$(\text{DNN})^2$: Doubly Non-Negative Relaxations for Deep Neural Networks
Existing linear program (LP) and semidefinite program (SDP) relaxations for rectified linear unit (ReLU) neural network (NN) verification yield overly-conservative safety guarantees due to significant relaxation gaps. While the completely positive program (CPP) formulation closes this gap, it is NP-hard to solve. Its cheapest tractable relaxation, the doubly non-negative program (DNN), retains critical constraints as an SDP, but one whose size exceeds the reach of interior-point methods at practical scale. While Burer-Monteiro (BM) factorization has been applied to make SDP-based verification scalable, no such result exists for the strictly tighter DNN formulation. A key obstacle is that ...
| Authors | Hanna Jiamei Zhang, Alan Papalia, Michael Everett et al. |
|---|---|
| Primary category | cs.LG |
| Published | 25 August 2026 |
| Last updated at source | 25 August 2026 |
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