DIP-FAT improves adversarial training by diversifying perturbations.
problem Adversarial examples fool deep neural networks, leading to overfitting and poor performance.
method DIP-FAT uses random directions to diversify perturbations in adversarial training.
result DIP-FAT reduces overfitting and improves clean data accuracy.
Geometric insights reveal transferable adversarial directions across classifiers and models.
problem Adversarial perturbations transfer between different inputs, models, and architectures.
method Geometric analysis of linear classifiers and two-layer ReLU networks.
result Transferable adversarial directions exist for linear separators and ReLU networks with high probability.
This work improves structured prediction by learning the balance between signal and random noise.
problem Structured prediction with random perturbations.
method Learning the variance of randomized structured predictors to balance signal and noise.
result Learning the balance improves structured prediction effectiveness.
New method UADs improves transferability of adversarial perturbations.
problem Transferability of adversarial perturbations across different DNN architectures.
method Proposes Universal Adversarial Directions (UADs) to improve transferability.
result UADs can achieve a Nash equilibrium, indicating potential transferability.
Study examines sensitivity in utility maximization models, proving directional differentiability.
problem Sensitivity analysis for utility maximization in incomplete market models.
method Weak perturbation method, leveraging convex analysis and support functions.
result Proves Hadamard directional differentiability of value function w.r.t. model parameters.
Binary field theory splits Khovanov homology theories.
problem Understanding Khovanov homology theories over binary field.
method Analyzing Bar-Natan perturbation and reduced theories over F2. result Direct sum of two reduced theories is isomorphic.
Improved DOA estimation with distributed sensors across multiple frequencies.
problem Sensor gain uncertainties and directional perturbations in multi-frequency scenarios.
method Distributed optimization with local coherence models and iterative exchange of information.
result Advantages in statistical and computational efficiency through parallel iterative technique.
A new pruning method reduces neural network computation without retraining.
problem Efficiently reduce neural network computation while maintaining accuracy.
method Structured directional pruning via perturbation orthogonal projection.
result Achieves state-of-the-art pruned accuracy without retraining.
New method GSAT improves robustness against structured perturbations.
problem Structured perturbations in biological data.
method Formulates GSAT as a non-convex concave minimax optimization problem and solves it with GDADMM.
result Improves robustness against group-sparse and rank-constrained perturbations.
New method improves interpretability of text adversarial examples.
problem Generating interpretable adversarial examples in text is challenging.
method Sparse Projected Gradient Descent (SPGD) with directional and sparsity constraints.
result Improves interpretability and likelihood of adversarial examples compared to state-of-the-art methods.
The paper analyzes deep neural network classification regions and their decision boundaries.
problem Understanding the geometric properties of deep neural network classifiers.
method Empirical investigation of deep neural networks' classification regions and decision boundaries.
result Deep neural networks learn connected classification regions with flat decision boundaries.
DEceit constructs effective universal pixel-restricted perturbations for deep image classifiers.
problem Creating effective universal pixel-restricted perturbations for deep neural networks.
method DEceit algorithm for black-box feedback, targeting 10% of pixels in images.
result Perturbing only 10% of pixels achieves high Fooling Rate and visual similarity.
In this paper we prove a global existence theorem, in the direction of cosmological expansion, for sufficiently small perturbations of a family of n+1-dimensional, n≥3, spatially compact spacetimes which generalizes the k=−1 Friedmann--Robertson--Walker vacuum spacetime. Our results demonstrate causal geodes…
New method defends against multiple perturbation models in adversarial attacks.
problem Defending against multiple types of adversarial attacks.
method Developed a natural generalization of PGD-based procedure to incorporate multiple perturbation models.
result Trained robust models against ℓ∞, ℓ2, and ℓ1 attacks, achieving 47.0% adversarial accuracy on CIFAR10. Universal perturbations can fool deep neural networks with tiny changes.
problem Deep neural networks are vulnerable to very small, imperceptible changes that misclassify natural images.
method Systematic algorithm for computing universal perturbations, analyzing their properties.
result State-of-the-art deep neural networks are highly vulnerable to universal perturbations that are quasi-imperceptible to humans.
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.
Gradient descent-based adversarial training converges to robust classifiers on linearly separable data.
problem Understanding the inductive bias of adversarial training for robustness.
method Gradient descent on binary classification tasks with linearly separable data, focusing on inductive bias and convergence rates.
result Gradient descent-based adversarial training converges to the maximum margin classifier at a faster rate than clean data training.
