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.
The study identifies conditions under which algorithmic stability explains generalization in interpolating learning systems.
problem Understanding when algorithmic stability explains generalization in interpolating learning systems.
method Modeling training as a function-space trajectory and measuring sensitivity to single-sample perturbations.
result There exist interpolating regimes with small risk where contractive sensitivity cannot hold, showing that stability is not a universal explanation.
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.
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.
Sharp stability threshold found for deep residual architectures.
problem Ensuring stable training and inference in deep residual networks.
method Sublinear-growth principle and optimal-control analysis.
result Stable training condition: input-magnitude exponent q ≤ 1.
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.
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.
The paper optimizes policies constrained to Schur stabilizing controllers using a Newton-type algorithm.
problem Optimizing policies under linear constraints in control systems.
method Newton-type algorithm on a manifold of Schur stabilizing controllers with a Riemannian metric.
result Local convergence guarantees for the Newton-type algorithm without relying on exponential mapping or retractions.
The paper develops a convex parameterization for robust RNNs ensuring stability and robustness.
problem Lack of stability and robustness guarantees in RNNs for sequence-to-sequence mapping applications.
method Formulated convex sets of RNNs with stability and robustness guarantees using incremental quadratic constraints.
result The proposed model structure ensures global exponential stability and bounds on incremental ℓ2 gain. Improved stability analysis of neural network systems using Zames-Falb multipliers.
problem Analyzing stability of linear systems with neural network nonlinearities.
method Using integral quadratic constraints, sector-bounded and slope-restricted structure, and acausal Zames-Falb multipliers.
result Flexible and versatile framework for stability analysis with improved computational efficiency.
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-…
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 …
Reinforcement learning is a powerful paradigm for learning optimal policies from experimental data. However, to find optimal policies, most reinforcement learning algorithms explore all possible actions, which may be harmful for real-world systems. As a consequence, learning algorithms are rarely applied on safety-crit…
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.
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.
This work improves adversarial robustness in sparse coding models.
problem The gap between theoretical models and practical deployment in adversarial robustness.
method Combining a sparsity-promoting encoder with a linear classifier, and providing a robustness certificate.
result Bounding the robust risk and providing a robustness certificate for end-to-end classification.
Paper provides efficient robustness certificates for neural networks.
problem Ensuring neural networks are robust against adversarial attacks.
method Two-step approach: 1) Efficient convex optimization for robustness certificates with bounded Hessian eigenvalues, 2) Curvature-based regularization during training.
result Significantly higher certified robust accuracy achieved compared to existing methods.
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.
Conformal Candidate Certification advances offline MBO by certifying candidate designs with statistical guarantees.
problem Offline model-based optimization
method Conformal Candidate Certification (CCC)
result CCC certifies 16.7% of an aggressive proposal pool with 0.990 empirical coverage at nominal 0.90.
This paper analyzes how periodic and soft target updates stabilize linear Q-learning.
problem Theoretical explanation of stabilization mechanisms for linear Q-learning.
method Exact analysis using switched linear system dynamics and the joint spectral radius.
result Periodic and soft target updates can guarantee convergence to the exact projected Q-Bellman solution under specific conditions.
New robustness certificates for streaming models with a sliding window.
problem Applying robustness certificates to streaming data with correlated inputs.
method Deriving robustness certificates for models using a sliding window over a sequence of potentially correlated inputs.
result Guarantees hold for the average model performance across the entire stream, independent of stream size.
Survey examines challenges of ML in avionic systems certification.
problem Challenges in current certification standards for ML in avionic systems.
method Literature review focusing on robustness and explainability of ML results.
result Current certification standards do not support ML in avionic systems.
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.
Randomized classifiers have been shown to provide a promising approach for achieving certified robustness against adversarial attacks in deep learning. However, most existing methods only leverage Gaussian smoothing noise and only work for ℓ2 perturbation. We propose a general framework of adversarial certificati…
The paper improves risk certificate tightness for neural networks using PAC-Bayes bounds.
problem Improving the usability of risk certificates for neural networks based on PAC-Bayes bounds.
method Theoretical contributions including KL divergence bounds, efficient methodology for optimization, and methods for optimizing non-differentiable objectives.
result First non-vacuous generalization bounds on CIFAR-10 for neural networks.
