arXiv research

New method certifies neural network robustness under random input noise.

New method enhances neural network robustness against adversarial attacks.

New method certifies neural network robustness to random input noise.

New BO method optimizes multiple objectives under input noise.

This paper proposes a novel type of random forests called a denoising random forests that are robust against noises contained in test samples. Such noise-corrupted samples cause serious damage to the estimation performances of random forests, since unexpected child nodes are often selected and the leaf nodes that the i…

Adversarial noises are linearly separable for random neural networks.

FCNv2 robustness tested under noise and random initial conditions.

Recent advances in machine learning (ML) algorithms, especially deep neural networks (DNNs), have demonstrated remarkable success (sometimes exceeding human-level performance) on several tasks, including face and speech recognition. However, ML algorithms are vulnerable to \emph{adversarial attacks}, such test-time, tr…

Geometry-aware noise improves model generalization on complex manifolds.

The paper proposes a method to detect and filter noisy or mislabeled data using pointwise mutual information.

RESTA defends LLMs against jailbreaking attacks by adding random noise to embeddings.

Research reveals simplicity bias in random logistic map, impacting data analysis and forecasting.

Lower bound proves ridgeless regression performs poorly near interpolation threshold.

This paper analyzes the interpolation error of nonlinear Attention compared to linear regression.

Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are missing in current Neural ODE networks. In this paper, we propose a new continuous ne…

Financial correlation matrices measure the unsystematic correlations between stocks. Such information is important for risk management. The correlation matrices are known to be ``noise dressed''. We develop a new and alternative method to estimate this noise. To this end, we simulate certain time series and random matr…

Hierarchical randomized smoothing improves model robustness for complex data.

CNNs learn about input data uncertainties, improving classification performance.

Traditional GANs use a deterministic generator function (typically a neural network) to transform a random noise input $z$ to a sample $\mathbf{x}$ that the discriminator seeks to distinguish. We propose a new GAN called Bayesian Conditional Generative Adversarial Networks (BC-GANs) that use a random generator function…

Image classifiers often suffer from adversarial examples, which are generated by strategically adding a small amount of noise to input images to trick classifiers into misclassification. Over the years, many defense mechanisms have been proposed, and different researchers have made seemingly contradictory claims on the…

Adversarial examples have been shown to exist for a variety of deep learning architectures. Deep reinforcement learning has shown promising results on training agent policies directly on raw inputs such as image pixels. In this paper we present a novel study into adversarial attacks on deep reinforcement learning polic…

Gradient descent amplifies random features in neural networks to useful ones.

Extends randomized smoothing to certify robustness against various threat models and adversarial perturbations.

The paper creates nonparametric confidence bands for band-limited functions.

This work extracts stochastic dynamical systems with $\alpha$-stable Lévy noise.

We study the trade-offs between convergence rate and robustness to gradient errors in designing a first-order algorithm. We focus on gradient descent (GD) and accelerated gradient (AG) methods for minimizing strongly convex functions when the gradient has random errors in the form of additive white noise. With gradient…

This paper considers the problem of subspace clustering under noise. Specifically, we study the behavior of Sparse Subspace Clustering (SSC) when either adversarial or random noise is added to the unlabelled input data points, which are assumed to be in a union of low-dimensional subspaces. We show that a modified vers…

Random neural networks with ReLU activations are non-Gaussian processes.

We study empirical covariance matrices in finance. Due to the limited amount of available input information, these objects incorporate a huge amount of noise, so their naive use in optimization procedures, such as portfolio selection, may be misleading. In this paper we investigate a recently introduced filtering proce…

The paper develops methods to analyze sensitivity in stochastic models using surrogate models.

Bayesian optimisation is a sample-efficient search methodology that holds great promise for accelerating drug and materials discovery programs. A frequently-overlooked modelling consideration in Bayesian optimisation strategies however, is the representation of heteroscedastic aleatoric uncertainty. In many practical a…

Study on benign overfitting in leaky ReLUs with moderate input dimensions.

Polynomial chaos surrogates handle intrinsic noise in stochastic models.

GraphMoE generates random graphs using neural networks and graphlets.

Paper explores neural network approximations on sphere domains.

We derive upper bounds on the generalization error of a learning algorithm in terms of the mutual information between its input and output. The bounds provide an information-theoretic understanding of generalization in learning problems, and give theoretical guidelines for striking the right balance between data fit an…

Recent work has extensively shown that randomized perturbations of neural networks can improve robustness to adversarial attacks. The literature is, however, lacking a detailed compare-and-contrast of the latest proposals to understand what classes of perturbations work, when they work, and why they work. We contribute…

AIRBO optimizes robustly under uncertain inputs.

With a constant improvement in the network architectures and training methodologies, Neural Networks (NNs) are increasingly being deployed in real-world Machine Learning systems. However, despite their impressive performance on "known inputs", these NNs can fail absurdly on the "unseen inputs", especially if these real…

Many biological learning systems such as the mushroom body, hippocampus, and cerebellum are built from sparsely connected networks of neurons. For a new understanding of such networks, we study the function spaces induced by sparse random features and characterize what functions may and may not be learned. A network wi…

Paper introduces a new regularization method for kernel gradient descent learning.

Study on estimating unstable open-loop matrices from state trajectories.

Adversarial perturbations dramatically decrease the accuracy of state-of-the-art image classifiers. In this paper, we propose and analyze a simple and computationally efficient defense strategy: inject random Gaussian noise, discretize each pixel, and then feed the result into any pre-trained classifier. Theoretically,…

Randomized SVD shows phase transitions in noisy data.

Noise injection improves inference privacy in DNN models.

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…

It is well-known that classifiers are vulnerable to adversarial perturbations. To defend against adversarial perturbations, various certified robustness results have been derived. However, existing certified robustnesses are limited to top-1 predictions. In many real-world applications, top-$k$ predictions are more rel…

This paper proposed a bias-compensated normalized maximum correntropy criterion (BCNMCC) algorithm charactered by its low steady-state misalignment for system identification with noisy input in an impulsive output noise environment. The normalized maximum correntropy criterion (NMCC) is derived from a correntropy based…