Noise stability improves understanding of Transformer models.
problem Lack of robustness metrics for real-valued domains and junta-like input dependence in modern LLMs.
method Proposed noise stability as a new metric and developed a practical regularization method.
result Noise stability regularization method accelerates training by 35-75%.
Paper proposes a new framework to improve stability-based bounds in deep learning.
problem Explaining generalization in overparameterized neural networks.
method Decomposes excess risk dynamics into signal and noise components, applying stability-based bounds only to the noise.
result The decomposition framework improves stability-based bounds and explains generalization in neural networks.
Noise in RNNs promotes flatter minima and more stable dynamics.
problem Understanding and optimizing the training of RNNs with noise.
method Formalizing RNNs as stochastic differential equations and analyzing the effect of noise in the hidden states.
result Noise injection in RNNs leads to flatter minima, more stable dynamics, and improved robustness.
New findings on maximizing noise stability in partitions of Gaussian space.
problem Maximizing noise stability in partitions of Gaussian space.
method Analyzing the correlation between sets and their noise stability, proving conditional conjectures and hardness results.
result Hyperstable partitions maximize noise stability and have specific properties.
Noise can stabilize systemic risk models with uncertain robustness.
problem Understanding systemic risk in financial systems with uncertain parameters.
method Analyzing a mean-field model of systemic risk with uncertain coefficients and noise.
result Noise can induce stability in systemic risk models, contrary to intuition.
A new method for feature selection robust to noise and design variability.
problem Feature selection in high-dimensional regression under sampling variability and measurement error.
method Injects controlled additive noise into the design matrix, fits a base selector, and aggregates selection frequencies.
result Improved robustness compared to Stability Selection and standard base selectors.
Noise-robust Koopman operator framework for control with improved stability and performance.
problem Developing a stable and noise-robust Koopman operator for control tasks.
method Proposes a learning framework using Hankel matrix and neural network approximations for system dynamics, ensuring long-term stability and noise robustness.
result Demonstrates improved model performance and noise robustness in control tasks compared to existing methods.
Enhanced stability improves privacy in machine learning.
problem Improving privacy in machine learning training while maintaining accuracy.
method Study of stability in private empirical risk minimization, focusing on strongly-convex loss functions and uniform stability.
result An algorithm with uniform stability of β implies a bound of O(√β) on the scale of noise required for differential privacy.
NROWAN-DQN improves stability and exploration in noisy networks.
problem Noisy networks struggle with stable exploration in complex tasks.
method Noise reduction and online weight adjustment for stable actions.
result NROWAN-DQN outperforms prior algorithms in stability and exploration.
Study on the noise in SGD minibatches near local minima.
problem Understanding the noise in SGD minibatches near local minima.
method Detailed analysis of SGD noise in linear regression and derivation of a general formula for different types of minima.
result Provides insight into the stability of training neural networks and suggests large learning rates can help generalization.
Work on SGDm under heavy-tailed noise, revealing its generalization properties.
problem Understanding generalization of SGDm under heavy-tailed noise.
method Analysis of continuous-time limit (SDE) and discrete-time SGDm, establishing generalization bounds.
result SGDm can have worse generalization in the presence of heavy-tailed noise for quadratic loss functions.
SGD handles label noise with bounds improving over SGLD.
problem Label noise in non-convex optimization.
method Stochastic gradient descent with uniform dissipativity and smoothness conditions, using Wasserstein distance and algorithmic stability.
result Generalization error bounds with a rate of n−2/3, better than SGLD's n−1/2. Paper proposes a new method to stabilize noisy gradient algorithms.
problem Stochastic-gradient Langevin algorithms can introduce bias when taming denominators depend on stochastic-gradient realizations.
method Proposes a structure-preserving framework for designing tamed denominators that avoid unnecessary taming and maintain the stabilizing effect of taming.
result The method avoids stationary bias and explains the stationary error split into bias and remaining error.
New method embeds dynamic networks with stability for node behavior.
problem Embed time-evolving node representations with stability.
method Unfolded adjacency spectral embedding for dynamic networks.
result Method satisfies cross-sectional and longitudinal stability.
Study on sample complexity of policy gradient for stabilizing linear systems under multiplicative noise.
problem Learning optimal feedback gain for stabilizing linear systems with multiplicative noise.
method Analyzes the sample complexity of policy gradient methods, addressing the cusp obstruction and using symmetry to control divergent parts of the gradient.
result Proves that projected mini-batch policy gradient attains total sample complexity of O(1/η) when noise density is known and O(η^(-(2s+1)/(2s))) when estimated, for C^s noise densities with s ≥ 2.
PiNGDA learns beneficial noise for graph augmentation stability.
problem Challenges in generating effective and stable graph augmentations.
method PiNGDA uses positive-incentive noise to scientifically analyze and generate beneficial graph augmentations.
result PiNGDA improves GCL performance by learning beneficial noise on graph topology and attributes.