Study shows stability of Schwarzschild spacetime under specific perturbations.
problem Linear stability of Schwarzschild spacetime under axial perturbations.
method Complex line bundle interpretation and connection-level object analysis.
result Suitably regular initial data decay to a linearized Kerr metric.
Adversarial training adds dynamic perturbations to neural networks for robustness.
problem Accuracy trade-off and lack of diversity in adversarial examples.
method Dynamic adversarial perturbations in the parameter space of neural networks, updating perturbation biases during training.
result Adversarial training with negligible cost and reduced accuracy trade-off.
Optimal ship paths on perturbed spheroids found using control theory.
problem Finding time-optimal ship paths on an ellipsoid with a perturbation.
method Optimal control theory with Finsler metric of Randers type.
result Solutions to the problem on an oblate ellipsoid.
The paper proves the existence and uniqueness of certain spacelike hypersurfaces with specific curvature and boundary conditions.
problem Existence and uniqueness of convex, entire, spacelike hypersurfaces with constant σk curvature. method Investigation of hypersurfaces with prescribed set of lightlike directions and perturbation on the ideal boundary at infinity.
result Existence and uniqueness of complete entire spacelike constant σk curvature hypersurfaces with prescribed lightlike directions and perturbation. The study finds regular null hypersurfaces in a perturbed Schwarzschild black hole exterior.
problem Existence of regular null hypersurfaces in a perturbed Schwarzschild black hole.
method Proof of existence for null hypersurfaces in a perturbed Schwarzschild spacetime.
result Existence of many foliations by regular null hypersurfaces in the exterior region of a perturbed Schwarzschild black hole.
Study examines how body segments respond to random vibrations.
problem Understanding human body responses to random vibrations.
method 35 participants were tested with random noise signals. Multiple linear regression models were created to determine influential predictors of peak translational gains.
result Multiple predictors, including motion direction and body segment, significantly influence peak translational gains.
This paper restores interpretability to adversarial training in text by restricting perturbations to existing words.
problem Lack of interpretability in adversarial training methods for text.
method Restrict perturbations to existing words in the input embedding space.
result Maintains or improves task performance while maintaining interpretability.
Active learning reduces spin network inference complexity by 10^6-fold.
problem Difficulty in inferring direct interactions in complex networks.
method Information geometry framework to quantify inference difficulty and information gain from perturbations.
result Designed perturbations reduce sampling complexity by 10^6-fold across various network architectures.
Two-layer networks trained on low-dimensional subspaces are vulnerable to adversarial examples.
problem Vulnerability of two-layer neural networks to adversarial examples on low-dimensional subspaces.
method Analysis of gradient behavior and effect of initialization scale and regularization.
result Decreasing initialization scale or adding L2 regularization can improve robustness to adversarial perturbations orthogonal to the data.
Deep RL policies are vulnerable to adversarial perturbations, but vanilla training yields more robust policies.
problem Vulnerability of deep reinforcement learning policies to adversarial perturbations.
method Analysis of deep reinforcement learning policy landscape and comparison of vanilla vs. adversarial training.
result Vanilla training yields more robust policies compared to adversarial training.
The study shows instability of Nikodym maximal function bounds on Riemannian manifolds under metric perturbation.
problem Instability of Nikodym maximal function bounds on Riemannian manifolds under metric perturbation.
method Analyzing the instability of $L^{ rac{d+2}2}$ bounds for the Nikodym maximal function over manifolds of constant sectional curvature and extending to any d-dimensional Riemannian manifold with a local totally geodesic submanifold. result The instability of the bounds for the Nikodym maximal function on Riemannian manifolds under metric perturbation.
GCNNs gain rotation invariance with more training augmentation, making SVD-Universal more effective.
problem Improving robustness of GCNNs to adversarial attacks.
method SVD-Universal technique applied to GCNNs trained with larger rotations.
result SVD-Universal becomes more effective as GCNNs gain rotation invariance.
This work introduces adversarial sparsity to measure robustness beyond adversarial accuracy.
problem Evaluating robustness to adversarial attacks beyond just accuracy.
method Adversarial sparsity, which quantifies the difficulty of finding perturbations.
result Sparsity provides valuable insights into neural networks and suggests improvements in robustness.
BOBYQA optimizes deep networks with fewer queries than other methods.
problem Generating adversarial examples with fewer queries than non-model-based methods.
method Model-based derivative-free optimisation algorithm (BOBYQA).
result BOBYQA achieves state-of-the-art results with fewer queries than other methods.
