The study introduces a new function to analyze special holonomy manifolds.
problem Analyzing harmonic forms on special holonomy manifolds.
method Introducing a global perturbation potential function and studying its effects on harmonic forms.
result Established vanishing theorems on L2 harmonic forms under certain conditions. Graph cuts find global optima for Potts models in slight perturbations.
problem Finding optimal solutions in Potts models with graph cuts.
method α-expansion algorithm for MAP inference, with certification for perturbations.
result All local minima are global minima in slight perturbations, and solutions are close to original.
Global existence and geometry of constant mass aspect function foliation in perturbed Schwarzschild spacetime studied.
problem Null Penrose inequality on a null hypersurface.
method Global existence of constant mass aspect function foliation on a nearly spherically symmetric incoming null hypersurface in a vacuum perturbed Schwarzschild spacetime.
result Geometry of the constant mass aspect function foliation compared to the spherically symmetric foliation in the Schwarzschild spacetime.
String geometry theory connects strings to space-time and finds string vacua.
problem Identify and find the global minimum of the string vacuum.
method Identify perturbative vacua, derive path-integrals, and solve the global minimum using analytical and numerical methods.
result The global minimum of the effective potential is the string vacuum.
SAMS-VAE models cellular perturbations using sparse additive mechanisms.
problem Modeling effects of diverse interventions on cells.
method Sparse Additive Mechanism Shift Variational Autoencoder (SAMS-VAE).
result SAMS-VAE identifies disentangled, perturbation-specific latent subspaces.
In this paper we prove the Penrose inequality for metrics that are small perturbations of the Schwarzschild anti-de Sitter metrics of positive mass. We use the existence of a global foliation by weakly stable constant mean curvature spheres and the monotonicity of the Hawking mass.
SGD converges to global minimum for certain non-convex functions.
problem Theoretical challenges in optimizing non-convex functions in machine learning.
method Perturbed SGD on a broad class of non-convex functions.
result SGD converges to global minimum for certain non-convex functions.
Groups' boundary actions are stable under small perturbations.
problem Stability of group actions on their boundaries.
method Proving semi-conjugacy of perturbed actions to the standard action.
result Perturbed actions are globally semi-conjugate to the standard action.
Researchers found infinite links with specific bridge positions.
problem Finding links with minimal bridge positions.
method Applying Takao et al.'s criterion to create links with locally minimal n-bridge and globally minimal m-bridge positions. result Provided an infinite family of links with specific bridge positions.
A new SSL method improves medical image classification using global latent mixing.
problem Costly annotation of large-scale medical image data sets.
method Linear mixing of labeled and unlabeled data in both input and latent space.
result Improved performance in semi-supervised classification of thoracic disease and skin lesion.
The paper studies the Heath-Jarrow-Morton-Musiela equation of the bond market. The equation is analyzed in weighted spaces of functions defined on [0,+∞). Sufficient conditions for local and global existence are obtained . For equation with the linear diffusion term the conditions for global existence are close …
Mixup inference improves adversarial robustness by mixing inputs with clean samples.
problem Adversarial examples can fool deep networks due to local non-linearity.
method Develops mixup inference, which mixes inputs with clean samples to shrink adversarial perturbations.
result Mixup inference enhances adversarial robustness for mixup-trained models.
The restricted planar three-body problem has a rich history, yet many unanswered questions still remain. In the present paper we prove the existence of a global surface of section near the smaller body in a new range of energies and mass ratios for which the Hill's region still has three connected components. The appro…
Study shows adversarial robustness and common perturbation robustness are independent.
problem Understanding the relationship between adversarial robustness and common perturbation robustness in neural networks.
method Conducted experiments to benchmark neural network robustness to common perturbations and adversarial examples.
result Adversarial robustness and common perturbation robustness are independent attributes.
Bayesian optimisation generates saliency maps for black-box models.
problem Generating saliency maps for models without access to parameters.
method Bayesian optimisation sampling method to find global salient regions.
result Approach outperforms grid-based methods and performs similarly to gradient-based methods.
New algorithm optimizes robust estimation under mixed local and global corruptions.
problem Combining local and global corruptions in robust statistics.
method Information-theoretic approach using sliced-Wasserstein metric.
result Optimal error achieved in polynomial time for stronger local perturbations.
The study finds regular null hypersurfaces in a perturbed Schwarzschild black hole exterior.
problem Existence of regular null hypersurfaces in a perturbed Schwarzschild black hole.
method Proof of existence for null hypersurfaces in a perturbed Schwarzschild spacetime.
result Existence of many foliations by regular null hypersurfaces in the exterior region of a perturbed Schwarzschild black hole.
