New algorithm minimizes regret in stochastic linear bandits with perturbed history.
problem Minimizing cumulative regret in stochastic linear bandits.
method Perturbed-history exploration in a linear bandit (LinPHE) algorithm.
result Achieves a O ( d n ) O(d \sqrt{n}) O ( d n ) gap-free bound on cumulative regret. The paper strengthens a theorem on crossings under linear perturbations with Hausdorff measure estimates.
problem Understanding multiple-point crossings under linear perturbations.
method Establishes a transversality theorem with Hausdorff measure estimates for exceptional parameter sets.
result Explicit upper bounds on the Hausdorff dimension of the exceptional set.
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. Study linear perturbations of Spin(7) metrics, finding only rank one nilpotent matrices.
problem Linear perturbations of Spin(7) metrics.
method Applying the method of linear perturbations to Spin(7)-structures.
result Only rank one nilpotent matrices determine nontrivial perturbations.
Study linear perturbations in Schwarzschild black hole spacetime.
problem Linear perturbations of Schwarzschild black hole spacetime.
method Investigate linearised perturbation of constant mass aspect function foliation at null infinity.
result Linearised perturbations of Bondi energy and mass vanish, and all linear momentum can be achieved.
Refined theorem on linear perturbations with applications in singularity theory and optimization.
problem Linear perturbations and their implications in singularity theory and optimization.
method New perspective of Hausdorff measures for refined transversality theorem.
result Applications in singularity theory and optimization.
EVILL uses randomised perturbations to improve exploration in bandit problems.
problem Improving exploration in structured stochastic bandit problems.
method Solves for the minimiser of a linearly perturbed regularised negative log-likelihood function.
result EVILL matches the performance of Thompson-sampling-style methods in theory and practice.
In this work, we have presented a simple analytical approximation scheme for generic non-linear FBSDEs. By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown that it is possible to carry out a recursive approximation to an arbitrarily highe…
New bounds for nearly-linear networks without training.
problem Generalization of neural networks close to linearity.
method Perturbation of linear networks to derive bounds.
result First non-vacuous bounds for neural nets.
Charge measurements for instantons and gravitational perturbations.
problem Evaluating charges in Hermitian non-Kähler Einstein 4-manifolds and their perturbations.
method Evaluation of charges via Killing spinors and perturbation analysis of gravitational instantons.
result Generic gravitational perturbations admit a closed 2-form measuring the charge change.
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.
In his celebrated paper "Generic projections", John Mather has shown that almost all linear projections from a submanifold of a vector space into a subspace are transverse with respect to a given modular submanifold. In this paper, an improvement of Mather's result is stated. Namely, we show that almost all linear pert…
The paper studies the asymptotic behavior of adversarial training under ℓ ∞ \ell_\infty ℓ ∞ -perturbation.
problem Theoretical guarantees for sparsity-recovery in adversarial training.
method Investigation of the asymptotic distribution of the adversarial training estimator in generalized linear models.
result The asymptotic distribution of the adversarial training estimator under ℓ ∞ \ell_\infty ℓ ∞ -perturbation could have a positive probability mass at 0 when the true parameter is 0. State-of-the-art machine learning models frequently misclassify inputs that have been perturbed in an adversarial manner. Adversarial perturbations generated for a given input and a specific classifier often seem to be effective on other inputs and even different classifiers. In other words, adversarial perturbations s…
Paper develops robust Bayesian models for linear regression under adversarial perturbations.
problem Ensuring reliable machine learning models under data perturbations.
method Formulates adversarial Bregman divergence loss, computes adversarial perturbation, introduces adversarially robust posteriors, derives generalization certificates.
result Derives first rigorous generalization certificates for adversarially robust Bayesian linear regression.
We derive a system of equations governing the coupled gravitational and electromagnetic perturbations of Reissner-Nordström spacetime. The equations are derived in the context of global non-linear stability of Reissner-Nordström under axially symmetric polarized perturbations, as a generalization of the recent work on …
Two randomized algorithms improve regret bounds for generalized linear bandits.
problem Improving regret bounds for generalized linear bandits.
method Two randomized algorithms: GLM-TSL and GLM-FPL.
result Upper bounds of O ( d n log K ) O(d \sqrt{n \log K}) O ( d n log K ) on regret for both algorithms. Efficient algorithm controls unknown systems with adversarial perturbations.
problem Controlling unknown linear systems with adversarial perturbations and convex losses.
method Measures regret against an optimal linear policy, provides efficient algorithm with sublinear regret bound.
result First efficient algorithm with sublinear regret bound of T^{2/3}.
