Laplace
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Related Articles from SNS
Membership Reference Attack against Laplace Mechanism of Differential Privacy
arXiv:2409.08784v4 Announce Type: replace Abstract: The differential privacy is a widely accepted conception of privacy protection and the Laplace mechanism is a famous instance of differential privacy mechanisms to deal with numerical data. In this paper, we point out that the differential privacy does not take liner property of queries into account, resulting in information leakage. In order to show the information leakage, we construct a membership reference attacks against the Laplace...
A tensor-train multidimensional inverse Laplace transform
arXiv:2606.06093v1 Announce Type: new Abstract: Laplace transforms and their numerical inverses arise throughout applied mathematics, physics, finance, and probability theory. Numerical inversion, however, quickly becomes intractable in high dimensions because the number of quadrature evaluations grows exponentially with dimension. We develop a tensor train (TT) formulation of the multidimensional inverse Laplace transform.
A tensor-train multidimensional inverse Laplace transform
arXiv:2606.06093v1 Announce Type: cross Abstract: Laplace transforms and their numerical inverses arise throughout applied mathematics, physics, finance, and probability theory. Numerical inversion, however, quickly becomes intractable in high dimensions because the number of quadrature evaluations grows exponentially with dimension. We develop a tensor train (TT) formulation of the multidimensional inverse Laplace transform.
Latent Laplace Diffusion for Irregular Multivariate Time Series
arXiv:2605.19805v2 Announce Type: replace Abstract: Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift. To bridge this gap, we present Latent Laplace Diffusion (LLapDiff), a generative framework that models the target as a low-dimensional latent trajectory, enabling horizon-wide generation without step-by-step...
A Mixed Virtual Element Method for the p-Laplace equation
arXiv:2606.07477v1 Announce Type: new Abstract: We introduce and analyze a mixed Virtual Element Method for the $p$-Laplace equation in a non-Hilbertian setting, covering the full range $p \in (1, \infty)$. The discrete framework combines standard mixed Virtual Element spaces with a novel non-linear stabilization term designed to mimic the power-law structure of the continuous operator. We establish discrete inf-sup stability under non-Hilbertian norms and rigorously prove the continuity and...
Solver-in-the-Loop joint operator learning: fractional Laplace-Beltrami features for interface reconstruction
arXiv:2411.05341v2 Announce Type: replace Abstract: In this work, we propose a joint operator learning method for reconstructing images of conductivity coefficients from boundary data. Inspired by the idea of employing partial differential equation (PDE) solvers as preconditioners for this inverse problem, we investigate a ``solver-in-the-loop'' training mechanism. It allows the interaction of learnable parameters integrated in a PDE solver module and those in neural networks for...
Sinkhorn Normalization of Diffusion Kernels
arXiv:2507.06161v2 Announce Type: replace Abstract: Smoothing a signal based on local neighborhoods is a core operation in machine learning and geometry processing. On well-structured domains such as vector spaces and manifolds, the Laplace operator derived from differential geometry offers a principled approach to smoothing via heat diffusion, with strong theoretical guarantees. However, constructing such Laplacians requires a carefully defined domain structure, which is not always available.
Traveling surface wave propagation on shallow water with variable bathymetry and current
Announce Type: replace Abstract: Energy transmission over long distances by waves is a key mechanism for many natural processes. This possibility arises when an inhomogeneous medium is arranged in such a manner that it enables a certain type of wave to propagate with virtually no reflection or scattering. By application of the Laplace cascade method for integrating second-order hyperbolic equations, a general algorithm for finding the parameters of inhomogeneous non-reflecting flows is proposed.
Instance-Level Post Hoc Uncertainty Quantification in Object Detection
Announce Type: new Abstract: Object detection is a safety-critical component of autonomous driving. It is essential to quantify the uncertainty in bounding-box predictions for safety assurance. Post hoc uncertainty quantification without retraining aligns with real-world deployment requirements; therefore, we employ the Laplace approximation.
Simultaneous recovery of multiple parameters in nonlocal diffusion equations from internal measurements
Announce Type: new Abstract: This paper is devoted to simultaneously recovering multiple parameters from internal measurements for nonlocal diffusion equations. The uniqueness of the inverse problem is established by employing the asymptotic behavior of solutions, analytic continuation, the Laplace transform, and properties of analytic functions. For numerical reconstruction, we apply the Levenberg-Marquardt method to obtain a stable approximate solution of the inverse problem.