Training Safe Neural Networks with Global SDP Bounds

TL;DR

This paper introduces a new training method for neural networks that provides formal safety guarantees by using semidefinite programming, effectively verifying safety over large input regions in high-dimensional spaces.

Contribution

It develops an ADMM-based training scheme that achieves provably perfect recall on high-dimensional datasets, advancing neural network verification techniques.

Findings

Achieved perfect recall on the Adversarial Spheres dataset with input dimension up to 40

Introduced a scalable SDP-based verification method for high-dimensional safety guarantees

Enhanced the reliability of neural networks for safety-critical applications

Abstract

This paper presents a novel approach to training neural networks with formal safety guarantees using semidefinite programming (SDP) for verification. Our method focuses on verifying safety over large, high-dimensional input regions, addressing limitations of existing techniques that focus on adversarial robustness bounds. We introduce an ADMM-based training scheme for an accurate neural network classifier on the Adversarial Spheres dataset, achieving provably perfect recall with input dimensions up to $d=40$. This work advances the development of reliable neural network verification methods for high-dimensional systems, with potential applications in safe RL policies.