Adapted metrics found on complex manifolds.
problem Finding metrics suitable for complex manifolds.
method Characterizing adapted metrics as critical points of a functional.
result Gauduchon metric is adapted on locally conformally product manifolds.
Paper studies well adapted connections for specific metric manifolds.
problem Characterizing well adapted connections for (J2=±1)-metric manifolds. method Proves existence and derives explicit formula for well adapted connections in four geometries.
result Characterizes coincidence of well adapted connections with Levi Civita and Chern connections.
Locally adaptive nearest neighbors improve automated systems' performance and are easier to interpret.
problem Improving automated systems' performance and interpretability.
method Developed a method for k nearest neighbors algorithms to learn locally adaptive metrics.
result Locally adaptive metrics improve performance and are interpretable.
M-ADDA uses deep metric learning to adapt target datasets from similar source datasets.
problem Unsupervised domain adaptation for unlabeled target datasets.
method Metric learning and adversarial training to make target and source embeddings indistinguishable.
result M-ADDA outperforms ADDA on MNIST and USPS digit datasets.
Adaptive loss function improves performance by aligning training and evaluation metrics.
problem Loss-metric mismatch in machine learning training.
method Adaptive loss alignment through meta-learning of a dynamic loss function.
result Significant performance improvements across various tasks and data.
New metric and method for sEMG-based gesture recognition under domain shifts.
problem Measuring and adapting to domain divergence in sEMG-based gesture recognition.
method Probability distribution-based metric, 2-stage autoregressive RNN architecture.
result Improved autoregressive, RNN-based architecture enhances performance.
Study various connections on (J2=±1)-metric manifolds.
problem Characterize and compare linear connections on (J2=±1)-metric manifolds. method Examined first canonical, Chern, well adapted, Levi Civita, Kobayashi-Nomizu, Yano, Bismut, and totally skew-symmetric torsion connections.
result Every connection studied is a canonical connection when it exists and is adapted.
COMID-SADL learns adaptive metrics for nonstationary data.
problem Learning metrics when constraint generation is nonstationary.
method COMID-SADL, an adaptive, online approach.
result Significant performance improvements over existing methods.
Bayesian approach improves AdaLoRA's performance and efficiency.
problem Improving the efficiency and performance of adaptive low-rank adaptation.
method Utilized Bayesian metrics and the Improved Variational Online Newton (IVON) optimizer for adaptive parameter budget allocation.
result Bayesian counterpart outperforms sensitivity-based importance metric and is faster than AdaLoRA.
Unified theory for adaptive image convolutions using metric perspectives.
problem Fixed kernels in convolutions limit adaptability in image processing.
method Metric perspective on images as 2D manifolds with local distances, proposing metric convolutions.
result Metric convolutions provide better generalisation and competitive performance.
Adaptive PCA algorithms for changing environments.
problem Static adversarial regret is not suitable for changing environments.
method Online adaptive algorithms for PCA and variance minimization with sub-linear adaptive regret guarantees.
result The proposed algorithms adapt to changing environments.
Study shows reinforcement learning algorithm's performance depends on metric space's size.
problem Continuous state and action spaces with metrics.
method Refined analysis of Sinclair et al. (2019) algorithm.
result Regret scales with the zooming dimension, a new parameter capturing near optimal actions.
Optimizes hard-to-optimize metrics using adaptive surrogates.
problem Training models with black-box and hard-to-optimize metrics.
method Expresses metric as a function of surrogates, solves optimization problem over relaxed surrogate space.
result Approach performs on par with known methods and adds value when metric form is unknown.
The Newman-Penrose-Perjes formalism is applied to smooth contact structures on riemannian 3-manifolds. In particular it is shown that a contact 3-manifold admits an adapted riemannian metric if and only if it admits a metric with a divergence-free, constantly twisting, geodesic congruence. The shear of this congruence …
A new distribution adapts to local data density.
problem Fitting complex probability distributions over manifolds.
method Developed a locally adaptive normal distribution (LAND) using a non-parametric metric.
result LAND generalizes the normal distribution to manifold settings.
