arXiv research

The abstract explores a new wave equation linking quantum mechanics and complex adaptive systems.

Study reveals adversarially robust domain adaptation is harder to generalize across domains.

Optimizes sample and round complexity in adaptive sampling from multiple distributions.

We consider the problem of adaptation to the margin and to complexity in binary classification. We suggest an exponential weighting aggregation scheme. We use this aggregation procedure to construct classifiers which adapt automatically to margin and complexity. Two main examples are worked out in which adaptivity is a…

First we show that a curvature-adapted proper complex equifocal submanifold is a principal orbit of a Hermann type action under certain condition. Next we show that a proper complex equifocal submanifold is curvature-adapted under certain condition.

Given a closed real analytic Riemannian manifold, we construct and study a one parameter family of adapted complex structures on the manifold of its geodesics.

Adaptive region-based active learning seeks labels for complex data.

We introduce curvature-adapted foliations of complex hyperbolic space and study some of their properties. Generalized pseudo-Einstein hypersurfaces of complex hyperbolic space are classified. Analogous results for curvature-adapted hypersurfaces of quaternionic hyperbolic space are also obtained.

This study explores complex structures on Lie algebras from graph perspectives.

Improved elimination strategies for adaptive bandit identification reduce sample complexity and computational burden.

Cross-regularization adapts model complexity during training.

The paper studies hyperkähler structures and adapted complex structures using the Monge-Ampère equation.

ATLAS adapts HMC step size and trajectory length for complex geometries.

New bounds adaptively control spectral complexity of trained Transformers.

Paper proposes Adaptive Pareto Exploration for identifying Pareto optimal arms in multi-objective scenarios.

New algorithm reduces optimization complexity in adaptive mirror descent.

New model-based methods adapt pre-trained policies to unseen environments efficiently.

We develop a generalization of manifold calculus in the sense of Goodwillie-Weiss where the manifold is replaced by a simplicial complex. We consider functors from the category of open subsets of a fixed simplical complex into the category of topological spaces and prove an analogue of the approximation theorem. Namely…

This paper tackles adaptive control of unknown Markov jump systems with sample complexity and regret bounds.

Improved variance reduction for Riemannian non-convex optimization with adaptive batch size.

Develops a generic two-layer framework for adaptive ABMs.

In most adaptive signal processing applications, system linearity is assumed and adaptive linear filters are thus used. The traditional class of supervised adaptive filters rely on error-correction learning for their adaptive capability. The kernel method is a powerful nonparametric modeling tool for pattern analysis a…

C-ADAM is a new adaptive solver for complex nested problems.

DIVA generates diverse tasks for complex simulators, enabling adaptive agent training.

Adaptive sampling method improves efficiency in complex target distributions.

Adaptive exploration scheme for evaluating multiple policies with different rewards.

We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L_2 regularization: We introduce the γ-adapted-dimension, which is a simple function of the spectrum of a distribution's covariance matrix, and show distribution-specific upper and lower bounds on the s…

A new algorithm estimates mean adaptively to covariance, faster and more flexible than existing methods.

Paper develops an efficient mean estimator for 1-bit communication constraints.

Paper proposes a 1-bit mean estimation method with near-optimal sample complexity.

Proposes a new tensor decomposition method for functional temporal data with adaptive complexity.

New algorithm reduces interventional strategy complexity for causal graph discovery.

Adapts PDE method to prove $L^\infty$ estimates for complex Hessian equations.

In this paper, we investigate a curvature-adapted and proper complex equifocal submanifold in a symmetric space of non-compact type. The class of these submanifolds contains principal orbits of Hermann type actions as homogeneous examples. In future, the results in this paper will be used to give a submanifold geometri…

Sampling from distributions to find the one with the largest mean arises in a broad range of applications, and it can be mathematically modeled as a multi-armed bandit problem in which each distribution is associated with an arm. This paper studies the sample complexity of identifying the best arm (largest mean) in a m…

Adapted metrics found on complex manifolds.

Adaptive approximations improve variational inference for complex models.

In this paper, we give a new construction of the adapted complex structure on a neighborhood of the zero section in the tangent bundle of a compact, real-analytic Riemannian manifold. Motivated by the "complexifier" approach of T. Thiemann as well as certain formulas of V. Guillemin and M. Stenzel, we obtain the polari…

Adaptive algorithm selects models for stochastic linear bandits based on problem complexity.

New MCMC method learns sparse preconditioner for high-dimensional problems.

Let M be a real analytic Riemannian manifold. An adapted complex structure on $TM$ is a complex structure on a neighborhood of the zero section such that the leaves of the Riemann foliation are complex submanifolds. This structure is called entire if it may be extended to the whole of $TM$. We prove here that the only …

Unified analysis of generalization and sample complexity for semi-supervised domain adaptation.

We propose a general framework for studying adaptive regret bounds in the online learning framework, including model selection bounds and data-dependent bounds. Given a data- or model-dependent bound we ask, "Does there exist some algorithm achieving this bound?" We show that modifications to recently introduced sequen…

New method reduces Gibbs partition function estimation complexity.

Study integrability of specific geometric structures on odd Courant algebroids.

Given a complex manifold $M$ equipped with a holomorphic action of a connected complex Lie group $G$, and a holomorphic principal $H$--bundle $E_H$ over $X$ equipped with a $G$--connection $h$, we investigate the connections on the principal $H$--bundle $E_H$ that are (strongly) adapted to $h$. Examples are provided by…

UDN adapts depth to data complexity, outperforming standard neural networks.

We study curvature-adapted submanifolds of general symmetric spaces. We generalize Cartan's theorem for isoparametric hypersurfaces of spheres and Wang's classification of isoparametric Hopf hypersurfaces in complex projective spaces to any compact symmetric space. Our second objective is to investigate such hypersurfa…