Improved robustness for deep neural networks with tighter bounds and attacks.
problem Loose upper bounds and prohibitive computation in existing adversarial robustness methods.
method Primal approach with exact Lipschitz certificates for ReLU networks and modern architectures, and novel Wasserstein Distributional Attacks.
result Tighter upper bounds and greater flexibility in attack points compared to existing methods.
New method provides tighter robustness guarantees for adversarial attacks.
problem Ensuring robustness against adversarial attacks in machine learning models.
method Developed a Second-order Smoothing (SoS) robustness certificate using Gaussian random smoothing.
result SoS certificates are tighter and provide improved robustness on high-dimensional datasets.
Geometric technique determines exactness of SDP robustness certificate.
problem Certifying robustness of neural networks to adversarial examples.
method Geometric projection onto hyperbola, SDP relaxation of ReLU activation.
result SDP certificate is exact for a single hidden layer under mild assumptions.
We create consistent option surfaces without arbitrage.
problem Constructing consistent option surfaces free of arbitrage across different maturities.
method Combining PCA-Smolyak approximation with chain-consistent diffusion and c-EMOT bridge.
result Computable certificates for strong convexity, solver correctness, and Dupire/Greeks stability.
Scalable method bounds Lipschitz constant of generative models.
problem Bounding the Lipschitz constant of generative models.
method Layerwise convex approximations using zonotopes.
result Efficient and tight bounds on generative models.
High sensitivity of neural networks against malicious perturbations on inputs causes security concerns. To take a steady step towards robust classifiers, we aim to create neural network models provably defended from perturbations. Prior certification work requires strong assumptions on network structures and massive co…
While neural networks have achieved high performance in different learning tasks, their accuracy drops significantly in the presence of small adversarial perturbations to inputs. Defenses based on regularization and adversarial training are often followed by new attacks to defeat them. In this paper, we propose attack-…
New method closes certification gap for adversarially trained models.
problem Certifying robustness of adversarially trained neural networks.
method Nonconvex low-rank SDP relaxation with polynomial-time optimization.
result Strong certifications comparable to SDP methods, but with fewer variables.
Enhances robustness of deep neural networks with randomized smoothing.
problem Improving robustness of deep neural networks against noisy inputs and adversarial attacks.
method Introduces a variance-margin trade-off approach to increase certified robust radius using pre-trained models.
result Significant improvement in certified accuracy compared to state-of-the-art methods.
New method certifies global robustness of neural networks efficiently.
problem Adversarial examples threaten certifiably robust neural networks.
method Formalized global robustness, adapted widely-used architectures with efficient global Lipschitz bounds.
result Certifiable robust models achieve state-of-the-art verifiable accuracy with negligible costs.
The paper develops a theory for speculative decoding acceptance criteria.
problem Speculative decoding's acceptance criteria and their rejection regions.
method Characterization of rejection regions as lower level sets of the target distribution, derivation of exact and margin-based certificates.
result Relaxed and tree-based acceptance criteria substantially enlarge the region of certified acceptance.
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.
Improved robustness of machine learning models with controlled Lipschitz constants.
problem Vulnerability of state-of-the-art models to adversarial attacks.
method Proposes a CLL loss that calibrates the margin and Lipschitz constant penalties, improving robustness certificates.
result Consistently outperforms other losses on CIFAR-10, CIFAR-100, and Tiny-ImageNet datasets.
Develops certificates for local population-risk increments using cross-fitted ridge calibration.
problem Certifying local population-risk increments in statistical models.
method Cross-fitted ridge calibration for linear feature classes, separating Taylor fluctuations and remainders.
result Certifies measurable updates from the same sample with penalties dependent on empirical geometry.
Tight estimation of the Lipschitz constant for deep neural networks (DNNs) is useful in many applications ranging from robustness certification of classifiers to stability analysis of closed-loop systems with reinforcement learning controllers. Existing methods in the literature for estimating the Lipschitz constant su…
In this paper we propose an algorithm for exact partitioning of high-order models. We define a general class of m-degree Homogeneous Polynomial Models, which subsumes several examples motivated from prior literature. Exact partitioning can be formulated as a tensor optimization problem. We relax this high-order combi…
ELF simplifies normalizing flows, making them more efficient and universal.
problem Computational inefficiency of normalizing flows.
method ELF introduces a simple, one-layer network with closed-form Lipschitz constants, combining the ease of residual flows with the performance of autoregressive flows.
result ELF is a provably universal density approximator, more efficient computationally and parameter-wise.