New stability analysis improves generalization of multipass SGD.
problem Improper preconditioning affects generalization in multipass SGD.
method Developed on-average stability analysis for multipass SGD.
result Proper preconditioning yields optimal effective dimension dependence.
New method uses generative models to improve phase retrieval stability.
problem Improving stability of solutions in phase retrieval problems.
method Unified reconstruction approach using generative models to mitigate overfitting.
result Mitigates overfitting to generative model for varying noise levels.
Noise Injection Node Regularization improves robustness in neural networks.
problem Improving robustness of neural networks against various perturbations.
method Injecting structured noise into neural networks during training.
result Significant improvement in robustness against data perturbations.
Method selects significant spatial covariates in noisy data.
problem Identifying true spatial covariates in noisy data.
method Combines sparsity-promoting estimation with noise-robust model selection.
result Method reliably recovers true covariates under diverse noise scenarios.
The paper analyzes stability of random matrix products with Markovian noise.
problem Analyzing stability of random matrix products with Markovian noise.
method Using a super-Lyapunov drift condition and controlled growth of matrix-valued functions, the paper provides an exponential stability result for the p-th moment of random matrix product.
result Finite-time p-th moment bounds for linear stochastic approximation and TD learning algorithms.
Diffusion-GAN uses diffusion to improve GAN training stability and realism.
problem Stability and realism issues in training GANs.
method Diffusion-GAN employs a forward diffusion chain to generate Gaussian-mixture distributed instance noise, with adaptive diffusion process and timestep-dependent discriminator.
result Diffusion-GAN produces more realistic images with higher stability and data efficiency.
Unified stability bounds for noisy SGD across convex and non-convex losses.
problem Deriving generalization bounds for noisy stochastic gradient descent.
method Unified approach using Lyapunov functions and applied probability.
result Time-uniform stability bounds for SGD on various loss functions.
We analyze why some models resist unlearning using linear stability theory.
problem Understanding and predicting when machine learning models resist unlearning.
method Linear stability theory applied to machine learning models, focusing on data coherence and optimization dynamics.
result Data coherence and signal-to-noise ratio (SNR) influence unlearning resistance; lower SNR makes unlearning easier.
SGD noise helps select flat minima by concentrating in sharp directions and being proportional to loss value.
problem Understanding the implicit regularization of SGD and selecting flat minima in over-parameterized models.
method Relating SGD's linear stability to the Frobenius norm of the Hessian and analyzing the alignment property of SGD noise.
result Flat minima are linearly stable for SGD, and their sharpness is bounded independently of model size and sample size.
Finding optimal correction of errors in generic stabilizer codes is a computationally hard problem, even for simple noise models. While this task can be simplified for codes with some structure, such as topological stabilizer codes, developing good and efficient decoders still remains a challenge. In our work, we syste…
SPPCSO addresses multicollinearity in high-dimensional data, improving model stability and predictive accuracy.
problem Multicollinearity in high-dimensional data leads to unstable estimation and reduced predictive accuracy.
method SPPCSO integrates principal component regression and L1 regularization to adaptively adjust shrinkage factors.
result SPPCSO achieves stable and reliable estimation in high-noise settings, distinguishing signal variables from noise.
New LP method recovers MAP solution from noisy stable instances.
problem MAP inference on noisy stable instances.
method Designing an algorithm to find nearby perturbation stable instances and using LP relaxation.
result LP approximately recovers the MAP solution from noisy stable instances.
Three-candidate plurality voting is stable for small correlations.
problem Stability of plurality voting in small correlation scenarios.
method Calculus of variations and noise stability analysis.
result Proof of Plurality is Stablest Conjecture for 3 candidates.
The paper analyzes how disturbances affect the convergence of algorithms in complex systems.
problem Analyzing the impact of disturbances on algorithm convergence in complex systems.
method Leveraging converse Lyapunov theorems, the paper derives stability bounds and convergence rates in the presence of disturbances.
result Key inequalities quantify the impact of disturbances on algorithmic performance.
New stability bounds for GD in overparameterised shallow nets without NTK assumptions.
problem Generalisation and excess risk bounds for shallow neural networks.
method Oracle inequalities and stability analysis of GD without kernelisation.
result Oracle type bounds reveal GD's generalisation is controlled by an interpolating network with shortest GD path.
RCLA reduces noise in topological data analysis, preserving essential structure.
problem Noise in large datasets obscures topological features in persistent homology.
method Grid-based RCLA integrates data reduction and denoising with a threshold parameter.
result RCLA provides a theoretical guarantee and automatic parameter selection.
