Large language models produce human-like text that drive a growing number of applications. However, recent literature and, increasingly, real world observations, have demonstrated that these models can generate language that is toxic, biased, untruthful or otherwise harmful. Though work to evaluate language model harms is under way, translating foresight about which harms may arise into rigorous benchmarks is not straightforward. To facilitate this translation, we outline six ways of characterizing harmful text which merit explicit consideration when designing new benchmarks. We then use these characteristics as a lens to identify trends and gaps in existing benchmarks. Finally, we apply them in a case study of the Perspective API, a toxicity classifier that is widely used in harm benchmarks. Our characteristics provide one piece of the bridge that translates between foresight and effective evaluation.

Most real world applications require dealing with stochasticity like sensor noise or predictive uncertainty, where formal specifications of desired behavior are inherently probabilistic. Despite the promise of formal verification in ensuring the reliability of neural networks, progress in the direction of probabilistic specifications has been limited. In this direction, we first introduce a general formulation of probabilistic specifications for neural networks, which captures both probabilistic networks (e.g., Bayesian neural networks, MC-Dropout networks) and uncertain inputs (distributions over inputs arising from sensor noise or other perturbations). We then propose a general technique to verify such specifications by generalizing the notion of Lagrangian duality, replacing standard Lagrangian multipliers with "functional multipliers" that can be arbitrary functions of the activations at a given layer. We show that an optimal choice of functional multipliers leads to exact verification (i.e., sound and complete verification), and for specific forms of multipliers, we develop tractable practical verification algorithms. We empirically validate our algorithms by applying them to Bayesian Neural Networks (BNNs) and MC Dropout Networks, and certifying properties such as adversarial robustness and robust detection of out-of-distribution (OOD) data. On these tasks we are able to provide significantly stronger guarantees when compared to prior work -- for instance, for a VGG-64 MC-Dropout CNN trained on CIFAR-10 in a verification-agnostic manner, we improve the certified AUC (a verified lower bound on the true AUC) for robust OOD detection (on CIFAR-100) from $0 \% \rightarrow 29\%$. Similarly, for a BNN trained on MNIST, we improve on the $\ell_\infty$ robust accuracy from $60.2 \% \rightarrow 74.6\%$. Further, on a novel specification -- distributionally robust OOD detection -- we improve on the certified AUC from $5\% \rightarrow 23\%$.

Convex relaxations have emerged as a promising approach for verifying properties of neural networks, but widely used using Linear Programming (LP) relaxations only provide meaningful certificates when networks are specifically trained to facilitate verification. This precludes many important applications which involve \emph{verification-agnostic} networks that are not trained specifically to promote verifiability. On the other hand, semidefinite programming (SDP) relaxations have shown success on verification-agnostic networks, such as adversarially trained image classifiers without additional regularization, but do not currently scale beyond small networks due to poor time and space asymptotics. In this work, we propose a first-order dual SDP algorithm that provides (1) any-time bounds (2) requires memory only linear in the total number of network activations and (3) has per-iteration complexity that scales linearly with the complexity of a forward/backward pass through the network. By exploiting iterative eigenvector methods, we express all solver operations in terms of forward and backward passes through the network, enabling efficient use of hardware optimized for deep learning. This allows us to dramatically improve the magnitude of $\ell_\infty$ perturbations for which we can verify robustness verification-agnostic networks ($1\% \to 88\%$ on MNIST, $6\%\to 40\%$ on CIFAR-10). We also demonstrate tight verification for a quadratic stability specification for the decoder of a variational autoencoder.

Neural networks in real-world applications have to satisfy critical properties such as safety and reliability. The analysis of such properties typically requires extracting information through computing pre-images of the network transformations, but it is well-known that explicit computation of pre-images is intractable. We introduce new methods for computing compact symbolic abstractions of pre-images by computing their overapproximations and underapproximations through all layers. The abstraction of pre-images enables formal analysis and knowledge extraction without affecting standard learning algorithms. We use inverse abstractions to automatically extract simple control laws and compact representations for pre-images corresponding to unsafe outputs. We illustrate that the extracted abstractions are interpretable and can be used for analyzing complex properties.

We propose a new abstraction refinement procedure based on machine learning to improve the performance of nonlinear constraint solving algorithms on large-scale problems. The proposed approach decomposes the original set of constraints into smaller subsets, and uses learning algorithms to propose sequences of abstractions that take the form of conjunctions of classifiers. The core procedure is a refinement loop that keeps improving the learned results based on counterexamples that are obtained from partial constraints that are easy to solve. Experiments show that the proposed techniques significantly improve the performance of state-of-the-art constraint solvers on many challenging benchmarks. The mechanism is capable of producing intermediate symbolic abstractions that are also important for many applications and for understanding the internal structures of hard constraint solving problems.