Stabilizes deep Bayesian neural networks with self-stabilizing priors.
problem Brittleness and difficulty in training deep Bayesian neural networks.
method Signal propagation theory, reformulated ELBO, self-stabilizing priors.
result Improved convergence and robustness in training deeper networks and noisier settings.
PAC-Bayes bounds have been proposed to get risk estimates based on a training sample. In this paper the PAC-Bayes approach is combined with stability of the hypothesis learned by a Hilbert space valued algorithm. The PAC-Bayes setting is used with a Gaussian prior centered at the expected output. Thus a novelty of our …
Blade uses diffusion priors to accurately and calibratedly infer complex systems.
problem Derivative-free Bayesian inversion for high-dimensional, nonlinear problems with costly forward models.
method Blade employs an ensemble of interacting particles and diffusion models as priors, querying forward models only through evaluations.
result Blade produces well-calibrated posterior samples that existing methods cannot, improving with more iterations and particles.
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.
New Gaussian priors for neural networks improve scalability and Bayesian inference stability.
problem Scalability and stability issues in Bayesian neural network inference.
method Introduces a new Gaussian neural network prior with decreasing variance in network width, enabling stable MCMC sampling.
result The new prior enables stable MCMC sampling for Bayesian neural network inference, improving scalability and stability.
Dealing with high variance is a significant challenge in model-free reinforcement learning (RL). Existing methods are unreliable, exhibiting high variance in performance from run to run using different initializations/seeds. Focusing on problems arising in continuous control, we propose a functional regularization appr…
Proposes a method to learn system dynamics and region of attraction from trajectories.
problem Learning accurate dynamics and region of attraction from system trajectories.
method Uses local stability information as a prior to learn vector field and region of attraction.
result Efficient sampling and accurate estimate of dynamics in inner approximation of region of attraction.
Regularization improves generalization in Bayesian RL, shown through algorithmic stability.
problem Ensuring good generalization in Bayesian reinforcement learning.
method Algorithmic stability, using regularization and fast convergence rates for mirror descent.
result Regularization makes the optimal policy stable, improving generalization.
This paper enhances stability selection by evaluating overall results robustness and identifying optimal regularization values.
problem Improving the robustness and reliability of high-dimensional variable selection.
method Developed a stability estimator to evaluate stability of stability selection results, calibrating key parameters.
result Identified optimal regularization value and improved stability of variable selection.
Improved graph neural network bounds using graph diffusion matrix.
problem Empirical performance of graph neural networks on real-world graphs.
method Unified model of graph neural networks, focusing on feature diffusion matrix stability.
result Generalization bounds scale with largest singular value of feature diffusion matrix, smaller than prior bounds.
The paper presents a model-free method for stabilizing unknown control systems.
problem Stabilizing unknown control systems in engineering.
method Solving discounted LQR problems with increasing discount factors.
result The method efficiently recovers a stabilizing controller for linear and smooth nonlinear systems.
A new family of penalty functions, adaptive to likelihood, is introduced for model selection in general regression models. It arises naturally through assuming certain types of prior distribution on the regression parameters. To study stability properties of the penalized maximum likelihood estimator, two types of asym…
Stabilizing black-box algorithms through task-oriented randomization
problem Ensuring stability of black-box models
method Task-oriented randomization
result Established rigorous theoretical foundations and demonstrated effectiveness through simulations and real-world applications
Bayesian UQ matches frequentist UQ for adaptively collected data.
problem Uncertainty quantification for adaptive data collection.
method Extends Bernstein-von Mises theorem to adaptively collected data.
result Bayesian UQ asymptotically matches Wald-type frequentist UQ.
Adversarial attacks against neural networks in a regression setting are a critical yet understudied problem. In this work, we advance the state of the art by investigating adversarial attacks against regression networks and by formulating a more effective defense against these attacks. In particular, we take the perspe…
Probabilistic solvers improve stability for stiff systems.
problem Performance penalties for small steps in stiff systems.
method Probabilistic exponential integrators that include fast linear dynamics in the prior.
result Proven L-stability and probabilistic error accounting.
Study accelerates gradient methods in machine learning, revealing risk and stability connections.
problem Understanding the statistical risk of accelerated gradient methods in machine learning.
method Continuous-time analysis of Nesterov's accelerated gradient method and Polyak's heavy ball method for least squares regression.
result Connections between early stopping, stability, and curvature of loss function are revealed.