In this paper, we describe the space of adapted connections on a metric contact manifold through the space of their torsion tensors. The torsion tensor is an element of the space of TM-valued two-forms, which splits into various subspaces. We study the parts of the torsion tensor according to this splitting to complete…
Study on MHD equilibria on curved spaces without symmetries.
problem Analyzing MHD equilibria on curved spaces without symmetries.
method Examined MHD equilibria on Riemannian 3-manifolds with various adapted metrics.
result Found that for an open and dense set of adapted metrics, MHD equilibria on compact 3-manifolds without boundary admit no continuous Killing symmetries.
A new method for neural networks adapts to different domains without labeled data.
problem Adapting neural networks to new domains without labeled data.
method Metric-based regularization to maximize similarity of domain-specific activation distributions by aligning moments.
result The method achieves higher classification accuracies than existing approaches.
There are introduced and studied a pair of associated Schouten-van Kampen affine connections adapted to the contact distribution and an almost contact B-metric structure generated by the pair of associated B-metrics and their Levi-Civita connections. By means of the constructed non-symmetric connections, the basic clas…
Study shows polystability of tangent and canonical sheaves on Kähler-Einstein log Fano pairs.
problem Stability of tangent and canonical sheaves on Kähler-Einstein log Fano pairs.
method Analysis of adapted tangent and canonical sheaves under singular Kähler-Einstein metrics.
result Adapted tangent and canonical sheaves are polystable.
Researchers describe a unique hyper-Kähler structure on a specific domain.
problem Describing a unique hyper-Kähler structure on a specific domain.
method Explicit description and computation of invariant potentials and moment maps.
result An explicit description of the unique adapted hyper-Kähler structure.
The paper adapts metrics to anti-de Sitter structures, characterizing their degeneracies.
problem Characterizing degeneracies of metrics on anti-de Sitter structures.
method Adapting Hitchin component metrics to anti-de Sitter structures.
result Characterized degeneracies of the pressure metric and showed the Loftin metric is nowhere degenerate.
Adapts example weights to optimize black-box metrics.
problem Optimizing metrics defined by black-box functions.
method Adaptive example weighting and iterative post-shifting.
result Improves classification performance compared to baselines.
A new metric DJP-MMD improves domain adaptation by balancing transferability and discriminability.
problem Improving domain adaptation performance by balancing transferability and discriminability.
method Discriminative Joint Probability Maximum Mean Discrepancy (DJP-MMD) replaces the traditional joint MMD.
result DJP-MMD outperforms traditional MMDs in image classification tasks.
New method tracks evolving data metrics.
problem Nonstationary changes in data constraints.
method Online Convex Ensemble StrongLy Adaptive Dynamic Learning (OCELAD).
result Significant performance improvements and robustness.
Paper investigates robustness to interference as a new training signal for meta-learning.
problem Improving incremental learning through robust representations.
method Directly minimizing catastrophic interference as a training signal.
result Representations learned to minimize interference lead to better incremental learning.
We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are doubling, or nearly doubling. On the algorithmic front, we describe an analogue of PCA f…
This paper proposes a new AED framework for multi-metric experiments with fixed budget.
problem Statistical power challenges in testing multiple metrics simultaneously.
method Two-phase structure: adaptive exploration followed by validation. SHRVar algorithm with relative-variance-based sampling.
result Achieves provable error probability that decreases exponentially.
This study revisits UQ validation methods based on consistency and adaptivity concepts.
problem Lack of comprehensive validation methods for UQ metrics across input feature ranges.
method Revisit and extend common validation methods for UQ metrics based on consistency and adaptivity concepts.
result Improved understanding and capabilities of UQ metrics validation methods.
Study proves only round sphere has certain adapted complex structure on Zoll metrics.
problem Characterizing Zoll metrics with specific complex structures.
method Analytic geometry, foliations, and algebraization techniques.
result Only round sphere has entire adapted complex structure on Zoll metrics.
New algorithm improves online learning with expert advice and metric learning.
problem Improving online learning performance in changing environments.
method Parameter-free online learning algorithm using coin betting.
result Strongly adaptive regret bound improvement of at least sqrt(log(T)).
AdaS adapts SGD learning rate based on knowledge gain metrics.
problem Empirical step-size selection in SGD optimization lacks consistency and insight.
method Introduces AdaS algorithm that adapts SGD learning rate based on knowledge gain metrics.
result AdaS outperforms existing adaptive learning methods in convergence and generalization.
