# Training Safe Neural Networks with Global SDP Bounds

arXiv: https://arxiv.org/abs/2409.09687 · HTML: https://mlsanity.com/paper/2409.09687/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 27 references that are in the map.
- First posted on arXiv 15 Sep 2024.

## Builds on (most cited first, 17 of 17)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers](https://mlsanity.com/paper/2011.13824/) (2020)
- [Formal Security Analysis of Neural Networks using Symbolic Intervals](https://mlsanity.com/paper/1804.10829/) (2018)
- [Semidefinite relaxations for certifying robustness to adversarial examples](https://mlsanity.com/paper/1811.01057/) (2018)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [Complete Verification via Multi-Neuron Relaxation Guided Branch-and-Bound](https://mlsanity.com/paper/2205.00263/) (2022)
- [Reach-SDP: Reachability Analysis of Closed-Loop Systems with Neural Network Controllers via Semidefinite Programming](https://mlsanity.com/paper/2004.07876/) (2020)
- [Reachability Analysis of Neural Feedback Loops](https://mlsanity.com/paper/2108.04140/) (2021)
- [The Fourth International Verification of Neural Networks Competition (VNN-COMP 2023): Summary and Results](https://mlsanity.com/paper/2312.16760/) (2023)
- [Provably Bounding Neural Network Preimages](https://mlsanity.com/paper/2302.01404/) (2023)
- [DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization](https://mlsanity.com/paper/1706.02586/) (2017)
- [Adversarial Training and Provable Robustness: A Tale of Two Objectives](https://mlsanity.com/paper/2008.06081/) (2020)
- [A Unified View of SDP-based Neural Network Verification through Completely Positive Programming](https://mlsanity.com/paper/2203.03034/) (2022)
- [Sparse Polynomial Optimisation for Neural Network Verification](https://mlsanity.com/paper/2202.02241/) (2022)
- [PREMAP: A Unifying PREiMage APproximation Framework for Neural Networks](https://mlsanity.com/paper/2408.09262/) (2024)
- [Sparse non-SOS Putinar-type Positivstellens"atze](https://mlsanity.com/paper/2110.10079/) (2021)

## Abstract (arXiv)

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.