New theorem for deep neural networks improves classification margins.
problem Improving classification margins in deep neural networks.
method Local class-purity theorem and margin p-values for training and testing samples.
result Enhanced understanding and computation of classification margins.
LC-LMT makes certified defense more efficient and robust.
problem Scalable certified defense methods are resource-intensive and only achieve small robustness.
method LC-LMT, a lightweight Lipschitz margin training method.
result LC-LMT achieves higher robustness and ε-robustness more efficiently. This paper presents a margin-based multiclass generalization bound for neural networks that scales with their margin-normalized "spectral complexity": their Lipschitz constant, meaning the product of the spectral norms of the weight matrices, times a certain correction factor. This bound is empirically investigated for…
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.
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.
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…
Introduces gradient decay in Softmax for better generalization.
problem Improving generalization performance in neural networks.
method Gradient decay hyperparameter in Softmax for varying gradient rates based on probability.
result Gradient decay rate affects generalization performance and can be tuned for better optimization.
LiST improves neural network robustness and calibration without manual tuning.
problem Developing robust and calibrated neural networks simultaneously.
method Lipschitz Scaling Training (LiST) that iteratively adjusts the global Lipschitz constant.
result LiST yields an out-of-the-box calibrated network with competitive accuracy and robustness.
Graph-based framework for provably robust adversarial training.
problem Adversarial robustness of machine learning models.
method Formulates adversarial robustness as loss minimization with a Lipschitz constraint, using graph-based discretization and primal-dual algorithms.
result Establishes a connection between elliptic operators and adversarial learning, and proves fundamental lower bounds on adversarial sensitivity.
Study minimax rates for binary classifier estimation with margin conditions.
problem Estimating binary classifiers with geometric margin conditions.
method Derive lower bounds for worst-case learning rates over various function classes.
result Identify optimal rates close to O(n−1) for different function classes. New risk bound derived for multi-category margin classifiers.
problem Guaranteed risk dependency on categories, sample size, and margin parameter.
method Derived a new risk bound using Rademacher complexity and chaining method.
result Improved dependency on categories over state of the art.
New bounds improve neural network generalization by considering data-dependent properties.
problem Exponential dependence on depth in existing bounds for neural networks.
method Augmenting functions to make their composition Lipschitz and covering the augmented functions.
result Rademacher complexity bounds scale polynomially in depth when data-dependent properties are small.
New bounds explain deterministic non-smooth deep nets without large Lipschitz constants.
problem Challenges in explaining generalization of deterministic non-smooth deep nets.
method De-randomized PAC-Bayes margin bounds for deterministic non-convex and non-smooth predictors.
result New bounds avoid large Lipschitz constants, providing generalization guarantees.
Adversarial Lipschitz Regularization improves Wasserstein GANs without gradient norm penalties.
problem Training stability and sample quality issues in Wasserstein GANs.
method Explicit Lipschitz penalty using adversarial training.
result Explicit Lipschitz penalty leads to competitive performance in Wasserstein GANs.
The paper proposes a method to train NNs with a small Lipschitz constant to improve robustness.
problem Neural networks' susceptibility to adversarial perturbations in safety-critical applications.
method The paper introduces a framework to train multi-layer NNs by minimizing their Lipschitz constant, using an optimization scheme based on the Alternating Direction Method of Multipliers.
result The proposed training procedure successfully increases the robustness of neural networks.
Deep networks converge in direction, with implications for predictions and margins.
problem Understanding convergence and alignment in deep learning networks.
method Developed a theory of unbounded nonsmooth Kurdyka-Łojasiewicz inequalities for functions definable in an o-minimal structure.
result Network weights, predictions, training errors, and margin distribution converge in direction and align with gradient flow.
New method improves GAN training stability and quality.
problem Improving training stability and sample quality in GANs.
method Proposes a new method for Lipschitz continuity in GANs that is efficient and unbiased.
result Demonstrates the effectiveness of the new method in various GAN training scenarios.
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.
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.
New method for differentially private optimization with general Lipschitz conditions.
problem Differentially private optimization under general Lipschitz conditions.
method Generalized Lipschitz condition for per-sample gradients, tuning clip norm based on minimum per-sample Lipschitz constant.
result Efficacy of the recommended clip norm tuning method verified on 8 datasets.
