相关论文: Why Smooth Stability Assumptions Fail for ReLU Lea…

We study the type of solutions to which stochastic gradient descent converges when used to train a single hidden-layer multivariate ReLU network with the quadratic loss. Our results are based on a dynamical stability analysis. In the…

Despite a great deal of research, it is still unclear why neural networks are so susceptible to adversarial examples. In this work, we identify natural settings where depth-$2$ ReLU networks trained with gradient flow are provably…

Algorithmic stability is a classical framework for analyzing the generalization error of learning algorithms. It predicts that an algorithm has small generalization error if it is insensitive to small perturbations in the training set such…

Dynamical systems theory has recently been applied in optimization to prove that gradient descent algorithms bypass so-called strict saddle points of the loss function. However, in many modern machine learning applications, the required…

In this paper, we study the implicit regularization of stochastic gradient descent (SGD) through the lens of {\em dynamical stability} (Wu et al., 2018). We start by revising existing stability analyses of SGD, showing how the Frobenius…

This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…

We study the generalization of two-layer ReLU neural networks in a univariate nonparametric regression problem with noisy labels. This is a problem where kernels (\emph{e.g.} NTK) are provably sub-optimal and benign overfitting does not…

It has been shown that neural network classifiers are not robust. This raises concerns about their usage in safety-critical systems. We propose in this paper a regularization scheme for ReLU networks which provably improves the robustness…

Stability is a general notion that quantifies the sensitivity of a learning algorithm's output to small change in the training dataset (e.g. deletion or replacement of a single training sample). Such conditions have recently been shown to…

This paper presents sufficient conditions for the stability and $\ell_2$-gain performance of recurrent neural networks (RNNs) with ReLU activation functions. These conditions are derived by combining Lyapunov/dissipativity theory with…

Stability is a fundamental property of dynamical systems, yet to this date it has had little bearing on the practice of recurrent neural networks. In this work, we conduct a thorough investigation of stable recurrent models. Theoretically,…

Algorithmic stability is among the most potent techniques in generalization analysis. However, its derivation usually requires a stepsize $\eta_t = \mathcal{O}(1/t)$ under non-convex training regimes, where $t$ denotes iterations. This…

We develop a finite-dimensional sensitivity framework for studying stability in learning systems whose states include representations, parameters, and update variables. The central object is the \emph{Learning Stability Profile}, a…

We study the computational problem of the stationarity test for the empirical loss of neural networks with ReLU activation functions. Our contributions are: Hardness: We show that checking a certain first-order approximate stationarity…

Explainability models are now prevalent within machine learning to address the black-box nature of neural networks. The question now is which explainability model is most effective. Probabilistic Lipschitzness has demonstrated that the…

In this work, we study the implications of the implicit bias of gradient flow on generalization and adversarial robustness in ReLU networks. We focus on a setting where the data consists of clusters and the correlations between cluster…

Exponential generalization bounds with near-tight rates have recently been established for uniformly stable learning algorithms. The notion of uniform stability, however, is stringent in the sense that it is invariant to the data-generating…

A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…

We study the optimization landscape and the stability properties of training problems with squared loss for neural networks and general nonlinear conic approximation schemes. It is demonstrated that, if a nonlinear conic approximation…

This work studies the behavior of shallow ReLU networks trained with the logistic loss via gradient descent on binary classification data where the underlying data distribution is general, and the (optimal) Bayes risk is not necessarily…