Reproduce “LMI-Net: Linear Matrix Inequality--Constrained Neural Networks via Differentiable Projection Layers” on OpenResearch

About this paper

Sunbochen Tang, Andrea Goertzen, Navid Azizan

LMI-Net, developed by researchers at MIT, introduces a neural network architecture that inherently satisfies input-dependent Linear Matrix Inequality (LMI) constraints by employing a differentiable projection layer. This approach ensures formal guarantees for learned control and certification tasks, achieving inference speeds 9-35 times faster than traditional numerical solvers while maintaining strict constraint satisfaction.

Key insights

• Complex LMI constraints can be robustly enforced within neural networks by decomposing them into simpler convex sets and iteratively projecting onto their intersection using methods like Douglas-Rachford splitting.
• Efficient end-to-end training of such constrained networks is possible by employing implicit differentiation, which avoids costly unrolling of all projection iterations for gradient computation.
• The number of Douglas-Rachford iterations can be tuned at inference time, offering a post-training trade-off between computational speed and the tightness of feasibility guarantees for the LMI-constrained output.

Summary by alphaXiv.