Bayesian framework improves LLM evaluation stability and transparency.
problem Pass@k and avg@N are unstable and misleading for LLMs.
method Bayesian evaluation with posterior estimates and credible intervals.
result Posterior-based evaluation yields stable and transparent rankings.
MMCGAN uses explicit manifold learning to improve GAN performance.
problem GAN mode collapse and unstable training.
method Introduces Minimum Manifold Coding (MMC) as a prior to guide GAN training.
result MMCGAN effectively alleviates mode collapse and stabilizes GAN training.
New bounds show faster convergence for learning algorithms.
problem Improving risk bounds for learning algorithms.
method Using algorithmic stability and common assumptions like Polyak-Lojasiewicz condition, smoothness, and Lipschitz continuity.
result Achieves convergence rate of O ( log 2 ( n ) / n 2 ) O(\log^2(n)/n^2) O ( log 2 ( n ) / n 2 ) with high probability. 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.
SGD works well with large learning rates at the edge of stability.
problem Stochasticity at the edge of stability in deep learning.
method Sharp convergence guarantees for SGD with multiclass cross-entropy loss.
result SGD self-stabilizes, ensuring convergence with large learning rates.
Proves constant scalar curvature Kähler metrics are very general.
problem Existence of constant scalar curvature Kähler metrics on smooth polarized varieties.
method Combining uniform arc K-stability and algebraic properties in families.
result The constant scalar curvature Kähler locus is very general.
Improved RL algorithm stabilizes unknown linear systems with polynomial regret.
problem Learning and stabilizing unknown linear dynamical systems.
method Proposes an algorithm with an improved exploration strategy for fast stabilization.
result Achieves i l d e O ( T ) ilde{\mathcal{O}}(\sqrt{T}) i l d e O ( T ) regret after T T T time steps. Stabilization of linear systems with unknown dynamics is a canonical problem in adaptive control. Since the lack of knowledge of system parameters can cause it to become destabilized, an adaptive stabilization procedure is needed prior to regulation. Therefore, the adaptive stabilization needs to be completed in finite…
New TD method stabilizes average-reward learning.
problem Stability issues in average-reward TD learning.
method Implicit fixed point update for average-reward TD( λ λ λ ). result Improved numerical stability and broader step-size range.
Paper addresses LSTM stability for thermal systems using infinity-norm.
problem Stability of LSTM networks in thermal systems.
method Derived ISS ∞ _{\infty} ∞ condition for LSTM, developed training strategy. result ISS ∞ _{\infty} ∞ -promoted LSTM outperforms other models in thermal system case study. Study on stability of GCNNs under graph perturbations.
problem Limited theoretical understanding of GCNN stability.
method Proposes a probabilistic framework to analyze GCNN stability under various graph perturbations.
result Demonstrates the importance of data distribution in stability analysis.
New Hida-Matérn kernels enable flexible process priors and efficient GP inference.
problem Flexible modeling of stationary processes with oscillatory components.
method Introducing a new class of covariance functions (Hida-Matérn kernels) and their state space representations.
result Efficient Gaussian Process inference and improved numerical stability.
Kernel-guided training stabilizes GANs by controlling discrepancies.
problem Stability and interpretability issues in GANs.
method Kernel-based regularization to control discrepancies in GAN loss function.
result Theoretical guarantees on stability of the training dynamics.
We consider the problem of estimating the class prior in an unlabeled dataset. Under the assumption that an additional labeled dataset is available, the class prior can be estimated by fitting a mixture of class-wise data distributions to the unlabeled data distribution. However, in practice, such an additional labeled…
New method improves generative modeling on convex domains using regularized mirror maps and Student-t priors.
problem Challenges in generative modeling on convex domains with heavy-tailed targets.
method Mirror Flow Matching with regularized mirror maps and Student-t priors.
result Empirically outperforms baselines and achieves competitive sample quality.
New framework uses score-based priors to solve ill-conditioned polynomial equations, improving signal recovery from noisy data.
problem Recovering signals from low-order moments in inverse problems, especially ill-conditioned polynomial equations.
method Integrates score-based diffusion priors with moment-based estimators to regularize and solve nonlinear inverse problems.
result Diffusion priors improve recovery from third-order moments and make super-resolution MTD feasible.
