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Researchers have developed neural network verification algorithms motivated by the need to characterize the robustness of deep neural networks. The verifiers aspire to answer whether a neural network guarantees certain properties with…
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…
Boolean optimization finds a wide range of application domains, that motivated a number of different organizations of Boolean optimizers since the mid 90s. Some of the most successful approaches are based on iterative calls to an NP oracle,…
Failures in satellite components are costly and challenging to address, often requiring significant human and material resources. Embedding a hybrid AI-based system for fault detection directly in the satellite can greatly reduce this…
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…
The prevalence of neural networks in society is expanding at an increasing rate. It is becoming clear that providing robust guarantees on systems that use neural networks is very important, especially in safety-critical applications. A…
The point estimates of ReLU classification networks---arguably the most widely used neural network architecture---have been shown to yield arbitrarily high confidence far away from the training data. This architecture, in conjunction with a…
When optimizing a nonlinear objective, one can employ a neural network as a surrogate for the nonlinear function. However, the resulting optimization model can be time-consuming to solve globally with exact methods. As a result, local…
The reasoning capabilities of large language models (LLMs) have been significantly improved through reinforcement learning (RL). Nevertheless, LLMs still struggle to consistently verify their own reasoning traces. This raises the research…
Barrier functions are a general framework for establishing a safety guarantee for a system. However, there is no general method for finding these functions. To address this shortcoming, recent approaches use self-supervised learning…
Although neural networks are widely used, it remains challenging to formally verify the safety and robustness of neural networks in real-world applications. Existing methods are designed to verify the network before deployment, which are…
We introduce a new framework for the exact point-wise $\ell_p$ robustness verification problem that exploits the layer-wise geometric structure of deep feed-forward networks with rectified linear activations (ReLU networks). The activation…
Formal verification is only as good as the specification of a system, which is also true for neural network verification. Existing specifications follow the paradigm of data as specification, where the local neighborhood around a reference…
The NP-hard problem of optimizing a shallow ReLU network can be characterized as a combinatorial search over each training example's activation pattern followed by a constrained convex problem given a fixed set of activation patterns. We…
As deep neural networks are increasingly being deployed in practice, their efficiency has become an important issue. While there are compression techniques for reducing the network's size, energy consumption and computational requirement,…
We provide the global optimization community with new optimality proofs for six deceptive benchmark functions (five bound-constrained functions and one nonlinearly constrained problem). These highly multimodal nonlinear test problems are…
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…
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…
Solving non-convex, NP-hard optimization problems is crucial for training machine learning models, including neural networks. However, non-convexity often leads to black-box machine learning models with unclear inner workings. While convex…
Binarized neural networks (BNNs) are feedforward neural networks with binary weights and activation functions. In the context of using a BNN for classification, the verification problem seeks to determine whether a small perturbation of a…