This study proposes an approach based on a perturbation technique to construct global solutions to dynamic stochastic general equilibrium models (DSGE). The main idea is to expand a solution in a series of powers of a small parameter scaling the uncertainty in the economy around a solution to the deterministic model, i…
WSFN overcomes saddle points for non-convex functionals in Wasserstein space.
problem Minimizing non-convex functionals over the Wasserstein space with saddle point avoidance.
method WSFN is a second-order method that preconditions the Wasserstein gradient to avoid saddle points.
result WSFN escapes saddle regions and reaches a global minimizer in polynomial time.
Generic smooth minimal hypersurfaces exist in 8D manifolds.
problem Existence of smooth minimal hypersurfaces in high-dimensional manifolds.
method Global perturbation argument and a novel geometric invariant.
result Generic metrics on 8D manifolds admit smooth minimal hypersurfaces.
SAM optimizer struggles to converge to global minima or stationary points in practical settings.
problem Limited convergence of SAM optimizer to global minima or stationary points in practical scenarios.
method Deterministic and stochastic versions of SAM with constant perturbation size and gradient normalization were studied.
result SAM has limited capability to converge to global minima or stationary points in many scenarios.
This paper provides a coopetitive model for a global green economy, taking into account the environmental sustainability. In particular, we propose a differentiable coopetitive game G (in the sense recently introduced by D. Carf`ı) to represent a global green economy interaction, among a country c and the rest of the w…
Einstein manifolds are rigid under certain metric deformations.
problem Characterizing Einstein manifolds that resist volume-preserving metric deformations.
method Various characterizations and constructions of mass-decreasing perturbations.
result Constructs mass-decreasing perturbations of specific metrics.
Introduces a new geometric framework for non-perturbative BV-theory.
problem Non-perturbative generalization of BV-theory in infinite-dimensional spaces.
method Derived differential geometry and homotopical algebraic geometry.
result Concrete model of derived smooth stacks for encoding non-perturbative BV-theory.
We derive a system of equations governing the coupled gravitational and electromagnetic perturbations of Reissner-Nordström spacetime. The equations are derived in the context of global non-linear stability of Reissner-Nordström under axially symmetric polarized perturbations, as a generalization of the recent work on …
Noise helps neural networks escape local optima.
problem Understanding the role of noise in neural network training.
method Perturbed gradient descent and noise annealing.
result Noise guarantees convergence to global optimum in polynomial time.
Study robustness of global feature effect explanations in machine learning models.
problem Vulnerability of global feature effect explanations to data and model perturbations.
method Theoretical bounds and experimental evaluation of partial dependence plots and accumulated local effects.
result Quantifies the gap between best and worst-case scenarios of misinterpreting machine learning predictions globally.
DEKF maintains stability in LSTM learning with bounded perturbations.
problem Stability of DEKF in LSTM-based online learning.
method Modeling DEKF as a perturbed extended Kalman filter and deriving stability conditions.
result DEKF learns LSTM parameters with similar stability properties to the global extended Kalman filter.
Stability of Minkowski space-time in higher dimensions proven for arbitrary small perturbations.
problem Stability of Minkowski space-time solution to Einstein-Yang-Mills equations in higher dimensions.
method Global stability proof for arbitrary small perturbations using wave coordinates and gauge invariant norms.
result Global stability of Minkowski space-time in higher dimensions n≥5 for arbitrary small perturbations. We study the determination of the second-order normal form for perturbed Hamiltonians Hε=H0+εH1+2ε2H2, relative to the periodic flow of the unperturbed Hamiltonian H0. The formalism presented here is global, and can be easily implemented in any CAS. We illustrate it by means of two examples: the H…
In this paper we prove a global existence theorem, in the direction of cosmological expansion, for sufficiently small perturbations of a family of n+1-dimensional, n≥3, spatially compact spacetimes which generalizes the k=−1 Friedmann--Robertson--Walker vacuum spacetime. Our results demonstrate causal geodes…
We address some global solvability issues for classes of smooth nonsingular vector fields L in the plane related to cohomological equations Lu=f in geometry and dynamical systems. The first main result is that L is not surjective in C∞(R2) iff the geometrical condition -- the existence of separatrix str…
Study perturbs mean curvature flow near non-spherical shrinkers.
problem Understanding the dynamics near non-spherical shrinkers under mean curvature flow.
method Invariant manifold theory from hyperbolic dynamics.
result Generic perturbation makes flow leave a neighborhood of non-spherical shrinkers.
