Efficiently optimizes expensive functions in parallel.
problem Optimizing expensive, derivative-free functions efficiently.
method Stochastic approximation and infinitessimal perturbation analysis.
result Method finds high-quality solutions faster than alternatives.
DBPA assesses LLM perturbations using frequentist hypothesis testing.
problem Quantifying input perturbation impacts on LLM outputs.
method DBPA reformulates perturbation analysis as frequentist hypothesis testing, using Monte Carlo sampling for empirical null and alternative distributions.
result DBPA provides interpretable p-values and scalar effect sizes for LLM perturbations.
The paper introduces extremal perturbations for better attribution analysis in deep networks.
problem Identifying input parts responsible for model outputs.
method Extremal perturbations, smooth masks, and technical innovations for computation.
result Demonstrates excellent sensitivity to spatial properties of deep neural networks.
Unified framework for nuclear reactor perturbation analysis using CNN and LSTM.
problem Monitoring reactor cores for safety and perturbation identification.
method 3D-CNN and LSTM networks for frequency and time domain analysis, respectively.
result High accuracy in recognising perturbation type and precise source localisation in frequency domain.
New analysis shows how deep networks are vulnerable to small, image-agnostic perturbations.
problem Vulnerability of deep networks to small, image-agnostic perturbations.
method Quantitative analysis linking robustness to geometry of decision boundaries.
result Deep networks are vulnerable to small perturbations along positively curved decision boundaries.
New spectral analysis improves clustering in sparse graphs.
problem Improving classical matrix perturbation results for eigenvectors.
method New perturbation bounds considering the nature of perturbations.
result Simple clustering algorithm recovers communities in sparse graphs.
Improved online Lasso reduces regret in sparse linear contextual bandits.
problem Sparse linear contextual bandit problem with inefficient sampling.
method Perturbed adversary approach to alleviate sampling inefficiency.
result Online Lasso achieves O ( k T log d ) \mathcal{O}(\sqrt{kT\log d}) O ( k T log d ) regret bound. Unified analysis of perturbation-based strategies in stochastic and adversarial bandit problems.
problem Optimality of perturbation-based strategies in multi-armed bandit problems.
method Unified regret analysis for stochastic and adversarial settings, using perturbations of sub-Weibull and bounded support.
result Unified bounds for perturbations in both stochastic and adversarial settings, with optimal perturbations of Frechet-type.
Study analyzes perturbations in singular subspaces under random noise.
problem Understanding singular vector and subspace changes in signal-plus-noise models.
method Generalized Davis-Kahan-Wedin theorem for any unitarily invariant norm, considering ℓ ∞ \ell_\infty ℓ ∞ and ℓ 2 , ∞ \ell_{2,\infty} ℓ 2 , ∞ bounds. result Fine-grained insights into singular vector and subspace perturbations, including ℓ ∞ \ell_\infty ℓ ∞ and ℓ 2 , ∞ \ell_{2,\infty} ℓ 2 , ∞ bounds. This study benchmarks transcriptomics models for perturbation analysis, finding scVI and PCA superior.
problem Limited evaluation of transcriptomics foundation models for perturbation analysis.
method Developed a novel evaluation framework using diverse public datasets from different sequencing techniques and cell lines.
result scVI and PCA identified as superior models for understanding biological perturbations.
New method proves inequalities for self-shrinkers using perturbation.
problem Proving Łojasiewicz inequalities for self-shrinkers.
method Perturbative analysis of a new auxiliary quantity.
result New method interpolates between higher order and differential geometric approaches.
Framework for generating adversarial examples from learning algorithms.
problem Adversarial perturbations leading to erroneous classification.
method Perturbation analysis framework based on convex programming.
result Closed-form solutions for new adversarial attacks.
Novel method measures DNN sensitivity to perturbations.
problem Vulnerability of DNNs to adversarial examples.
method Perturbation manifold and influence measure.
result Demonstrated usefulness for model building tasks.
Study magnetic perturbations in Riemannian and Lorentzian Calderón problems.
problem Determining metrics from boundary measurements under magnetic perturbations.
method Runge approximation for Riemannian case, microlocal analysis for Lorentzian case.
result Metrics can be uniquely determined in both Riemannian and Lorentzian cases under specific perturbations.
Study reveals class-dependent effects in perturbation-based feature attribution metrics for time series classification.
problem Varying effectiveness of perturbation-based metrics across different classes in time series models.
method Systematic empirical analysis across multiple datasets, model architectures, and perturbation strategies.
result Perturbation-based metrics show varying effectiveness across classes, with some metrics performing better for certain classes.
