arXiv research

Bagging stabilizes models without distributional assumptions.

Paper relaxes stability and generalization assumptions for SGD.

Extends Minkowski stability proof to minimal decay assumptions.

New stability framework relaxes boundedness assumptions for generalization bounds.

Extends global stability of Minkowski spacetime to minimal decay assumptions.

Paper proves stability of solutions for specific hyperbolic systems.

Improved MLE for Hawkes Processes stabilizes unstable optimization.

In this short article, we improve the dynamical stability and instability results for Ricci-flat metrics under Ricci flow proved by Sesum and Haslhofer, getting rid of the integrability assumption.

Many of our core assumptions about how neural networks operate remain empirically untested. One common assumption is that convolutional neural networks need to be stable to small translations and deformations to solve image recognition tasks. For many years, this stability was baked into CNN architectures by incorporat…

New methods provide stable ranking without assumptions on data distributions.

We can talk about two kinds of stability of the Ricci flow at Ricci flat metrics. One of them is a linear stability, defined with respect to Perelman's functional $\mathcal{F}$. The other one is a dynamical stability and it refers to a convergence of a Ricci flow starting at any metric in a neighbourhood of a considere…

New findings on stability and Q-conditions for free group actions in hyperbolic spaces.

Differentially Private algorithms often need to select the best amongst many candidate options. Classical works on this selection problem require that the candidates' goodness, measured as a real-valued score function, does not change by much when one person's data changes. In many applications such as hyperparameter o…

Sharp stability in Almgren problem solved in any dimension.

Paper studies stability of generalized Ricci solitons with mathematical rigor.

Study stabilizes Morse-Bott cohomology for equivariant manifolds.

Proves conjecture about sphere widths under rotational symmetry.

New algorithms robustly estimate mean with near-optimal error rates.

In this paper we establish stability of the Ricci de Turck flow near Ricci-flat metrics with isolated conical singularities. More precisely, we construct a Ricci de Turck flow which starts sufficiently close to a Ricci-flat metric with isolated conical singularities and converges to a singular Ricci-flat metric under a…

The Lookahead optimizer improves SGD's performance and generalization without restrictive assumptions.

Stability of positive mass theorem proven under Ricci curvature bounds.

Study fixed angle inverse scattering with Riemannian metrics, proving uniqueness and stability.

We develop efficient algorithms to estimate the stability of Ordinary Least Squares regression results.

Stability of catenoid in 4D Minkowski space proven without symmetry assumptions.

Novel approach ensures stability of compact schemes for variable PDEs.

Third in a series, this paper constructs non-trivial Cayley fibrations with conical singularities.

Random forests are stable and provide reliable prediction intervals.

Recently, many regularized procedures have been proposed for variable selection in linear regression, but their performance depends on the tuning parameter selection. Here a criterion for the tuning parameter selection is proposed, which combines the strength of both stability selection and cross-validation and therefo…

Given a family of groups admitting a braided monoidal structure (satisfying mild assumptions) we construct a family of spaces on which the groups act and whose connectivity yields, via a classical argument of Quillen, homological stability for the family of groups. We show that stability also holds with both polynomial…

Under the assumption of asymptotic relative Chow-stability for polarized algebraic manifolds $(M, L)$, a series of weighted balanced metrics $ω_m$, $m \gg 1$, called polybalanced metrics, are obtained from complete linear systems $|L^m|$ on $M$. Then the asymptotic behavior of the weights as $m \to \infty$ will be stud…

New stability bounds for GD in overparameterised shallow nets without NTK assumptions.

Study shows minimizing the norm of the ERM solution stabilizes kernel ridge-less regression.

Study identifies and validates a method for system identification of Markov jump linear systems.

The present paper provides a new generic strategy leading to non-asymptotic theoretical guarantees on the Leave-one-Out procedure applied to a broad class of learning algorithms. This strategy relies on two main ingredients: the new notion of $L^q$ stability, and the strong use of moment inequalities. $L^q$ stability e…

Wasserstein GAN(WGAN) is a model that minimizes the Wasserstein distance between a data distribution and sample distribution. Recent studies have proposed stabilizing the training process for the WGAN and implementing the Lipschitz constraint. In this study, we prove the local stability of optimizing the simple gradien…

New approach uses 'forward-looking' counterfactuals for treatment choice.

Stability of black holes proven in full subextremal range with positive cosmological constant.

The paper proves LOO CV is reliable under estimator stability.

Away from the central axis, we prove the stability of the Positive Mass Theorem in the $W^{1,p}$ sense for asymptotically flat axisymmetric manifolds with nonnegative scalar curvature satisfying some additional technical assumptions. We also derive estimates for the volumes of regions, the areas of axisymmetric surface…

The paper proves a stability conjecture for manifolds with zero Euler characteristic.

New bounds link SGD's generalization to heavy tails without topological assumptions.

We study a generalized Abreu Equation in $n$-dimensional polytopes and derive interior estimates of solutions under the assumption of the uniform $K$-stability.

Stability of catenoid in hyperbolic space proven without symmetry assumptions.

We study the Abreu's equation in n-dimensional polytopes and derive interior estimates of solutions under the assumption of the uniform K-stability.

We study the stability of partitions involving two or more phases in convex domains under the assumption of at most two-phase contact, thus excluding in particular triple junctions. We present a detailed derivation of the second variation formula with particular attention to the boundary terms, and then study the sign …

New algorithm improves stability of optimization algorithms by adapting step-size.

We study the geometry of stable maximal hypersurfaces in a variety of spacetimes satisfying various physically relevant curvature assumptions, for instance the Timelike Convergence Condition (TCC). We characterize stability when the target space has constant sectional curvature as well as give sufficient conditions on …

In this paper we establish stability results for symmetric spaces of noncompact type under Ricci flow, i.e. we will show that any small perturbation of the symmetric metric is flown back to the original metric under an appropriately rescaled Ricci flow. It will be important for us which smallness assumptions we have to…