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We prove that finding all globally optimal two-layer ReLU neural networks can be performed by solving a convex optimization program with cone constraints. Our analysis is novel, characterizes all optimal solutions, and does not leverage…

Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…

Due to their expressive power, neural networks (NNs) are promising templates for functional optimization problems, particularly for reach-avoid certificate generation for systems governed by stochastic differential equations (SDEs).…

Formal verification of transformers has become increasingly important due to their widespread deployment in safety-critical applications. Compared to classic neural networks, the inferences of transformers involve highly complex…

Certified defenses against small-norm adversarial examples have received growing attention in recent years; though certified accuracies of state-of-the-art methods remain far below their non-robust counterparts, despite the fact that…

Deep neural networks have been widely adopted in many vision and robotics applications with visual inputs. It is essential to verify its robustness against semantic transformation perturbations, such as brightness and contrast. However,…

Certified robustness is a critical property for deploying neural networks (NN) in safety-critical applications. A principle approach to achieving such guarantees is to constrain the global Lipschitz constant of the network. However,…

We explore the concept of co-design in the context of neural network verification. Specifically, we aim to train deep neural networks that not only are robust to adversarial perturbations but also whose robustness can be verified more…

Deep Neural Network-based systems are now the state-of-the-art in many robotics tasks, but their application in safety-critical domains remains dangerous without formal guarantees on network robustness. Small perturbations to sensor inputs…

The growing reliance on artificial intelligence in safety- and security-critical applications is raising concerns about the robustness of neural networks to erroneous or adversarial input. Certification is a methodology for ensuring model…

Deep neural networks deployed in safety-critical, resource-constrained environments must balance efficiency and robustness. Existing methods treat compression and certified robustness as separate goals, compromising either efficiency or…

State-of-the-art neural network verifiers are fundamentally based on one of two paradigms: either encoding the whole verification problem via tight multi-neuron convex relaxations or applying a Branch-and-Bound (BaB) procedure leveraging…

In recent years, the notion of local robustness (or robustness for short) has emerged as a desirable property of deep neural networks. Intuitively, robustness means that small perturbations to an input do not cause the network to perform…

Recently, techniques have been developed to provably guarantee the robustness of a classifier to adversarial perturbations of bounded L_1 and L_2 magnitudes by using randomized smoothing: the robust classification is a consensus of base…

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…

Prior work on neural network verification has focused on specifications that are linear functions of the output of the network, e.g., invariance of the classifier output under adversarial perturbations of the input. In this paper, we extend…

Certificates of polynomial nonnegativity can be used to obtain tight dual bounds for polynomial optimization problems. We consider Sums of Nonnegative Circuit (SONC) polynomials certificates, which are well suited for sparse problems since…

We present a theoretically grounded approach to train deep neural networks, including recurrent networks, subject to class-dependent label noise. We propose two procedures for loss correction that are agnostic to both application domain and…

It has been observed in practical applications and in theoretical analysis that over-parametrization helps to find good minima in neural network training. Similarly, in this article we study widening and deepening neural networks by a…

Machine learning models are highly vulnerable to label flipping, i.e., the adversarial modification (poisoning) of training labels to compromise performance. Thus, deriving robustness certificates is important to guarantee that test…