Paper improves neural network robustness certification with tighter radii estimates.
problem Certifying neural networks' robustness against adversarial attacks.
method Advanced algorithms for discrete and continuous domains, optimizing sample size, standard deviation, and temperature.
result Significant improvement in certified test-set accuracy with tighter certified radii bounds.
Improves safety region certification for smoothed classifiers without changing smoothing scheme.
problem Certified safety regions for smoothed classifiers are often small compared to optimal.
method Generalizes certified radius calculation as nested optimization problem, uses 0th-1st order information, and designs efficient estimators.
result Certified safety regions are significantly larger than current methods, achieving significant improvements on various metrics.
New method improves certified robustness for classifier confidence.
problem Certifying confidence in classifier predictions.
method Randomized smoothing with modified Neyman-Pearson lemma.
result Certified radii for prediction confidence improved.
New approach to certifiably robust neural networks using Boolean function perspective.
problem Lack of principled understanding and certified robustness for ℓ∞ perturbations. method New perspective on Boolean functions, deriving impossibility results, and developing a unified Lipschitz network.
result Unified Lipschitz network that bypasses expressive power limitations and achieves better certified robustness.
Minimal spectral radii found for specific matrix types.
problem Finding smallest spectral radii for certain matrix classes.
method Analyzing skew-reciprocal integer matrices of fixed even dimensions.
result Most classes of matrices have smaller spectral radii than their reciprocal counterparts.
Novel framework improves randomized smoothing for various norms.
problem Developing robust defenses against adversarial attacks.
method Proposed a novel framework for devising and analyzing randomized smoothing schemes.
result Significantly improved certified accuracy in ℓ1 on standard datasets.
In this paper, we obtain two-sided bounds for the volumes of the Aloff-Wallach spaces W(p,q), compute maximal and minimal sectional curvature for the spaces W(n,n+1), and use this information to estimate the injectivity radii: We derive an upper bound for the injectivity radii of W(p,q) and a lower bound for the …
The paper studies geometric structures of curvature radii on Riemannian manifolds.
problem Exploring geometric structures of curvature radii on Riemannian manifolds.
method The main method involves constructing a pair of global vector fields f1,f2 that encode intrinsic geometry. result Existence of sub-Riemannian manifolds associated with curvature radii and investigation of their properties.
Develop a decision-calibrated conformal framework for pacing decisions in streaming advertising.
problem Pacing decisions in streaming advertising
method Develop a decision-calibrated conformal framework
result The proposed score is the smallest valid uncertainty measure that uniformly protects all deployable pacing policies.
We study one extremal problem on the product of power of generalized inner radii of non-overlapping domains in Cn.
New proof shows not all Salem numbers are growth rates of Coxeter groups.
problem Identifying growth rates of Coxeter groups using Salem numbers.
method New proof using spectral radii and Coxeter transformations.
result Not every Salem number is a growth rate of hyperbolic Coxeter groups.
New method certifies regression robustness without data distribution assumptions.
problem Certifying robustness of regression models against poisoning attacks.
method Reduces certified regression to certified classification using median decision function.
result Proposes six new provably-robust regression models.
Study nearest-neighbor radii under dependent sampling, finding they remain informative.
problem Analyzing nearest-neighbor radii under dependent sampling.
method Consider strong mixing dependent observations, establish distribution-free almost sure convergence and sharp non-asymptotic moment bounds.
result Nearest-neighbor geometry remains informative under dependence sampling.
SingleProp speeds up robust neural network training with minimal certification.
problem Efficiently defending neural networks against adversarial attacks with certified guarantees.
method SingleProp regularizer that requires only one forward pass per training iteration.
result Comparable certified accuracy to state-of-the-art defenses, but significantly faster training.
The study finds parametrizations for surfaces of revolution with a linear curvature ratio.
problem Deriving surfaces of revolution with a specific curvature ratio.
method Derives parametrizations for surfaces of revolution with an affine-linear relation between their curvature radii.
result Explicit parametrizations found for a countably-infinite number of surfaces.
New attack tricks certifiably robust models into mislabeling images.
problem Defeating certified defenses against adversarial examples.
method Spoofed robustness certificates and large perturbations.
result Certifiably robust models can be fooled by large perturbations.