Study perturbs Dirac operators in any dimension, focusing on Majorana fermions.
problem Understanding perturbations of Dirac operators in various dimensions.
method Analyzes canonical perturbations of Dirac operators on Hermitian Clifford modules.
result Characterizes the low-energy spectrum of these operators on complete surfaces.
The paper constructs new bimetric conformal invariants using metric perturbations.
problem Developing new conformal invariants in Riemannian geometry.
method Using linear metric perturbations and conformal invariants.
result New bimetric conformal invariants on 4D manifolds are derived.
Linear classifiers can be made robust to strong adversarial examples attacks.
problem Understanding and quantifying adversarial examples in linear classification.
method Proposed a more practical definition of strong adversarial examples, showing robustness to attacks.
result Linear classifiers can be made robust to strong adversarial examples attacks.
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.
In this paper, we propose an efficient Monte Carlo implementation of non-linear FBSDEs as a system of interacting particles inspired by the ideas of branching diffusion method. It will be particularly useful to investigate large and complex systems, and hence it is a good complement of our previous work presenting an a…
New approach reduces unconstrained linear bandits to simpler optimization problems.
problem Unconstrained linear bandits problem.
method Perturbation-based approach combined with comparator-adaptive OLO algorithms.
result First high-probability guarantees for both static and dynamic regret in unconstrained linear bandits.
The SPS method constructs confidence regions for true parameters with optimal sample complexity.
problem Constructing exact, non-asymptotic confidence regions for true system parameters.
method Sign-Perturbed Sums (SPS) method, generalized to various types of problems.
result High probability upper bounds for SPS confidence regions show optimal shrinkage rate.
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.
Adversarial training can lead to overfitting without compromising robustness.
problem Explaining benign overfitting in adversarially robust linear classification.
method Theoretical analysis and numerical experiments on adversarial training.
result Adversarially trained linear classifiers can achieve near-optimal risks despite overfitting noisy data.
TULiP estimates uncertainty for deep learning models safely.
problem Reliable uncertainty estimation for deep learning models in the open world.
method TULiP considers a hypothetical perturbation, bounds its effect, and computes uncertainty from sampled predictions.
result TULiP achieves state-of-the-art performance in OOD detection benchmarks.
We build blowing-up solutions for linear perturbation of the Yamabe problem on manifolds with boundary, provided the dimension of the manifold is n>6 and the trace-free part of the second fundamental form is non-zero everywhere on the boundary.
Researchers construct a gauge-invariant energy functional for axially symmetric perturbations around Kerr black holes.
problem Understanding energy of axially symmetric perturbations around Kerr black holes.
method Hamiltonian dimensional reduction to a 2 + 1 2+1 2 + 1 Einstein-wave map system, constructing a positive-definite, gauge-invariant energy functional. result The energy functional serves as a Hamiltonian for the constrained evolution of linear perturbations.
This work proves Kerr black holes are dynamically stable under certain perturbations.
problem Dynamical stability of Kerr black holes under axially symmetric perturbations.
method Dimensional reduction to 2+1 Einstein-wave map system, construction of positive-definite energy functional, proving boundary terms vanish.
result Strictly conserved positive energy for axially symmetric linear perturbations of Kerr black holes.
This work precisely characterizes and improves the tradeoff between robustness and accuracy in linear regression.
problem Tradeoff between robustness and accuracy in adversarial training.
method Characterizes the effect of augmentation on standard error in linear regression; proves RST improves robust error without sacrificing standard error.
result RST improves both standard and robust error for neural networks under various perturbations.
New geometric interpretation explains over-parameterized models and adversarial perturbations.
problem Geometric understanding of over-parameterized regression and adversarial perturbations.
method Alternative geometric interpretation of regression in feature space.
result Adversarial perturbations are a natural feature of biased models due to underlying geometry.