BioBO optimizes gene perturbation design using Bayesian optimization with biological priors.
problem Efficient design of genomic perturbation experiments in drug discovery.
method Integrates Bayesian optimization with multimodal gene embeddings and enrichment analysis.
result Improves labeling efficiency by 25-40% and identifies top-performing perturbations more effectively.
SGD converges with perturbed forward-backward passes, explained by geometric amplification.
problem Analyzing convergence of SGD with perturbed forward-backward passes in composite optimization.
method Characterized propagation and amplification of perturbations, derived convergence guarantees for non-convex and PL objectives.
result Perturbations cascade through the computational graph, affecting convergence order under specific conditions.
PAC-Bayesian bounds estimate adversarial robustness.
problem Estimating robustness to imperceptible input perturbations.
method PAC-Bayesian framework for averaging over hypotheses.
result General bounds valid for any type of adversarial attacks.
Study metric perturbations to make degenerate harmonic forms non-degenerate.
problem Dealing with degenerate harmonic 1-forms in Riemannian geometry.
method Combining analysis of local expansions with Nash-Moser implicit function theorem.
result Proves deformation to nearby non-degenerate Z/2-harmonic 1-forms.
Paper addresses eigenvector perturbation in small eigen-gap scenarios.
problem Fine-grained behavior of eigenvectors in the presence of small eigen-gaps.
method Develops de-biased estimators for linear functions of an unknown eigenvector.
result Achieves minimax lower bounds for a family of scenarios, even with small eigen-gaps.
Automates perturbation analysis for neural networks, enabling certified robustness on complex architectures.
problem Limited applicability of existing perturbation analysis methods to complex neural network architectures.
method Developed an automatic framework to generalize LiRPA algorithms to any neural network structure, enabling loss fusion and state-of-the-art certified defense results.
result Demonstrated LiRPA based certified defense on Tiny ImageNet and Downscaled ImageNet.
Study stability of contingent claim solutions under probabilistic perturbations.
problem Stability of solutions to discrete-time contingent-claim problems under uncertainty.
method Use Rockafellian perturbations to analyze stability of solutions.
result Establishes convergence of dual problems and shadow prices.
Paper analyzes GCNN sensitivity to probabilistic graph perturbations.
problem Investigating how GCNNs handle probabilistic graph errors.
method Establishes error bounds and linear relationships between GSO perturbations and GCNN outputs.
result GCNNs maintain stability under graph edge perturbations if GSO errors are bounded.
Residual networks analyzed using linearization for stability under perturbations.
problem Understanding the behavior of residual networks under small input perturbations.
method Linearization of residual units and network stages, using singular value decomposition for stability analysis.
result Most singular values of residual units are 1, but scaling and weights significantly affect them.
Paper develops robust estimators and strategies for stochastic MABs with heavy-tailed rewards.
problem Stochastic multi-armed bandits with heavy-tailed rewards.
method Proposes a novel robust estimator and perturbation-based exploration strategy.
result Develops upper and lower regret bounds for various perturbations.
Resurgence analysis of S U ( 2 ) SU(2) S U ( 2 ) Chern-Simons on a specific homology sphere.
problem Analyzing the resurgence of a specific Chern-Simons partition function.
method Borel resummation of the perturbative expansion of an exact partition function.
result Resurgence analysis reveals new insights into the partition function.
PerturBench benchmarks ML models for cellular perturbation analysis.
problem Standardizing benchmarking in modeling single cell transcriptomic responses to perturbations.
method Modular platform, diverse datasets, metrics, extensive evaluation, rank metrics.
result Simpler models are competitive and scale well with larger datasets.
Improved perturbation reduces matrix condition number to O(n) with minimal storage.
problem Reducing the condition number of deterministic matrices for efficient algorithmic use.
method Introduced pattern matrices and sparse perturbations with dependent entries.
result Condition number reduced to O(n) with O(n) random numbers in O(log n) precision.
The paper examines fair pricing and hedging stability under small numéraire perturbations.
problem Fair pricing and hedging stability under numéraire perturbations.
method Reformulating the stochastic control problem to show stability and deriving asymptotic formulas.
result Fair price and hedging strategy are stable with small numéraire perturbations.
Study the Dirac operator on a 3-sphere under metric perturbations.
problem Analyze the behavior of eigenvalues of the Dirac operator on a 3-sphere under metric perturbations.
method Derive explicit perturbation formulae for the two eigenvalues closest to zero, considering second variations.
result The eigenvalues closest to zero remain double eigenvalues and are completely determined by the increment of Riemannian volume.
Adding node feature kernels improves GCN robustness to graph perturbations.
problem GCNs' robustness to graph perturbations is a concern.
method Introduced random GCN and added node feature kernels to message passing.
result Perturbations of the graph structure can significantly degrade GCN performance.
