Related papers: Do stable neural networks exist for classification…
Deep neural networks have shown remarkable performance when trained on independent and identically distributed data from a fixed set of classes. However, in real-world scenarios, it can be desirable to train models on a continuous stream of…
Deep learning has achieved remarkable success across a wide range of domains, significantly expanding the frontiers of what is achievable in artificial intelligence. Yet, despite these advances, critical challenges remain -- most notably,…
Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on…
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…
Establishing Lipschitz stability estimates is crucial for ensuring the mathematical robustness of neural network (NN) approximations in machine learning (ML)-based parameter estimation, particularly in physics-informed settings. In this…
Most generalization bounds in learning theory are based on some measure of the complexity of the hypothesis class used, independently of any algorithm. In contrast, the notion of algorithmic stability can be used to derive tight…
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…
Spiking neural networks (SNNs) are a promising paradigm for energy-efficient computation, yet their theoretical foundations-especially regarding stability and robustness-remain limited compared to artificial neural networks. In this work,…
This work establishes rigorous, novel and widely applicable stability guarantees and transferability bounds for graph convolutional networks -- without reference to any underlying limit object or statistical distribution. Crucially,…
We discover restrained numerical instabilities in current training practices of deep networks with stochastic gradient descent (SGD), and its variants. We show numerical error (on the order of the smallest floating point bit and thus the…
The stability of statistical analysis is an important indicator for reproducibility, which is one main principle of scientific method. It entails that similar statistical conclusions can be reached based on independent samples from the same…
The existence of instabilities, for example in the form of adversarial examples, has given rise to a highly active area of research concerning itself with understanding and enhancing the stability of neural networks. We focus on a popular…
We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…
This note shows that, for a fixed Lipschitz constant $L > 0$, one layer neural networks that are $L$-Lipschitz are dense in the set of all $L$-Lipschitz functions with respect to the uniform norm on bounded sets.
Stability is a central property in learning and statistics promising the output of an algorithm $A$ does not change substantially when applied to similar datasets $S$ and $S'$. It is an elementary fact that any sufficiently stable algorithm…
Algorithmic stability is a central concept in statistics and learning theory that measures how sensitive an algorithm's output is to small changes in the training data. Stability plays a crucial role in understanding generalization,…
Although the property of strong metric subregularity of set-valued mappings has been present in the literature under various names and with various definitions for more than two decades, it has attracted much less attention than its older…
Despite the large success of deep neural networks (DNN) in recent years, most neural networks still lack mathematical guarantees in terms of stability. For instance, DNNs are vulnerable to small or even imperceptible input perturbations, so…
Verifying correctness of deep neural networks (DNNs) is challenging. We study a generic reachability problem for feed-forward DNNs which, for a given set of inputs to the network and a Lipschitz-continuous function over its outputs,…
Although overparameterized models have achieved remarkable practical success, their theoretical properties, particularly their generalization behavior, remain incompletely understood. The well known double descents phenomenon suggests that…