Study shows minimizing the norm of the ERM solution stabilizes kernel ridge-less regression.
problem Stability of kernel ridge-less regression.
method Minimizing the norm of the ERM solution to minimize CV stability.
result Interpolating solution with minimum norm minimizes CV stability.
We obtain several results about stability of the Bergman kernel on a tower of coverings on complex manifolds. An effective version of Rhodes' result is given for a tower of coverings on a compact Riemann surface of genus greater than or equal to 2. Stability of the Bergman kernel is established for towers of coverings …
Kernel networks' stability edge linked to Fisher Information singularity.
problem Understanding the stability edge in high-capacity kernel Hopfield networks.
method Statistical manifold analysis and Riemannian geometry.
result The Ridge of Optimization corresponds to the Edge of Stability, revealing a dual equilibrium.
Paper proves non-equivalence of RKHS stability and kernel absolute summability.
problem Equivalence of RKHS stability and kernel absolute summability.
method Analyzes Reproducing Kernel Hilbert spaces and positive semidefinite kernels.
result Stable RKHSs can be induced by non-absolutely summable kernels.
Study on reducing dimensionality in high-dimensional regression with kernel methods and stability analysis.
problem Analyzing errors in high-dimensional regression with dimensionality reduction and kernel regression.
method Derive a stability result for kernel regression with Wasserstein distance and apply it to PCA to deduce convergence rates.
result Two-step procedure yields useful convergence rates in semi-supervised settings.
The paper explores identifiability and stability in drifting fields using companion-elliptic kernels.
problem Identifying and stabilizing drifting fields in generative modeling.
method Introduces companion-elliptic kernel families and analyzes their properties to address identifiability and stability issues.
result Established field identifiability for arbitrary Borel probability measures and demonstrated that field convergence alone does not guarantee weak convergence.
Paper studies identifiability and stability of drifting fields in generative modeling.
problem Identify and stabilize drifting fields in generative modeling.
method Introduces companion-elliptic kernel families to address limitations of Laplace kernel.
result Establishes field identifiability and demonstrates scalar observables for weak convergence.
Study on stability of 3D sessile drops, identifying degenerate kernel.
problem Linear stability of three-dimensional sessile drops with a free contact line.
method Derived constrained second variation, formulated Jacobi problem, combined geometric and Fourier analysis.
result Kernel of the constrained Jacobi operator is exactly the space of horizontal translations under pressure-volume nondegeneracy.
We study the stability properties of nonlinear multi-task regression in reproducing Hilbert spaces with operator-valued kernels. Such kernels, a.k.a. multi-task kernels, are appropriate for learning prob- lems with nonscalar outputs like multi-task learning and structured out- put prediction. We show that multi-task ke…
Study proves existence, uniqueness, and stability for specific stochastic Volterra equations.
problem Analyzing existence, uniqueness, and stability of affine stochastic Volterra equations with L1-kernels. method Approximations with L2-kernels, stability result, duality argument, deterministic Riccati--Volterra integral equation. result Established weak uniqueness for the equations using Fourier--Laplace transform and a deterministic Riccati--Volterra integral equation.
Kernel-guided training stabilizes GANs by controlling discrepancies.
problem Stability and interpretability issues in GANs.
method Kernel-based regularization to control discrepancies in GAN loss function.
result Theoretical guarantees on stability of the training dynamics.
Kernel-guided training stabilizes GANs by controlling discrepancies.
problem Stability and interpretability issues in GANs.
method Kernel-based regularization to control discrepancies in GAN loss function.
result Theoretical guarantees on stability of the training dynamics.
New activation functions improve neural network stability and generalize well.
problem Proving theoretical generalization of non-parametric activation functions.
method Stability analysis of non-convex models trained with SGD.
result Neural networks with kernel activation functions generalize well with SGD.
Study shows how to reduce data needed for learning under geometric constraints.
problem Learning high-dimensional data with geometric priors.
method Spherical harmonic decompositions and kernel methods for invariance and geometric stability.
result Improvements in sample complexity by leveraging group invariance, with asymptotic behavior depending on spectral properties.
The paper proves LOO CV is reliable under estimator stability.
problem Ensuring the reliability of leave-one-out cross validation.
method Using concentration inequalities based on logarithmic Sobolev inequality.
result LOO CV is a valid procedure under estimator stability.