Privacy affects fairness in classification models, but not drastically.
problem The impact of differential privacy on fairness in classification models.
method Theoretical analysis proving Lipschitz continuity of fairness measures and a non-asymptotic bound on fairness levels.
result Privacy impacts fairness, but not significantly as the number of samples increases.
Adaptive LR improves neural network Lipschitz regularity without slowing convergence.
problem Training neural networks with high Lipschitz constant.
method Adaptive learning rate (decay) in gradient descent for two-layer networks.
result Decaying learning rate maintains convergence rate and Lipschitz regularity.
This work provides bounds on the performance of prediction models in the predict-then-optimize framework.
problem Generalizing the performance of prediction models in the predict-then-optimize framework with the SPO loss function.
method Deriving generalization bounds using the Natarajan dimension and exploiting the strength property of the feasible region.
result Improved generalization bounds for the SPO loss function, scaling logarithmically in the number of extreme points and linearly in the decision dimension.
New method prevents gradient attenuation in Lipschitz constrained convolutional networks.
problem Gradient norm attenuation in Lipschitz constrained convolutional networks.
method Block Convolution Orthogonal Parameterization (BCOP) to train scalable, expressive, provably Lipschitz convolutional networks.
result Empirically, BCOP parameterization is competitive with existing approaches to provable adversarial robustness and Wasserstein distance estimation.
GD-trained shallow ReLU nets learn Lipschitz functions with noise.
problem Learning Lipschitz functions with additive noise in overparameterized neural networks.
method Gradient Descent (GD) with early stopping, focusing on the Neural Tangent Kernel (NTK).
result Early-stopped GD achieves minimax optimal rates for learning Lipschitz functions.
Efficient local Lipschitz bounds improve neural network robustness.
problem Certifying robustness of neural networks is challenging and often leads to over-regularization.
method Proposes an efficient trainable local Lipschitz upper bound by considering activation functions and weight matrices.
result Consistently outperforms state-of-the-art methods in clean and certified accuracy on various datasets.
New method models fat-tailed distributions with anisotropic tail-adaptive flows.
problem Gaussian-based variational inference fails to accurately capture tail decay in fat-tailed distributions.
method Improved theory on tails of flows, developed anisotropic tail-adaptive flows (ATAF).
result ATAF models tail-anisotropy, outperforming prior work on synthetic and real-world targets.
MMA training maximizes margins for adversarial robustness.
problem Adversarial robustness of neural networks.
method Directly maximizes margins through adaptive adversarial training.
result MMA training improves adversarial robustness compared to fixed ε adversarial training.
Improved robustness of 1D CNNs for heart arrhythmia classification.
problem Improving the robustness of 1D CNNs for classification tasks.
method Parameterization using Cayley transform and controllability Gramian for Lipschitz-bounded CNNs.
result Improved robustness of trained Lipschitz-bounded 1D CNNs for heart arrhythmia classification.
The paper trains neural networks with robustness guarantees using semidefinite constraints.
problem Training neural networks with robustness and stability guarantees.
method Exploiting the banded structure of semidefinite constraints, an efficient and scalable training scheme based on interior point methods is set up.
result The method allows for enforcing Lipschitz constraints in large-scale deep neural networks, as demonstrated in numerical examples.
WCAT improves adversarial robustness on CIFAR-10.
problem Improving robustness against adversarial examples.
method Lipschitz regularization of the loss function.
result 11% improvement in adversarial robustness on CIFAR-10.
We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant---for multiple p-norms---of a feed forward neural network composed of commonly used layer types.…
Paper presents a method to accurately estimate Lipschitz constants for DNNs.
problem Estimating Lipschitz constants for deep neural networks is crucial for robustness and stability analysis.
method Convex optimization framework using quadratic constraints to solve SDP for accurate and efficient estimation.
result Our method provides the most accurate Lipschitz bounds compared to existing methods.
This research explores principles of Lipschitz continuity in neural networks for robustness and generalization.
problem Ensuring robustness and generalization in neural networks, especially to small input perturbations and out-of-distribution data.
method Two complementary perspectives: internal (training dynamics) and external (frequency signal propagation).
result Advances in understanding the principles of Lipschitz continuity in neural networks.