Study certifies missed relevant items in candidate generation with audit labels.
problem Certify missed relevant items in candidate generation with audit labels.
method Characterizes label complexity, develops exact finite-sample toolkit.
result Excluded-pool auditing is minimax rate-optimal for missed-mass certification.
This paper proposes a mechanism to produce equivalent Lipschitz surrogates for zero-norm and rank optimization problems by means of the global exact penalty for their equivalent mathematical programs with an equilibrium constraint (MPECs). Specifically, we reformulate these combinatorial problems as equivalent MPECs by…
New MIP formulations for neural network Lipschitz constant estimation.
problem Ensuring robustness of neural networks by calculating their Lipschitz constant.
method Reformulating the neural network Lipschitz estimation problem as a Quadratically Constrained MIP (MIQCQP) problem.
result Solutions of the MIQCQP formulations provide bounds on the Lipschitz constant, with conditions for exactness.
The paper certifies AI reliability via sampling and calibration, providing exact guarantees.
problem Ensuring trust in black-box AI systems' outputs.
method Self-consistency sampling and conformal calibration.
result Reliability levels derived from these methods offer finite-sample guarantees.
By using Bäcklund transformation for the sine-Gordon equation, new periodic exact solutions of the constant astigmatism equation zyy+(1/z)xx+2=0 are generated from a seed which corresponds to Lipschitz surfaces of constant astigmatism.
Christoffel function characterizes the corruption a bounded-degree certificate cannot remove in robust halfspace learning.
problem Robust halfspace learning under malicious noise
method Sum-of-Squares degree of outlier-removal certificate
result Christoffel function bounds the corruption a bounded-degree certificate cannot remove
New law establishes robustness for neural networks with bounded weights.
problem Ensuring robustness of neural networks against adversarial attacks.
method Deriving a lower bound on Lipschitz constant for arbitrary model classes with bounded Rademacher complexity.
result Established a law of robustness for weight-bounded neural networks, requiring log(n) layers for robust fitting.
New algorithms learn stability certificates from data, avoiding complex dynamics.
problem Synthesizing stability certificates from complex dynamical systems.
method Developed algorithms to learn certificate functions from trajectory data, establishing generalization error bounds.
result Efficiently learned certificates can be used for adaptive control.
Exact tail probability bounds for bounded kurtosis.
problem Determining worst-case tail probabilities under kurtosis constraints.
method AI-guided search and certifying pipeline to compute bounds.
result A four-regime map of tail probabilities with explicit formulas.
We find the exact worst-case tail probability for bounded kurtosis.
problem Determining the worst-case tail probability under bounded kurtosis constraints.
method AI-guided search and certificate verification around the certifying pipeline.
result A four-regime map of tail probabilities with explicit formulas and dual certificates.
New method tightens Lipschitz bounds for CNNs efficiently.
problem Lipschitz regularization of Convolutional Neural Networks (CNNs).
method Using Toeplitz matrix theory, introduces a tight and computationally efficient upper bound for convolutional layers.
result Developed an algorithm to train Lipschitz regularized CNNs.
This paper certifies cluster assignments from sum-of-norms clustering algorithms.
problem Certifying the correct cluster assignments from approximate solutions of sum-of-norms clustering.
method Presented a clustering test that identifies and certifies the correct cluster assignment from an approximate solution.
result The correct cluster assignment is guaranteed to be certified by a primal-dual path following algorithm after sufficient iterations.
Deep neural networks are known to be fragile to small adversarial perturbations. This issue becomes more critical when a neural network is interconnected with a physical system in a closed loop. In this paper, we show how to combine recent works on neural network certification tools (which are mainly used in static set…
Improved neural network robustness certification through tighter convex relaxations.
problem Certifying neural network robustness to perturbed and adversarial inputs.
method Exploiting ReLU network structure, novel partition-based certification procedure.
result Tightens existing linear programming relaxations to achieve zero relaxation error asymptotically.