Study the inductive bias of neural networks using neural tangent kernels.
problem Understanding the generalization properties of over-parameterized neural networks.
method Analysis of the neural tangent kernel and its corresponding function space (RKHS).
result Stability properties of functions with finite norm, including stability to image deformations in convolutional networks.
A novel Bayesian computation method using importance weighting improves numerical stability and performance.
problem Bayesian computation stability and performance issues.
method Nonparametric approach via feature means, importance weighting, and kernel Bayes' rule.
result Importance weighted kernel Bayes' rule yields superior numerical stability and performance.
In this paper we measured the stability of stochastic gradient method (SGM) for learning an approximated Fourier primal support vector machine. The stability of an algorithm is considered by measuring the generalization error in terms of the absolute difference between the test and the training error. Our problem is to…
In this paper, improving a preceding work, we obtain asymptotic polybalanced kernels associated to extremal Kaehler metrics on polarized algebraic manifolds. As a corollary, we have a stronger asymptotic relative Chow-polystability for extremal Kaehler polarized algebraic manifolds. Finally, related to the Yau-Tian-Don…
The study analyzes prediction errors in systems with memory kernels, providing bounds and stability results.
problem Prediction errors in stochastic dynamical systems with memory kernels.
method Analysis of generalized Langevin equations (GLEs) with Volterra equations, integrating synchronized noise coupling and weighted norms.
result Prediction discrepancies decay at a rate determined by the memory kernel's decay, quantitatively bounded by kernel estimation errors.
Improved MLE for Hawkes Processes stabilizes unstable optimization.
problem Unstable Maximum Likelihood Estimation (MLE) for Hawkes Processes.
method Simple stabilization procedure to improve MLE without restrictive assumptions.
result Stabilized MLE outperforms traditional methods over various sequence lengths.
The success of deep convolutional architectures is often attributed in part to their ability to learn multiscale and invariant representations of natural signals. However, a precise study of these properties and how they affect learning guarantees is still missing. In this paper, we consider deep convolutional represen…
Quantum kernels show no advantage in stock return prediction, but differ in stability metrics.
problem Determining if quantum kernels improve stock return prediction.
method Controlled horse race on Chinese A-share market with identical training subsamples and tuning budgets.
result Quantum kernels do not outperform classical RBF controls in cross-sectional stock return prediction.
Unified kernel framework extends to stochastic systems, improving numerical stability.
problem Extending kernel methods to stochastic dynamical systems with diffusion.
method Unified kernel framework, Feynman-Kac path-integral representations, collocation-based computational framework.
result Kernel equivalence under uniform ellipticity assumptions and improved numerical stability with moderate diffusion.
New mathematical foundations for stable RKHSs improve system identification.
problem Improving stability tests and modeling of impulse responses.
method Providing new structural properties and stability conditions for stable RKHSs.
result Any stable kernel admits feature maps induced by orthogonal eigenvectors in l2.
New Hida-Matérn kernels enable flexible process priors and efficient GP inference.
problem Flexible modeling of stationary processes with oscillatory components.
method Introducing a new class of covariance functions (Hida-Matérn kernels) and their state space representations.
result Efficient Gaussian Process inference and improved numerical stability.
This work improves GAN stability with theoretical conditions.
problem GANs exhibit unstable behavior during training.
method Developed a theoretical framework and conditions for GAN stability.
result Constructs a GAN that fulfills stability conditions.
Investigates O(n)-invariant metrics on SPD matrices, extending kernel metrics.
problem Limited coverage of O(n)-invariant metrics by kernel metrics.
method Characterization of O(n)-invariant metrics, intermediate classes construction.
result Introduction of cometric-stability as a key property for geodesics.
The choice of the kernel is critical to the success of many learning algorithms but it is typically left to the user. Instead, the training data can be used to learn the kernel by selecting it out of a given family, such as that of non-negative linear combinations of p base kernels, constrained by a trace or L1 regular…
Study on learning properties of scale-dependent kernels controlling stability and error.
problem Understanding the learning properties of scale-dependent kernels in nonparametric ridge-less least squares.
method Combines probabilistic results with interpolation theory to analyze stability and error.
result Different regimes of learning error depending on sample size and data dimension.
New method bounds singular values of convolutional kernels to stabilize gradients.
problem Stable gradients in convolutional neural networks.
method Frobenius norm regularization for convolutional kernels.
result Bounded singular values of transformation matrices.
