Edward W. Ayers

Zhangir Azerbayev, Bartosz Piotrowski, Hailey Schoelkopf et al.

We introduce ProofNet, a benchmark for autoformalization and formal proving of undergraduate-level mathematics. The ProofNet benchmarks consists of 371 examples, each consisting of a formal theorem statement in Lean 3, a natural language theorem statement, and a natural language proof. The problems are primarily drawn from popular undergraduate pure mathematics textbooks and cover topics such as real and complex analysis, linear algebra, abstract algebra, and topology. We intend for ProofNet to be a challenging benchmark that will drive progress in autoformalization and automatic theorem proving. We report baseline results on statement autoformalization via in-context learning. Moreover, we introduce two novel statement autoformalization methods: prompt retrieval and distilled backtranslation.

Jesse Michael Han, Jason Rute, Yuhuai Wu et al.

Labeled data for imitation learning of theorem proving in large libraries of formalized mathematics is scarce as such libraries require years of concentrated effort by human specialists to be built. This is particularly challenging when applying large Transformer language models to tactic prediction, because the scaling of performance with respect to model size is quickly disrupted in the data-scarce, easily-overfitted regime. We propose PACT ({\bf P}roof {\bf A}rtifact {\bf C}o-{\bf T}raining), a general methodology for extracting abundant self-supervised data from kernel-level proof terms for co-training alongside the usual tactic prediction objective. We apply this methodology to Lean, an interactive proof assistant which hosts some of the most sophisticated formalized mathematics to date. We instrument Lean with a neural theorem prover driven by a Transformer language model and show that PACT improves theorem proving success rate on a held-out suite of test theorems from 32\% to 48\%.

Edward Ayers, Francisco Eiras, Majd Hawasly et al.

Deep Neural Networks (DNNs) are finding important applications in safety-critical systems such as Autonomous Vehicles (AVs), where perceiving the environment correctly and robustly is necessary for safe operation. Raising unique challenges for assurance due to their black-box nature, DNNs pose a fundamental problem for regulatory acceptance of these types of systems. Robust training --- training to minimize excessive sensitivity to small changes in input --- has emerged as one promising technique to address this challenge. However, existing robust training tools are inconvenient to use or apply to existing codebases and models: they typically only support a small subset of model elements and require users to extensively rewrite the training code. In this paper we introduce a novel framework, PaRoT, developed on the popular TensorFlow platform, that greatly reduces the barrier to entry. Our framework enables robust training to be performed on arbitrary DNNs without any rewrites to the model. We demonstrate that our framework's performance is comparable to prior art, and exemplify its ease of use on off-the-shelf, trained models and its testing capabilities on a real-world industrial application: a traffic light detection network.