Analyzes hedging problems under various no-arbitrage conditions.
problem Existence of pricing functionals in general markets.
method Investigates duality properties and perturbation analysis of sub- and super-hedging problems.
result Perturbation analysis highlights the impact of smile extrapolation on exotic option bounds.
New research evaluates various perturbation methods for improving neural network robustness.
problem Understanding and improving robustness of Convolutional Neural Networks (CNNs) against adversarial attacks.
method Detailed evaluation of five main perturbation-based defenses, comparing random and deterministic approaches.
result Perturbation-based defenses are equivalent in efficacy, and attacks transfer between them.
Study shows image classifiers struggle with temporal changes in videos.
problem Temporal robustness of image classifiers in videos.
method Constructed datasets and evaluated various classifiers and detection models.
result Median classification accuracy drops of 16-10 points in robust datasets.
Paper proposes a fast algorithm for selecting submatrices with high singular values.
problem Selecting a submatrix with a high singular value.
method Perturbation analysis and a fast algorithm derived from a bound on the smallest singular value.
result A fast algorithm for feature extraction is derived.
Short proof shows how ridge regression works with random data.
problem Understanding prediction error in ridge regression with random design.
method Combination of exchangeability arguments, matrix perturbation, and operator convexity.
result Elementary proof of prediction error without complex inequalities.
Analyzes perturbed contact instantons with Legendrian boundary conditions using geometric analysis.
problem Analyzing nonlinear elliptic systems associated with contact Hamiltonian trajectories.
method Identifies correct action and energy functionals, develops elliptic regularity theory, and proves asymptotic convergence.
result Established C ∞ C^\infty C ∞ convergence of perturbed contact instantons under finite energy hypothesis. The universal perturbative invariants of rational homology spheres can be extracted from the Chern-Simons partition function by combining perturbative and nonperturbative results. We spell out the general procedure to compute these invariants, and we work out in detail the case of Seifert spaces. By extending some prev…
Study on stability of GCNNs under graph perturbations.
problem Limited theoretical understanding of GCNN stability.
method Proposes a probabilistic framework to analyze GCNN stability under various graph perturbations.
result Demonstrates the importance of data distribution in stability analysis.
Paper examines stability of Bayesian posterior measures using integral probability metrics.
problem Stability of Bayesian inference in large-scale inverse problems.
method New families of integral probability metrics for likelihood and prior perturbations.
result Constructs new stability results for Bayesian posterior measures.
New technique stabilizes singular values in concatenated matrices.
problem How singular values of concatenated matrices relate to individual components.
method Developed perturbation technique extending classical results to concatenated matrices.
result Dominant singular values remain stable under small perturbations in submatrices.
In this paper we prescribe a fourth order conformal invariant on the standard n − n- n − sphere, with n ≥ 5 n\geq5 n ≥ 5 , and study the related fourth order elliptic equation. We first find some existence results in the perturbative case. After some blow up analysis we build a homotopy to pass from the perturbative case to the non-pert…
Paper develops a new kernel approximation framework.
problem High time and space complexity of kernel methods for large datasets.
method Perturbation-based kernel approximation framework using classical perturbation theory.
result Framework generalizes and improves upon existing methods.
State-of-the-art classifiers are vulnerable to small adversarial perturbations.
problem Vulnerability of state-of-the-art classifiers to adversarial perturbations.
method Assumed smooth generative model, derived upper bounds on robustness, proved adversarial perturbation transfer.
result Existence of adversarial perturbations that transfer well across different classifiers with small risk.
We study the perturbations of two classes of static black ellipsoid solutions of four dimensional vacuum Einstein equations. Such solutions are described by generic off--diagonal metrics which are generated by anholonomic transforms of diagonal metrics. The analysis is performed in the approximation of small eccentrici…
Advances FTPL results for bandit problems with unbounded perturbations.
problem Improving analytical foundations of FTPL in bandit problems.
method Revisiting classical FTRL-FTPL duality for unbounded perturbations.
result Establishes Best-of-Both-Worlds (BOBW) results for FTPL under a broad family of asymmetric unbounded perturbations.
We propose a new input perturbation mechanism for publishing a covariance matrix to achieve ( ε , 0 ) (ε,0) ( ε , 0 ) -differential privacy. Our mechanism uses a Wishart distribution to generate matrix noise. In particular, We apply this mechanism to principal component analysis. Our mechanism is able to keep the positive semi-definitene…
The study proves the stability of smooth embeddings of Riemannian metrics into Euclidean space.
problem Stability of smooth embeddings of Riemannian metrics into Euclidean space.
method Local perturbation method to derive a time-dependent local perturbation method.
result Construction of a smooth parametrized family of isometric embeddings for a short time.