RINS-T solves time series inverse problems robustly without pretraining.
problem Recovering original signals from corrupted time series data.
method Implicit neural solvers with robust optimization techniques.
result RINS-T achieves high recovery performance without pretraining.
Study shows how to reduce data needed for learning under geometric constraints.
problem Learning high-dimensional data with geometric priors.
method Spherical harmonic decompositions and kernel methods for invariance and geometric stability.
result Improvements in sample complexity by leveraging group invariance, with asymptotic behavior depending on spectral properties.
This work examines the stability of GD and SGD near minima, revealing nonlinear dynamics that differ from linear analysis.
problem The stability of optimization algorithms like GD and SGD near minima is not well understood.
method The authors derive an exact criterion for stable oscillations of GD near minima in the multivariate setting, considering high-order derivatives.
result Nonlinear dynamics can diverge in expectation even if a single batch is unstable, challenging linear analysis.
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 stabilizes saddle-point optimization with unbounded gradients.
problem Stochastic saddle-point optimization faces instability due to large gradients.
method Proposes a regularization technique to stabilize iterates.
result Yields meaningful performance guarantees even with unbounded gradients.
A new data-adaptive prior stabilizes kernel learning in operators.
problem Learning kernels in operators from data is ill-posed due to nonlocal dependence.
method Introduces a data-adaptive prior to stabilize the Bayesian posterior mean.
result The data-adaptive prior achieves a stable posterior with small noise limits.
Flashback Learning balances model stability and plasticity in continual learning.
problem Balancing model stability and plasticity in continual learning.
method Flashback Learning (FL) uses a bidirectional regularization approach to balance stability and plasticity.
result FL improves model accuracy by up to 4.91% in Class-Incremental and 3.51% in Task-Incremental settings.
DAPS++ improves diffusion-based image restoration by decoupling prior and likelihood.
problem Decoupling prior and likelihood in diffusion-based inverse problems.
method Introducing DAPS++, which fully decouples diffusion-based initialization from likelihood-driven refinement.
result Achieves high computational efficiency and robust reconstruction performance.
New credit attribution methods for machine learning models using relaxed stability guarantees.
problem Ensuring proper attribution in generative models trained on existing works.
method Proposed new definitions of stability that allow for non-stable processing of a subset of datapoints with permission.
result Extended well-studied stability notions and provided a comprehensive characterization of learnability.
R2D2-Net improves Bayesian neural networks by preventing over-shrinkage of important weights.
problem Bayesian neural networks struggle with choosing appropriate priors, leading to over-shrinkage or poor predictive performance.
method Proposes R2D2-Net with an R^2-induced Dirichlet Decomposition prior and variational Gibbs inference algorithm.
result R2D2-Net effectively shrinks irrelevant coefficients while preventing key features from over-shrinkage.
New covering moves for 3-manifolds up to degree 4.
problem Relating colored link diagrams in 3-manifolds.
method Complete set of covering moves on braids in fixed degree d ≥ 4 d \geq 4 d ≥ 4 . result Two local tangle replacements are sufficient after stabilization to the same degree at least 4.
Study MAP estimation for PnP priors with SGD, proving convergence and demonstrating practical applications.
problem Theoretical analysis and practical implementation of PnP priors for Bayesian imaging problems.
method Maximum-a-posteriori estimation with Plug & Play priors and stochastic gradient descent.
result Convergence proof for MAP computation by PnP-SGD under realistic assumptions on the denoiser.
New method defends RL agents from poisoning attacks without MDP knowledge.
problem Poisoning attacks on RL systems can cause learning failures.
method Generic poisoning framework for online RL, Vulnerability-Aware Adversarial Critic Poison (VA2C-P).
result Successfully prevents RL agents from learning good policies or converging to target policies.
Rex solves the inverse problem for ODE/SDE solvers, improving precision and stability.
problem Inversion of ODE/SDE solvers is inaccurate and impractical for precision applications.
method Rex uses Lawson methods to convert explicit Runge-Kutta schemes into algebraically reversible ones.
result Rex achieves near-machine-precision reconstruction and improves generative models.
DAPS++ improves diffusion-based image restoration by decoupling prior and likelihood.
problem Decoupling prior and likelihood in diffusion-based inverse problems for better performance.
method Introducing DAPS++, which separates diffusion initialization from likelihood refinement.
result DAPS++ achieves high computational efficiency and robust reconstruction performance.