The paper proposes a method to create robust neural networks for automated driving.
problem Creating neural networks that can accurately predict road conditions and distances.
method The method introduces a non-standard loss function with tolerance to account for label variability and allows for deviations from labels.
result The proposed method results in a neural network that can robustly predict road conditions and distances, even with small label variations.
New example disproves complex contact theory for fat distributions with Reeb directions.
problem Whether fat (4,6)-distributions with Reeb directions always come from complex contact structures. method Constructed a counterexample of a fat distribution with two Reeb directions that does not support a complex contact structure.
result The space of complex-contact germs has infinite codimension within the space of fat (4,6)-distribution germs with Reeb directions. Develops a new attack model to better capture structural information in adversarial examples.
problem Lp norm-based adversarial attacks fail to capture structural information in input images.
method Structured Adversarial Attack (StrAttack) using ADMM framework to achieve strong group sparsity.
result StrAttack achieves strong group sparsity in adversarial perturbations with similar Lp norm distortion.
Improved neural network convergence with causal Bayesian modeling in retail performance.
problem Improving neural network convergence in retail performance models.
method Causal Bayesian neural network implementation, removal of weakest SEM path, Flipout layers, Vadam optimizer.
result Neural network convergence improved with removal of the weakest SEM path.
PWGF escapes saddle points in nonconvex optimization.
problem Escaping saddle points in nonconvex optimization.
method PWGF uses noisy perturbations via Gaussian process to escape saddle points.
result PWGF achieves second-order optimality for nonconvex objectives.
Stochastic Variational Optimization is a parallelizable method for gradient estimation.
problem Gradient estimation for differentiable objectives in parallel environments.
method Variational Optimization, Natural Evolution Strategies, Gaussian Perturbation, Directional Derivatives.
result Directional Derivatives are preferable to Variational Optimization for parallel Stochastic Gradient Descent.
A new method for adversarial attacks using physical parameters like lighting and geometry.
problem Vulnerability of machine learning image classifiers to adversarial attacks.
method Directly perturbs physical parameters (lighting and geometry) instead of pixel colors, using a differentiable renderer.
result Proposes parametric norm-balls for evaluating adversarial attacks, enabling physically-based attacks.
We develop a technique based on Malliavin-Bismut calculus ideas, for asymptotic expansion of dual control problems arising in connection with exponential indifference valuation of claims, and with minimisation of relative entropy, in incomplete markets. The problems involve optimisation of a functional of Brownian path…
This paper examines how adversarial perturbations affect model performance and equilibrium learning.
problem Adversarial perturbations and covariate shifts impact model performance and equilibrium learning.
method Characterizes the extrapolation region in regression and classification, analyzes dynamics of adversarial learning games.
result Establishes two directional convergence results: a blessing in regression and a curse in classification.
New methods help escape strict saddle points in nonsmooth optimization.
problem Escaping strict saddle points in nonsmooth optimization.
method An inexact stochastically perturbed gradient method applied to the Moreau envelope.
result A variety of algorithms for nonsmooth optimization can efficiently escape strict saddle points of the Moreau envelope.
This work improves neural network robustness to symbol substitutions using formal verification.
problem Neural networks' vulnerability to adversarial attacks, especially under discrete text perturbations.
method Formal verification using Interval Bound Propagation on a simplex model of input perturbations.
result Models show improved verified accuracy under perturbations with formal guarantees.
Privacy subsidy found in market trading with noisy direction signals.
problem Analyzing welfare and bid-ask spread in a market with privacy mechanisms.
method Closed-form derivation of bid-ask spread and welfare under flip-noise direction observation.
result Privacy subsidy of μηΔ from liquidity pool to traders, robust across models. The paper analyzes how quantization affects the Fisher Information Matrix's dominant eigenvalue.
problem The impact of quantization on the Fisher Information Matrix's dominant eigenvalue.
method The study examines spectral perturbation of the empirical Fisher Information Matrix under in-distribution input and quantized parameter perturbations.
result A bound on the eigenvalue under quantization noise, showing it strictly exceeds the unperturbed value at leading order.
DKMD is a fast signed statistic for comparing univariate distributions.
problem Comparing univariate distributions, especially preserving directionality.
method DKMD integrates kernel mean embeddings against an odd weighting function.
result DKMD preserves directionality and is robust to outliers.
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.
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.
Method differentiates diffusion model training to predict sample sensitivity.
problem Predict how diffusion model samples change with small perturbations.
method Closed-form procedure for computing directional derivatives of the map.
result Estimates sensitivity of diffusion model samples to additive perturbations.