Spectral Bounds
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Related Articles from SNS
Measuring Model Robustness via Fisher Information: Spectral Bounds, Theoretical Guarantees, and Practical Algorithms
arXiv:2606.04767v1 Announce Type: new Abstract: The robustness of deep neural networks is crucial for safety-critical deployments, yet existing evaluation methods are often attack-dependent and lack interpretability. We propose a principled, attack-agnostic robustness metric based on the spectral norm of the Fisher Information Matrix (FIM), which quantifies the worst-case sensitivity of the model's output distribution to input perturbations. Theoretically, we establish that the FIM equals...
Adjacency Spectral Radius Under Laplacian Sparsification: Deterministic and Probabilistic Bounds
arXiv:2606.07459v1 Announce Type: cross Abstract: Spielman-Srivastava spectral sparsification preserves Laplacian quadratic forms to within (1 +/- epsilon), but does not directly control the adjacency spectral radius lambda_1, which governs the NIMFA epidemic threshold and arises in spectral clustering. We prove |lambda_1(A_H) - lambda_1(A_G)| <= epsilon(2 Delta - lambda_1) deterministically, with a sharp epsilon*lambda_1 bound for reweighting sparsifiers via Perron-Frobenius monotonicity....
Self-Certifying Transport MCMC via Dual Spectral-Gap Certificates
arXiv:2605.30722v1 Announce Type: new Abstract: We propose CerT-MCMC, a framework that equips learned-transport Markov chain Monte Carlo with automatic, rigorous convergence certificates. A normalising flow maps a Gaussian reference to an approximation of the target posterior; the same flow then serves as both the independence Metropolis-Hastings proposal and the basis for a computable spectral-gap bound. We develop two complementary certificates.
Self-Certifying Transport MCMC via Dual Spectral-Gap Certificates
arXiv:2605.30722v2 Announce Type: replace Abstract: We propose CerT-MCMC, a framework that equips learned-transport Markov chain Monte Carlo with automatic, rigorous convergence certificates. A normalising flow maps a Gaussian reference to an approximation of the target posterior; the same flow then serves as both the independence Metropolis-Hastings proposal and the basis for a computable spectral-gap bound. We develop two complementary certificates.
Non-Vacuous Certification of Transport MCMC via Oscillation-Controlled Normalizing Flows
arXiv:2606.01078v1 Announce Type: new Abstract: Transport MCMC trains a normalizing flow to precondition Metropolis--Hastings proposals, achieving high empirical efficiency on challenging posteriors; yet no prior work produces a numerically non-vacuous, rigorous spectral-gap bound for such samplers. We establish the first such bounds. For independence MH on the banana family we certify (\gamma^\ast = 0.828) at (D = 2) (covering in the original space) and (\gamma^\ast \ge 7.6\times 10^{-4})...
A high-order Fourier Continuation (FC)-based spectral incompressible Smoothed Particle Hydrodynamics (ISPH) scheme for general boundary conditions in wall-bounded domains
arXiv:2606.06247v1 Announce Type: new Abstract: In this paper, a high-order Fourier Continuation (FC) algorithm is introduced into the spectral smoothed particle hydrodynamics (SPH) scheme to simulate the wall-bounded incompressible flows. This work aims to extend the spectral ISPH scheme towards the high-order simulation of flows with non-periodic wall boundary conditions. Herein, a polynomial-based Fourier continuation technique is applied to the velocity and pressure to make the domain...
Flexible FTN-Aided OTFS Modulation for High-Mobility LEO Satellite-to-Ground Communications
arXiv:2601.22526v2 Announce Type: replace Abstract: In low Earth orbit (LEO) satellite communications, the link quality fluctuates drastically during a satellite pass, exhibiting a wide dynamic range from the horizon to the zenith. Moreover, the high relative velocity induces severe Doppler shifts. While orthogonal time frequency space (OTFS) modulation effectively resolves the doubly-selective fading, its spectral efficiency is fundamentally bounded by the Nyquist limit.
Real-Time Sensing of Inaccessible Physical Fields via an Edge-Deployable Hardware-Portable Graph Neural Operator
arXiv:2604.01802v2 Announce Type: replace Abstract: Real-time inference of inaccessible interior physical fields from sparse boundary observations is a fundamental but unresolved problem in scientific machine learning, with direct relevance to safety-critical monitoring across many engineering applications. Existing neural operators achieve high accuracy but leave deployment to embedded edge platforms unaddressed. Here we introduce VIRSO (Virtual Irregular Real-Time Sparse Operator), the...
Spectral density estimation for normal matrices
Announce Type: new Abstract: The spectral density estimation problem asks for an algorithm that, given an $n\times n$ matrix $A$, outputs a probability measure that is a good approximation to the uniform distribution on the eigenvalues of $A$, called the spectral density of $A$. This paper considers the setting where $A$ is a large normal matrix that is accessible only through matrix-vector product queries. We provide an algorithm that makes just $m$ matrix-vector queries to $A$ and returns,...
Learning DNF through Generalized Fourier Representations
arXiv:2506.01075v2 Announce Type: replace Abstract: The Boolean Fourier representation has been widely used in learning theory, particularly for learning Disjunctive Normal Form (DNF) under uniform and product distributions. Extending these results to non-product distributions has remained a longstanding open problem. We address this challenge by introducing a generalized Fourier representation that enables learning under a broad class of non-product distributions.