Self-similar solutions to geometric flows are stable under small perturbations.
problem Stability of self-similar solutions in geometric flows.
method Global analytic solutions, compactness arguments, spatial equi-decay properties, and estimates of linearized operator.
result Perturbed solutions are asymptotically self-similar as time tends to infinity.
Singular fiber resolution does not describe the spontaneous breaking of gauge symmetry in F-theory, as the corresponding branch of the moduli space does not exist in the theory. Accordingly, even non-abelian gauge theories have not been fully understood in global F-theory compactifications. We present a systematic disc…
Deep learning detects cloud changes due to human aerosols.
problem Uncertainty in the effect of anthropogenic aerosols on cloud properties and Earth's energy balance.
method Deep convolutional neural networks to analyze cloud images.
result Identified and characterized specific cloud perturbations due to human aerosols.
Enhanced image recognition models learn from human-like memory and shape biases.
problem Improving robustness of image recognition models against various perturbations.
method Integrating human-like episodic memory and shape bias features into image recognition models.
result Combining human-like features improves robustness against both adversarial and natural perturbations.
We give a complete framework for the Gupta-Bleuler quantization of the free electromagnetic field on globally hyperbolic space-times. We describe one-particle structures that give rise to states satisfying the microlocal spectrum condition. The field algebras in the so-called Gupta-Bleuler representations satisfy the t…
This work introduces new ways to compare adversarial robustness of classifiers globally.
problem The limitations of point-wise measures in comparing adversarial robustness.
method Robustness curves and scale analysis to uncover global properties of robustness.
result Point-wise measures fail to capture important global properties of adversarial robustness.
This paper contains the second part of a two-part series on the stability and instability of extreme Reissner-Nordstrom spacetimes for linear scalar perturbations. We continue our study of solutions to the linear wave equation on a suitable globally hyperbolic subset of such a spacetime, arising from regular initial da…
We study the problem of stability and instability of extreme Reissner-Nordstrom spacetimes for linear scalar perturbations. Specifically, we consider solutions to the linear wave equation on a suitable globally hyperbolic subset of such a spacetime, arising from regular initial data prescribed on a Cauchy hypersurface …
Study of regularized least squares in RKKS with indefinite kernels.
problem Asymptotic properties of regularized least squares with indefinite kernels in RKKS.
method Introducing a bounded hyper-sphere constraint, theoretical demonstration of globally optimal solution, modified error decomposition techniques, matrix perturbation theory.
result Derivation of learning rates in RKKS, same as RKHS under certain conditions.
New framework assesses neural sensitivity to small perturbations.
problem Comparing neural representations' sensitivity to small changes.
method Local decodable information, Fisher information, and projected pullback/Fisher metric.
result Reveals differences in neural sensitivity not captured by activation alignment.
Study vector fields with complex singularities, proving bounds and formulas.
problem Understanding the Milnor number of vector fields with specific singularities.
method Global and local formulas expressing Milnor/Poincare-Hopf contributions, sharp lower bounds under perturbations.
result Sharp lower bounds for Milnor number contributions under holomorphic perturbations.
New proof shows perturbed non-compact Einstein spaces attract to unique global solution.
problem Proving global solutions for perturbed non-compact negative Einstein spaces.
method Developed energy estimates for a hyperbolic system of Maxwell type.
result Global unique solution for perturbed non-compact negative Einstein spaces.
Stability of singularity formation in Yang-Mills fields in higher dimensions.
problem Stability of self-similar blowup profiles for Yang-Mills equations in (1+d)-dimensions. method Analysis of explicitly known equivariant self-similar blowup solution and small equivariant perturbations.
result Global-in-space asymptotic stability of the self-similar blowup solution for Yang-Mills equations in (1+d)-dimensions for d≥5. We are focusing on bound constrained global optimization problems, whose objective functions are computationally expensive black-box functions and have multiple local minima. The recently popular Metric Stochastic Response Surface (MSRS) algorithm proposed by \cite{Regis2007SRBF} based on adaptive or sequential learnin…
The Piyavskii-Shubert algorithm is analyzed for global optimization of Lipschitz functions.
problem Maximizing a non-concave Lipschitz function over a compact domain.
method Sequential function evaluations using a bandit-optimization approach.
result New bounds on the number of evaluations needed for optimization accuracy.