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arXiv Machine Learning By Ege Gursoy, Nicolas Mansard

Sparse Sum-of-Squares Layers for Certified Learning

Read the original on arXiv Machine Learning →

The paper introduces Sparse Sum-of-Squares (SOS) Layers, a new type of differentiable layer that reuses the sparse structure of forward semidefinite programming (SDP) solves during backpropagation. By avoiding dense certificate construction, the method achieves up to 2.7× faster warm‑call times and reduces memory usage from 160 GiB to 1.7 GiB on large problems. Experiments demonstrate its effectiveness across sparse polynomial certification, control, combinatorial relaxations, robotics, oscillator chains, and pose‑graph synchronization, achieving zero certified violations on unseen instances with far fewer optimization solves than finite‑difference approaches.

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