Explicit BCH series radii found for special Banach-Malcev shift algebras.
problem Finding convergence radii for BCH series in specific algebraic structures.
method Established explicit convergence radii using continuity estimates and algebraic properties.
result Explicit formula for convergence radii derived and validated for various shift algebras.
BagCert efficiently certifies robustness against adversarial patches on image classifiers.
problem Adversarial patches pose a threat to autonomous systems' perception component.
method BagCert combines model architecture and certification procedure for efficient inference.
result BagCert certifies 10,000 examples in 43 seconds on a single GPU, achieving 86% clean and 60% certified accuracy against 5x5 patches.
Researchers compute the full spectrum of Laplace operator on distance spheres in symmetric spaces.
problem Computing the full Laplace spectrum on distance spheres in symmetric spaces.
method Lie-theoretic methods to explicitly compute the spectrum.
result Unified formula for the full spectrum of Laplace operator on distance spheres in symmetric spaces of rank one.
SAFER method certifies robustness to word substitutions without model structure.
problem Certified robustness against synonymous word substitutions in NLP models.
method Randomized smoothing with stochastic ensemble of randomized inputs.
result Significantly outperforms state-of-the-art methods for certified robustness.
New techniques extend certified unlearning to deep neural networks.
problem Applying certified unlearning to deep neural networks (DNNs) is challenging due to their nonconvex nature.
method Developed simple techniques and an efficient computation method for nonconvex objectives, considering nonconvergence training and sequential unlearning.
result Demonstrated the efficacy of the method on real-world datasets, showing advantages of certified unlearning in DNNs.
This work improves certifiably robust models by distilling knowledge from adversarially robust teachers.
problem Certifiably robust models suffer from poor standard performance.
method Knowledge distillation from adversarially robust teachers to improve standard performance.
result Distillation from adversarially robust teachers consistently improves certified training performance.
Work on making classifiers robust against adversarial attacks for top-k predictions.
problem Vulnerability of classifiers to adversarial perturbations, especially for top-k predictions.
method Randomized smoothing to turn any classifier into a robust one, using Gaussian noise.
result Derives a tight robustness in ℓ2 norm for top-k predictions, achieving 62.8% certified top-5 accuracy on ImageNet.
One epoch training yields certifiably robust models.
problem Vulnerability of machine learning models to adversarial attacks.
method Deterministic certification approach based on regularized loss.
result Certifiable robust models achieved in one epoch.
Paper presents certified defenses against adversarial patch attacks.
problem Certified defenses against adversarial patch attacks are needed.
method Proposes the first certified defense and faster training methods.
result Demonstrates robustness transfer across different patch shapes.
Paper proves rigidity of Doyle spirals in hexagonal lattice circle packings.
problem Proving Doyle conjecture for hexagonal lattice circle packings.
method Using Liouville theorem of discrete harmonic functions based on logarithmic radii ratio observation.
result Proves rigidity of Doyle spirals in hexagonal lattice circle packings with bounded radii ratios.
New regularizers tighten convex relaxation bounds for neural networks.
problem Large gap between certifiable and empirical robustness in neural networks.
method Two regularizers to train neural networks yielding tighter convex relaxation bounds.
result Higher certified accuracy with proposed regularizers.
Certified training improves robustness against adversarial attacks.
problem Certified training's gap with empirical robustness limits its practical utility.
method Combining adversarial attacks with network over-approximations.
result Certified training can prevent catastrophic overfitting and bridge the gap to multi-step baselines.
This paper proposes a framework for certifying neural network defenses against data poisoning attacks.
problem Vulnerability of neural networks to data poisoning attacks.
method Random selection based defenses that average predictions on sub-datasets sampled from the training set.
result The certified radius of bagging derived by the framework is tighter than previous work.
Improved defense against data poisoning attacks by aggregating smaller subsets.
problem Mitigating the impact of poisoned data on model robustness.
method Finite Aggregation method that combines duplicates of smaller disjoint subsets for training.
result Consistent improvement in certified robustness bounds, up to 4.77% on GTSRB.
New work shows limits of certifying neural network robustness.
problem Certified training improves robustness but decreases accuracy.
method Bayes error analysis to investigate robustness limits.
result Upper bound for certified robust accuracy established.