This paper resolves Breiman's dilemma in neural networks by analyzing phase transitions of margin dynamics.
problem Breiman's dilemma in neural networks: uniform margin improvement does not guarantee reduced generalization errors.
method Revisiting Breiman's dilemma in deep neural networks with spectrally normalized margins, analyzing phase transitions of normalized margin distributions.
result Margin-based generalization bounds can predict test error trends during training phase transitions.
Enhances ENet's prediction accuracy while maintaining uncertainty estimation.
problem Gradient shrinkage problem in ENet's loss function.
method Proposes a multi-task learning framework with a modified MSE loss function.
result Improves ENet's prediction accuracy without losing uncertainty estimation.
We compute the local Lipschitz constant of ReLU networks precisely.
problem Estimating the local Lipschitz constant of ReLU networks is hard.
method We use a novel approach involving the generalized Jacobian and backpropagation.
result We provide an algorithm to compute the exact Lipschitz constant of ReLU networks.
The study examines the limitations of bi-Lipschitz Normalizing Flows in approximating certain distributions.
problem The expressivity of bi-Lipschitz Normalizing Flows in approximating specific target distributions.
method Characterization of expressivity through lower bounds on Total Variation distance and discussion of potential remedies.
result Several target distributions are difficult to approximate using bi-Lipschitz Normalizing Flows, and lower bounds on their approximation are provided.
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.
We model how Lipschitz continuity changes during neural network training.
problem Understanding how Lipschitz continuity evolves during training.
method We use a system of stochastic differential equations to capture the dynamics of Lipschitz continuity under SGD.
result We identify three factors driving the evolution of Lipschitz continuity: gradient flow projection, gradient noise, and Hessian projection.
Unified analysis of self-training for deep networks on unlabeled data.
problem Theoretical understanding of self-training for deep networks on unlabeled data.
method Unified theoretical analysis using expansion assumption and input-consistency regularization.
result Proves high accuracy of minimizers of population objectives based on self-training and input-consistency regularization.
CLIP controls neural network stability by bounding Lipschitz constants.
problem Neural networks lack mathematical guarantees of stability, especially to adversarial examples.
method Develops a variational regularization method (CLIP) to control the Lipschitz constant of neural networks.
result CLIP provides a tighter bound on the actual Lipschitz constant compared to layer-wise methods.
New neural network design resists small ℓ∞-norm adversarial perturbations.
problem Vulnerability of neural networks to small ℓ∞-norm adversarial perturbations. method Designing ℓ∞-dist neurons and constructing ℓ∞-dist nets, proving their 1-Lipschitz property and expressive power. result Certified robustness of ℓ∞-dist nets with state-of-the-art performance on various datasets. Paper investigates Lipschitz constants of self-attention modules in neural networks.
problem Lipschitz constants of self-attention modules in neural networks.
method Proved standard dot-product self-attention is not Lipschitz for unbounded input domain. Proposed L2 self-attention that is Lipschitz. Derived upper bound on L2 self-attention's Lipschitz constant.
result Proved standard self-attention is not Lipschitz for unbounded input domain and proposed an alternative L2 self-attention that is Lipschitz.
LOT improves adversarial robustness by training 1-Lipschitz convolution layers.
problem Improving adversarial robustness of deep neural networks.
method LOT: Layer-wise Orthogonal Training for 1-Lipschitz convolution layers.
result LOT significantly enhances certified robustness of Lipschitz-bounded models.
Neural operators learn to solve LQ MFGs efficiently in infinite dimensions.
problem Solving many related LQ MFG problems in infinite-dimensional settings.
method Training neural operators to map problem data to equilibrium strategies.
result NOs reliably solve unseen LQ MFG variants with controlled parameters.
This study analyzes adversarial training on linearly separable data and finds that gradient updates can achieve large margins in polynomial iterations.
problem Ensuring robustness in machine learning models trained on linearly separable data.
method Analysis of adversarial training with gradient updates on linearly separable data.
result Gradient updates in adversarial training can achieve large margins in polynomial iterations, whereas non-smooth methods require exponentially many iterations.
Training dynamics reveal neural network complexity.
problem Understanding the complexity of neural networks during training.
method Relating the Lipschitz constant and training behavior of neural networks.
result Steady training and bounded complexity in far regions of input space.