Proposes ATM method to improve domain adaptation.
problem Mitigating distribution divergence between source and target domains.
method Adversarial Tight Match (ATM) method using Maximum Density Divergence (MDD).
result New state-of-the-art performance on domain adaptation benchmarks.
The paper proposes a uniformity regularization scheme to improve deep neural network transferability.
problem Improving deep neural network transferability and adaptation to new tasks.
method Introduces a uniformity regularization scheme to encourage high uniformity in embedding space.
result Uniformity regularization consistently offers benefits over baseline methods and achieves state-of-the-art performance in Deep Metric Learning and Meta-Learning.
Paper tackles unsupervised domain adaptation for unlabeled target domains.
problem Existing domain adaptation research focuses on labeled target domains, ignoring unlabeled ones.
method Developed an unsupervised knowledge transfer theorem and metric, implemented in GLG model.
result Proposed model outperforms existing baselines across three applications.
Flag manifolds are in general not symmetric spaces. But they are provided with a structure of Z2k-symmetric space. We describe the Riemannian metrics adapted to this structure and some properties of reducibility. We detail for the flag manifold SO(5)/SO(2)×SO(2)×SO(1) what are the conditions…
Proposes a framework to improve domain adaptation without labeled data.
problem Improving adaptability and preserving intrinsic data structure in unsupervised domain adaptation.
method Discriminative Manifold Propagation framework using soft labels and manifold metric alignment.
result The method achieves better transferability and discriminability compared to existing approaches.
SWD improves unsupervised domain adaptation by measuring classifier outputs.
problem Improving unsupervised domain adaptation between domains.
method Proposes sliced Wasserstein discrepancy (SWD) for feature distribution alignment.
result SWD effectively aligns source and target distributions for various tasks.
Study variational problem on manifold with special distributions.
problem Generalize Einstein metrics on manifold with multiple distributions.
method Define functional of pseudo-Riemannian metric and contorsion tensor, prove critical pairs make distributions totally umbilical.
result Metrics in critical pairs make all distributions totally umbilical.
Paper proposes adaptive margin loss to improve few-shot learning.
problem Few-shot learning's difficulty in generalizing from a few examples.
method Develops class-relevant and task-relevant additive margin losses.
result Boosts performance of metric-based meta-learning approaches.
New algorithm reduces control error in systems with changing dynamics.
problem Online control of systems with time-varying linear dynamics.
method Introduces adaptive regret metric and a novel meta-algorithm.
result First adaptive regret bound for online convex optimization with memory.
Efficient algorithm for reinforcement learning in large state-action spaces with adaptive discretization.
problem Efficient reinforcement learning in large, potentially continuous state-action spaces.
method Adaptive Q-learning policy with data-driven adaptive discretization. result Demonstrates improved performance compared to existing methods, especially in adapting to the problem's structure.
Low regularity spacetimes split into simpler structures.
problem Proving splitting theorem for C1 metrics and weights. method Combining elliptic techniques and line-adapted curves.
result Extends Lorentzian splitting theorem to C1 settings. Metric learning makes it plausible to learn distances for complex distributions of data from labeled data. However, to date, most metric learning methods are based on a single Mahalanobis metric, which cannot handle heterogeneous data well. Those that learn multiple metrics throughout the space have demonstrated superi…
We characterize the existence of a locally conformally Kähler metric on a compact complex manifold in terms of currents, adapting the celebrated result of Harvey and Lawson for Kähler metrics.
Adaptive strategies reduce pension fund costs and risks.
problem Managing longevity and volatility risks in pension funds.
method Modular simulation framework with customizable metrics.
result Substantial reduction in pension plan costs and default risk.
We show that many standard results of Lorentzian causality theory remain valid if the regularity of the metric is reduced to C1,1. Our approach is based on regularisations of the metric adapted to the causal structure.
CADM proposes a cluster-specific distance metric for categorical data clustering.
problem Inadequate distance metrics for categorical data, especially varying within clusters.
method Cluster-customized adaptive distance metric for categorical data.
result Achieved competitive performance in categorical data clustering.