the tautological weak Finsler structure of a domain and we …
This paper tackles continuous domain generalization, improving model performance across unseen domains.
problem Existing domain generalization approaches fail to capture the complex, multidimensional nature of real-world variation.
method Introduces Continuous Domain Generalization (CDG), a principled framework grounded in geometric and algebraic theories. Proposes a Neural Lie Transport Operator (NeuralLio) for structure-preserving parameter transitions and a gating mechanism for robust generalization.
result Demonstrates significant improvement in generalization accuracy and robustness across various datasets.
Paper extends SI method for detecting CPs in complex systems' frequency domain.
problem Identifying change points in complex systems' frequency domain.
method Extends SI framework to frequency domain using DFT properties and develops valid p-values.
result Reliable detection of genuine CPs with strong statistical guarantees.
We consider isotropic non lower semicontinuous weighted perimeter functionals defined on partitions of domains in Rn. Besides identifying a condition on the structure of the domain which ensures the existence of minimizing configurations, we describe the structure of such minima, as well as their regularity…
Domain adaptation is transfer learning which aims to generalize a learning model across training and testing data with different distributions. Most previous research tackle this problem in seeking a shared feature representation between source and target domains while reducing the mismatch of their data distributions.…
New framework for domain adaptation using hierarchical optimal transport.
problem Improving domain adaptation when source and target data distributions differ.
method Proposes a new theoretical framework and hierarchical Wasserstein distance.
result Provides more explicit generalization bounds and aligns specific structures for successful adaptation.
Constructs examples of domains divided by groups in dimensions 3 and above.
problem Dividing convex sets with properly embedded cones.
method Uses Zariski dense relatively hyperbolic groups and properly embedded cones.
result Answers a question of Benoist and provides a topological criterion for convex projective structures.
In-BO optimizes complex constrained domains using SIn-GP surrogate models.
problem Optimizing in complex constrained domains with irregular shapes.
method Sparse Intrinsic Gaussian Processes (SIn-GP) on manifolds with heat kernel estimation.
result In-BO outperforms traditional BO in complex constrained domains.
Transferring knowledge across many streaming processes remains an uncharted territory in the existing literature and features unique characteristics: no labelled instance of the target domain, covariate shift of source and target domain, different period of drifts in the source and target domains. Autonomous transfer l…
We consider hyperbolic structures on the compression body C with genus 2 positive boundary and genus 1 negative boundary. Note that C deformation retracts to the union of the torus boundary and a single arc with its endpoints on the torus. We call this arc the core tunnel of C. We conjecture that, in any geometrically …
Study shows group structures are crucial for financial model explanations.
problem Inconsistent explanations from existing explainable machine learning methods.
method Examined group structures in financial datasets and developed group versions of Shapley values.
result Group versions of Shapley values provide consistent explanations.
In this paper we study domains in flag manifolds which are bounded in an affine chart and whose projective automorphism group acts co-compactly. In contrast to the many examples in real projective space, we will show that no examples exist in many flag manifolds. Moreover, in the cases where such domains can exist, we …
There are a number of examples of variations of Hodge structure of maximum dimension. However, to our knowledge, those that are global on the level of the period domain are totally geodesic subspaces that arise from an orbit of a subgroup of the group of the period domain. That is, they are defined by Lie theory rather…