New insights on stability in reservoir computing for better performance.
problem Stability in reservoir computing networks.
method Using the recurrent kernel limit for large reservoir sizes.
result Quantitative characterization of stability and chaos frontier.
Invariant kernels reduce rank and improve generalization across dimensions.
problem Symmetry in high-dimensional data impacts kernel matrix rank and learning algorithms.
method Compute invariant polynomial kernel ranks under various groups acting on data.
result Symmetry decreases kernel rank, making it independent of data dimension.
We give a condition which ensures that the Paneitz operator of an embedded three-dimensional CR manifold is nonnegative and has kernel consisting only of the CR pluriharmonic functions. Our condition requires uniform positivity of the Webster scalar curvature and the stability of the CR pluriharmonic functions for a re…
The paper derives uniform stability-based coverage bounds for conformal prediction methods.
problem Establishing theoretical guarantees for conformal prediction methods.
method Uniform stability perspective applied to full-conformal, jackknife+, and CV+ prediction regions.
result Coverage bounds for finite-dimensional models derived using a concentration argument.
Develops a new theory for neural systems stability and width effects.
problem Stability and finite-width effects in deep neural systems.
method Gauge-covariant stochastic effective field theory using classical commuting fields.
result Predicts the edge of chaos and low-frequency spectral deformation.
Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they are routinely used to describe topological properties of complicated shapes. PDs enjoy strong stability properties and have proven their utility in various learning contexts. They do not, however, live in a space naturally endo…
Proteins are commonly used by biochemical industry for numerous processes. Refining these proteins' properties via mutations causes stability effects as well. Accurate computational method to predict how mutations affect protein stability are necessary to facilitate efficient protein design. However, accuracy of predic…
Let M be a complete non-compact Riemannian manifold. In this paper, we derive sufficient conditions on metric perturbation for stability of Lp-boundedness of the Riesz transform, p∈(2,∞). We also provide counter-examples regarding in-stability for Lp-boundedness of Riesz transform.
This study analyzes convergence and stability of reinforcement learning algorithms.
problem Understanding the conditions under which reinforcement learning algorithms converge and remain stable.
method Theoretical analysis of convergence and stability of Episodic Upside-Down Reinforcement Learning, Goal-Conditioned Supervised Learning, and Online Decision Transformers.
result The algorithms can achieve near-optimal behavior if the transition kernel is close to a deterministic kernel.
ULFS-KDPE estimates parameters efficiently without influence functions.
problem Estimating pathwise differentiable parameters in nonparametric models.
method Kernel debiased plug-in estimator based on universal least favorable submodel.
result Semiparametric efficiency achieved without influence function derivation.
New random feature maps for Laplacian and related kernels.
problem Challenges in approximating the Laplacian kernel and its generalizations.
method Developed random feature maps for Laplacian and related kernels, providing efficient sampling schemes.
result Demonstrated the efficacy of these random feature maps on real datasets.
RNNs are reinterpreted as kernel methods using neural ODEs.
problem Improving generalization and stability of RNNs.
method Connecting RNNs to neural ODEs and reproducing kernel Hilbert spaces.
result RNNs can be viewed as linear functions of a specific feature set.
Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persist…
New method simplifies tomographic reconstruction using RKHS.
problem Tomographic reconstruction challenges.
method RKHS framework for X-ray transform.
result Sharp stability results without Fourier transform.
Wider networks improve natural accuracy but worsen perturbation stability, affecting overall robustness.
problem Understanding the tradeoff between natural accuracy and perturbation stability in wider neural networks for adversarial robustness.
method Careful examination of the relationship between network width, robust regularization parameter λ, and perturbation stability using neural tangent kernels.
result Wider networks can achieve better natural accuracy but worse perturbation stability, leading to potentially worse overall model robustness.
We prove Gray--Moser stability theorems for complementary pairs of forms of constant class defining symplectic pairs, contact-symplectic pairs and contact pairs. We also consider the case of contact-symplectic and contact-contact structures, in which the constant class condition on a one-form is replaced by the conditi…
This paper is a sequel to \cite{Xu}. In this paper, an estimation of the Bergman Kernel of Kähler hyperbolic manifold is given by the L2 estimate and the Bochner formula. As an application, an effective criterion of the very ampleness of the canonical line bundle of Kähler hyperbolic manifold is given, which is a ge…