Develops structured noise for more accurate graph classifier robustness certificates.
problem Isotropic noise limits robustness certificates for graph classifiers.
method Randomized smoothing with anisotropic noise distribution.
result Structured-aware robustness certificates provide more accurate predictions.
Defines a new modulus for Lipschitz surfaces and proves a homological duality theorem.
problem Lipschitz homology classes and their moduli.
method Defining a new modulus dModp and proving a homological duality theorem. result Every relative Lipschitz k-homology class has a unique dual class satisfying a specific modulus product equality. Looking for associations among multiple variables is a topical issue in statistics due to the increasing amount of data encountered in biology, medicine and many other domains involving statistical applications. Graphical models have recently gained popularity for this purpose in the statistical literature. Following t…
This paper examines weight initialization for 1-Lipschitz networks to improve robustness against adversarial attacks.
problem Improving the robustness of deep neural networks against adversarial attacks.
method Examined weight parametrization of AOL and SLL networks, calculated weight variance bounds, and demonstrated weight decay.
result Weight initialization causes deep 1-Lipschitz networks to decay to zero, and weight variance does not affect output variance distribution.
Techniques known as Nonlinear Set Membership prediction, Kinky Inference or Lipschitz Interpolation are fast and numerically robust approaches to nonparametric machine learning that have been proposed to be utilised in the context of system identification and learning-based control. They utilise presupposed Lipschitz p…
New framework improves adversarial robustness certification for various perturbations.
problem Certifying robustness against adversarial attacks in deep learning models.
method Unified functional optimization approach with non-Gaussian smoothing noise for multiple types of attacks.
result Achieves better certification results and identifies key trade-offs between accuracy and robustness.
Bayesian method synthesizes barrier certificates for unknown systems with latent states.
problem Certifying safety in systems with unknown dynamics and latent states.
method Bayesian inference with Metropolis-Hastings sampler and sum-of-squares program.
result Probabilistic validity of barrier certificates for unknown systems.
CITE algorithm provides anytime-valid certification of model outputs.
problem Challenges in controlling error levels in LLM self-consistency.
method Certification by Intersection-union Testing with E-processes (CITE) algorithm.
result Provable control of false certification at any prescribed level under arbitrary stopping rules.
Paper develops tighter risk certificates for contrastive learning models.
problem Statistical theory for contrastive learning is lacking, especially for practical models like SimCLR.
method Develops non-vacuous PAC-Bayesian risk certificates considering practical SimCLR factors.
result Risk certificates for contrastive loss and downstream prediction are much tighter than previous results.
Develops local population-risk certificates for model updates
problem Model updates in machine learning
method Certify population-risk increments around a model
result Certified upper endpoint yields a risk-controlled update rule
The performance of a reinforcement learning algorithm can vary drastically during learning because of exploration. Existing algorithms provide little information about the quality of their current policy before executing it, and thus have limited use in high-stakes applications like healthcare. We address this lack of …
ShuffleNet is a state-of-the-art light weight convolutional neural network architecture. Its basic operations include group, channel-wise convolution and channel shuffling. However, channel shuffling is manually designed empirically. Mathematically, shuffling is a multiplication by a permutation matrix. In this paper, …
We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range of applications in data science, where the objective is used for inducing spars…
Optimization geometrodynamics simplifies adaptive optimizer dynamics.
problem Hidden states in adaptive optimizers complicate gradient-based learning.
method Develops a variational theory to eliminate hidden states and compose across hierarchies.
result Yields interaction curvature that integrates to finite contrasts.
We consider the problem of noisy 1-bit matrix completion under an exact rank constraint on the true underlying matrix M∗. Instead of observing a subset of the noisy continuous-valued entries of a matrix M∗, we observe a subset of noisy 1-bit (or binary) measurements generated according to a probabilistic model. W…
TUV Austria proposes certification for ML applications to ensure reliability.
problem Ensuring trust in AI applications to meet societal reliance requirements.
method Holistic approach analyzing security, functionality, data quality, ethics, and criticality levels.
result Certification process for low-risk ML applications in supervised learning.
Valid certifies LLMs' domain adherence, bounding out-of-domain behavior.
problem Adversarial susceptibility of LLMs to generate out-of-domain outputs.
method VALID approach providing adversarial bounds as a certificate.
result Validates LLMs' domain adherence with meaningful certificates.