Study adversarial perturbations in classification, analyzing learning and certification.
problem Formal study of classification under adversarial perturbations from both learner and third-party perspectives.
method PAC-type semi-supervised learning framework, black-box certification under limited query budget, adversary analysis.
result Existence of a polynomial query complexity adversary implies the existence of a sample efficient robust learner.
New method improves robustness of smoothed classifiers against adversarial attacks.
problem Improving robustness of smoothed classifiers against adversarial attacks.
method Proposes worst-case adversarial loss over input distributions as a robustness certificate, and uses duality and smoothness properties to provide an easy-to-compute upper bound.
result Shows superior robustness performance over state-of-the-art certified or heuristic methods.
SREC markets are a relatively novel market-based system to incentivize the production of energy from solar means. A regulator imposes a floor on the amount of energy each regulated firm must generate from solar power in a given period and provides them with certificates for each generated MWh. Firms offset these certif…
This paper develops a general theoretical framework to analyze structured sparse recovery problems using the notation of dual certificate. Although certain aspects of the dual certificate idea have already been used in some previous work, due to the lack of a general and coherent theory, the analysis has so far only be…
Given a tame knot K presented in the form of a knot diagram, we show that the problem of determining whether K is knotted is in the complexity class NP, assuming the generalized Riemann hypothesis (GRH). In other words, there exists a polynomial-length certificate that can be verified in polynomial time to prove that K…
The paper compares machine learning methods with traditional techniques for pricing and sensitivities of financial products with path-dependent structures.
problem Evaluating financial products with early-termination clauses, especially those with path-dependent structures.
method The paper compares regression methods including randomized recurrent and feed-forward neural networks, and a novel approach using signatures of the underlying price process, with traditional polynomial basis functions for pricing and sensitivities.
result Machine learning algorithms often match the accuracy and efficiency of traditional methods for Asian and look-back options, while randomized neural networks are best for callable certificates.
New method certifies deep graph classifiers with tighter risk bounds.
problem Certifying the reliability of deep graph classifiers.
method Linearized deep assignment flows with random initial conditions, using PAC-Bayes risk certification.
result Computes tighter out-of-sample risk certificates efficiently.
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.
Recently, techniques have been developed to provably guarantee the robustness of a classifier to adversarial perturbations of bounded L_1 and L_2 magnitudes by using randomized smoothing: the robust classification is a consensus of base classifications on randomly noised samples where the noise is additive. In this pap…
Paper reviews robustness in machine learning models and discusses training and certification methods.
problem Ensuring reliability of machine learning models in safety-critical systems.
method Reviews formalisms and discusses training and certification techniques.
result Identifies future research directions in robust machine learning.
Patch adversarial attacks on images, in which the attacker can distort pixels within a region of bounded size, are an important threat model since they provide a quantitative model for physical adversarial attacks. In this paper, we introduce a certifiable defense against patch attacks that guarantees for a given image…
ClusTR improves clustering-based models' robustness without adversarial training.
problem Improving clustering-based models' robustness.
method Proposes ClusTR, a clustering-based training framework for robust models without adversarial training.
result ClusTR outperforms adversarially-trained models by up to 4% under strong PGD attacks.
This paper studies the market phenomenon of non-convergence between futures and spot prices in the grains market. We postulate that the positive basis observed at maturity stems from the futures holder's timing options to exercise the shipping certificate delivery item and subsequently liquidate the physical grain. In …
Proposes new convex relaxations for certifying spatial robustness of neural networks.
problem Lack of provable guarantees for robustness against vector field transformations.
method Novel convex relaxations for certifying robustness against vector field transformations.
result First time providing a certificate of robustness against vector field transformations.
New method certifies generative models' robustness.
problem Certifying generative models' robustness is challenging due to non-convex sets.
method ApproxLine, a scalable certification method capturing infinite sets or distributions over them.
result ApproxLine provides sound deterministic and probabilistic guarantees.
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.
We discuss the pricing methodology for Bonus Certificates and Barrier Reverse-Convertible Structured Products. Pricing for a European barrier condition is straightforward for products of both types and depends on an efficient interpolation of observed market option pricing. Pricing products We discuss the pricing metho…