Unified algorithm for linear bandits with improved regret bound.
problem Adversarial linear bandits with improved regret.
method Self-concordant perturbations in FTPL framework.
result Regret bound of O ( d n ln n ) \mathcal{O}(d\sqrt{n \ln n}) O ( d n ln n ) for hypercube and ℓ 2 \ell_2 ℓ 2 ball. Researchers found a way to measure energy in black hole perturbations.
problem Lack of positive-definite and conserved energy in black hole stability.
method Dimensional reduction and construction of a positive-definite energy functional.
result Conserved Hamiltonian energy for axially symmetric perturbations of Kerr black holes.
The paper tackles extrapolation of gene knockouts effects on RNA counts.
problem Modeling effects of gene knockouts on RNA counts for new perturbations.
method Formulated as a latent variable model with additive perturbation effects, proved identifiability, proposed PDAE for estimation.
result PDAE can accurately predict effects of unseen but identifiable perturbations.
New operators help focus on specific areas in complex math problems.
problem Concentration in complex mathematical structures.
method Construct conjugate-linear perturbations of twisted spinc Dirac operators using the conjugate-linear Hodge star operator.
result These perturbations satisfy the concentration principle.
Proves stability of charged black holes with small charge.
problem Linear stability of Reissner-Nordström spacetime for small charge.
method Proves stability of Reissner-Nordström family of charged black holes using linearized Einstein-Maxwell equations and geodesic null foliations.
result Solutions decay to a linearized Kerr-Newman metric, proving stability.
In this paper, we address the issue of linear stability of Schwarzschild space- time subject to certain axisymmetric perturbations. In particular, we prove that associ- ated solutions to the linearized vacuum Einstein equations centered at a Schwarzschild metric, with suitably regular initial data, decay to a linearize…
A new method for generating SPX and VIX risk scenarios using perturbed optimal transport.
problem Generating accurate risk estimates for SPX and VIX without full recalibration.
method A joint optimal transport calibration with perturbation methodology for sensitivities, combined with Skew Stickiness Ratio dynamics.
result The proposed method produces accurate risk estimates relative to full recalibration and is computationally faster.
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.
New bounds for transfer learning in linear models, improving generalization.
problem Understanding when auxiliary data helps in improving generalization in linear models.
method Derivation of exact error bounds and optimal task weights for linear regression and linear neural networks.
result First non-vacuous sufficient conditions for beneficial auxiliary learning in linear neural networks.
We consider a neural network architecture with randomized features, a sign-splitter, followed by rectified linear units (ReLU). We prove that our architecture exhibits robustness to the input perturbation: the output feature of the neural network exhibits a Lipschitz continuity in terms of the input perturbation. We fu…
This paper analyzes the sample complexity of SPS method for scalar linear regression.
problem Analyzing the sample complexity of the Sign-Perturbed Sums (SPS) identification method.
method The paper provides high probability upper bounds for the sizes of SPS confidence intervals under different sets of assumptions.
result The sizes of SPS confidence intervals shrink at a geometric rate around the true parameter, if observation noises are subgaussian.
Investigates fluid flow perturbations using geometric theory.
problem Analyzing linear perturbations in non-equilibrium fluid flows.
method Uses second order variations of the action and Jacobi fields.
result Demonstrates numerical simulations of perturbation dynamics.
This work presents a novel approach to train invertible linear layers by adding rank-one perturbations.
problem Training invertible linear layers during optimization with gradient-based methods is challenging.
method Train rank-one perturbations and add them to weight matrices infrequently, keeping track of inverses and determinants.
result Invertible linear layers improve mixing and mode separation in normalizing flows.
Study privacy and accuracy in high-dimensional LASSO with perturbation mechanisms.
problem Privacy-preserving sparse linear regression in high dimensions.
method Analyzes output and objective perturbation mechanisms using AMP.
result Sparsity affects privacy-accuracy trade-off; stronger regularization improves privacy.
Adversarial examples are perturbed inputs designed to fool machine learning models. Adversarial training injects such examples into training data to increase robustness. To scale this technique to large datasets, perturbations are crafted using fast single-step methods that maximize a linear approximation of the model'…