Residual Neural Networks (ResNets) achieve state-of-the-art performance in many computer vision problems. Compared to plain networks without residual connections (PlnNets), ResNets train faster, generalize better, and suffer less from the so-called degradation problem. We introduce simplified (but still nonlinear) vers…
The paper provides theoretical guarantees for behavior cloning using generative models.
problem Behavior cloning of complex expert demonstrations using generative models.
method The paper proposes a theoretical framework invoking low-level controllers to stabilize imitation around expert demonstrations. It shows that with suitable low-level stability guarantees and powerful generative models, pure supervised behavior cloning can match expert trajectories.
result The paper proves that with a suitable low-level stability guarantee and a powerful enough generative model, pure supervised behavior cloning can generate trajectories matching the per-time step distribution of essentially arbitrary expert trajectories in an optimal transport cost.
Despite their impressive performance, deep convolutional neural networks (CNNs) have been shown to be sensitive to small adversarial perturbations. These nuisances, which one can barely notice, are powerful enough to fool sophisticated and well performing classifiers, leading to ridiculous misclassification results. In…
This study improves convergence of two-timescale SA under Markovian noise in reinforcement learning.
problem Stability and convergence of two-timescale stochastic approximations under Markovian noise.
method Introduced a new control strategy for the fast timescale parameter.
result Established almost sure convergence of TDC with eligibility traces under off-policy learning with linear function approximation.
To date, the instability of prognostic predictors in a sparse high dimensional model, which hinders their clinical adoption, has received little attention. Stable prediction is often overlooked in favour of performance. Yet, stability prevails as key when adopting models in critical areas as healthcare. Our study propo…
New approach uses 'forward-looking' counterfactuals for treatment choice.
problem Using traditional 'retrospective' counterfactuals in treatment choice leads to counterintuitive results.
method Introduces 'counterfactual treatment choice' for forward-looking counterfactuals.
result Mismatches between interventional and forward-looking counterfactuals can lead to counterintuitive results.
Unified framework for robust causal directionality in quantum systems under MNAR observation.
problem Determining causal directionality in quantum systems under MNAR observation.
method Integrates CVAE-based latent constraints, MNAR-aware selection models, GEE-stabilized regression, penalized empirical likelihood, and Bayesian optimization.
result Achieves lower bias and variance, near-nominal coverage, and superior quantum-specific diagnostics.
This paper improves generative models by using data scaling and theoretical analysis.
problem Challenges in selecting noise distributions for stable learning in generative models.
method Introduces Scale-GAN, which uses data scaling and variance-based regularization.
result Data scaling controls the bias-variance trade-off and improves stability and accuracy.
Introduces TPV to analyze model robustness without labels.
problem Analyzing post-training robustness of machine learning models.
method Parameter perturbations and test prediction variance (TPV) as a unifying framework.
result TPV connects various perturbations under a single lens, providing insights into model stability.
A method to remove mean-shift noise from PCA using knockoffs.
problem High sensitivity of PCA to mean-shift contamination in high-dimensional data.
method Introducing knockoff mean-shift perturbation to separate and remove mean-shift components from PCA.
result The mean-shift spikes are spectrally separable from stable eigenvalues, allowing for robust PCA.
We study a generalization of the Heston model, which consists of two coupled stochastic differential equations, one for the stock price and the other one for the volatility. We consider a cubic nonlinearity in the first equation and a correlation between the two Wiener processes, which model the two white noise sources…
The paper guarantees global stability for stochastic subgradient methods in nonsmooth nonconvex optimization.
problem Minimizing nonsmooth nonconvex functions with convergence guarantees.
method Developed a framework for stochastic subgradient methods with global stability guarantees.
result Iterates are uniformly bounded and asymptotically stabilize around the stable set of the differential inclusion.
Study examines noise sensitivity of DNNs for binary classification.
problem Understanding non-robustness of DNN classifiers under noise.
method Defined and extended noise sensitivity and stability concepts for Boolean functions, applied to DNN models.
result Sorted out the relation between definitions and properties of DNN architectures under noise.
Unified framework explains why overfitting is benign in interpolating learning.
problem Understanding why overfitting is benign in highly overparameterized models.
method Spectral-transport stability framework.
result Sharp benign-overfitting criterion and explicit phase-transition rates.
Study shows exponential sample complexity for stabilizing certain linear systems.
problem Statistical hardness of learning to stabilize linear time-invariant systems.
method Analysis of sample complexity and co-stabilizability using robust control ideas.
result Sample complexity increases exponentially with system dimension.
Recurrent neural networks trained on regular languages exhibit stable states that can recover from noise.
problem Stability of internal states in recurrent neural networks trained on regular languages.
method Empirical study with analysis of network activation and transitions between states.
result Recurrent neural networks trained on regular languages can recover from random perturbations and maintain stable states.