Related papers: Efficient Neural Network Robustness Certification …

In this paper, we consider the problem of certifying the robustness of neural networks to perturbed and adversarial input data. Such certification is imperative for the application of neural networks in safety-critical decision-making and…

Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive…

The reliable deployment of neural networks in control systems requires rigorous robustness guarantees. In this paper, we obtain tight robustness certificates over convex attack sets for min-max representations of ReLU neural networks by…

Recent works show that Graph Neural Networks (GNNs) are highly non-robust with respect to adversarial attacks on both the graph structure and the node attributes, making their outcomes unreliable. We propose the first method for certifiable…

A globally robust deep neural network resists perturbations on all meaningful inputs. Current robustness certification methods emphasize local robustness, struggling to scale and generalize. This paper presents a systematic and efficient…

The robustness of deep neural networks has received significant interest recently, especially when being deployed in safety-critical systems, as it is important to analyze how sensitive the model output is under input perturbations. While…

Recent work provides promising evidence that Physics-Informed Neural Networks (PINN) can efficiently solve partial differential equations (PDE). However, previous works have failed to provide guarantees on the worst-case residual error of a…

A robustness certificate is the minimum distance of a given input to the decision boundary of the classifier (or its lower bound). For {\it any} input perturbations with a magnitude smaller than the certificate value, the classification…

We study neural networks with trainable low-degree rational activation functions and show that they are more expressive and parameter-efficient than modern piecewise-linear and smooth activations such as ELU, LeakyReLU, LogSigmoid, PReLU,…

Activation functions are non-linearities in neural networks that allow them to learn complex mapping between inputs and outputs. Typical choices for activation functions are ReLU, Tanh, Sigmoid etc., where the choice generally depends on…

Verification of neural networks enables us to gauge their robustness against adversarial attacks. Verification algorithms fall into two categories: exact verifiers that run in exponential time and relaxed verifiers that are efficient but…

As spiking neural networks (SNNs) are deployed increasingly in real-world efficiency critical applications, the security concerns in SNNs attract more attention. Currently, researchers have already demonstrated an SNN can be attacked with…

Deep neural networks have emerged as a widely used and effective means for tackling complex, real-world problems. However, a major obstacle in applying them to safety-critical systems is the great difficulty in providing formal guarantees…

We consider the problem of certifying the robustness of deep neural networks against real-world distribution shifts. To do so, we bridge the gap between hand-crafted specifications and realistic deployment settings by proposing a novel…

The choice of activation function in deep networks has a significant effect on the training dynamics and task performance. At present, the most effective and widely-used activation function is ReLU. However, because of the non-zero mean,…

Formal certification of Neural Networks (NNs) is crucial for ensuring their safety, fairness, and robustness. Unfortunately, on the one hand, sound and complete certification algorithms of ReLU-based NNs do not scale to large-scale NNs. On…

Recent work have demonstrated that robustness (to "corruption") can be at odds with generalization. Adversarial training, for instance, aims to reduce the problematic susceptibility of modern neural networks to small data perturbations.…

The robustness of convolutional neural networks (CNNs) is vital to modern AI-driven systems. It can be quantified by formal verification by providing a certified lower bound, within which any perturbation does not alter the original input's…

Graph convolutional neural networks (GCNs) are powerful tools for learning graph-based knowledge representations from training data. However, they are vulnerable to small perturbations in the input graph, which makes them susceptible to…

We consider neural networks with rational activation functions. The choice of the nonlinear activation function in deep learning architectures is crucial and heavily impacts the performance of a neural network. We establish optimal bounds…