New approach detects adversarial samples with certifiable guarantees.
problem Adversarial samples can trick CNNs, posing a threat.
method Certifiable Taboo Trap (CTT) approach to detect adversarial inputs.
result CTT outperforms existing defenses on various lp norms. We show how to turn any classifier that classifies well under Gaussian noise into a new classifier that is certifiably robust to adversarial perturbations under the ℓ2 norm. This "randomized smoothing" technique has been proposed recently in the literature, but existing guarantees are loose. We prove a tight robu…
A Gauss equation is proved for subspaces of Alexandrov spaces of curvature bounded above by K. That is, a subspace of extrinsic curvature less than or equal to A, defined by a cubic inequality on the difference of arc and chord, has intrinsic curvature less than or equal to K+A^2. Sharp bounds on injectivity radii of s…
New framework tightens certified robustness gaps in machine learning models.
problem Persistent gap between theoretical certified robustness and empirical accuracy.
method Leverages Lipschitz continuity and novel confidence intervals.
result Improves robust accuracy, compressing the gap between theory and practice.
Training neural networks to be certifiably robust is critical to ensure their safety against adversarial attacks. However, it is currently very difficult to train a neural network that is both accurate and certifiably robust. In this work we take a step towards addressing this challenge. We prove that for every continu…
Paper proposes faster certified robust training methods with short warmup.
problem Certified robust training methods require long warmup schedules, making training costly.
method Proposes three improvements: new weight initialization, BN, and regularization.
result Achieves 65.03% verified error on CIFAR-10 and 82.36% on TinyImageNet with short warmup.
Paper improves robustness certification by integrating ML and logical reasoning.
problem Limited robustness certification under perturbation radius.
method Integrates statistical ML models with logical reasoning using Markov logic networks.
result First certified robustness bound for MLN derived and experimentally validated.
The paper bounds radii and curvatures in Riemannian manifolds.
problem Bounding radii and curvatures in Riemannian manifolds.
method Analyzing scalar curvature, injectivity radius, and mean curvature.
result Proves bounds on injectivity and focal radii under specific conditions.
We propose an algorithm to enhance certified robustness of a deep model ensemble by optimally weighting each base model. Unlike previous works on using ensembles to empirically improve robustness, our algorithm is based on optimizing a guaranteed robustness certificate of neural networks. Our proposed ensemble framewor…
Improved training boosts certified robustness of L-infinity distance nets.
problem Certified robustness of L-infinity distance nets is not as strong as conventional networks.
method Improved training process combining scaled cross-entropy and clipped hinge loss with a decaying mixing coefficient.
result Certified accuracy of L-infinity distance nets improved from 33.30% to 40.06% on CIFAR-10.
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.
Policy certifies inventory levels meeting service requirements.
problem Maintaining stock levels meeting service requirements despite unknown demand.
method Data-driven order policy using online learning and integral action.
result Valid inference method for finite samples.
New framework certifies robustness for regression models.
problem Certifying robustness for regression models is challenging.
method Derives a prediction-centered certificate that exploits local geometry.
result Gradient information yields tighter robustness certificates.
New method certifies neural network function space norms from point evaluations.
problem Certifying neural network function space norms from point evaluations alone.
method Combining interval arithmetic enclosures, adaptive marking/refinement, and quadrature-based aggregation.
result Certified computation of Lp, W1,p, and W2,p norms. This paper provides a comprehensive benchmark and taxonomy for certifiably robust DNN defenses.
problem Certifiably robust defenses against adversarial attacks for deep neural networks.
method Taxonomy and benchmark of certifiably robust approaches.
result First comprehensive benchmark of certifiably robust approaches on different datasets.
We consider classical curvature flows: 1-parameter families of convex embeddings of the 2-sphere into Euclidean 3-space which evolve by an arbitrary (non-homogeneous) function of the radii of curvature. The associated flow of the radii of curvature is a second order system of partial differential equations which we sho…
Paper certifies intersection of minimum-volume confidence sets for multinomial outcomes.
problem Certifying intersection of minimum-volume confidence sets for multinomial outcomes.
method Exploits likelihood ordering to induce halfspace constraints, enabling adaptive geometric partitioning and computable bounds on p-values.
result Efficient and provably sound algorithm for certifying intersection, disjointness, or indeterminate result.