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arXiv Machine Learning By Max Lovig, Tianhao Wang, Zhou Fan

On Universality of Non-Separable Approximate Message Passing Algorithms

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The paper studies universality in non‑separable Approximate Message Passing (AMP) algorithms. It introduces a Bounded Composition Property (BCP) for polynomial non‑linearities and a BCP‑approximability condition for Lipschitz AMP, showing that these conditions guarantee state‑evolution universality for matrices with non‑Gaussian entries. The authors demonstrate that many common non‑separable non‑linearities—such as local denoisers, spectral denoisers, and compositions of separable functions with generic linear maps—satisfy these conditions, thereby extending universality results beyond Gaussian or rotationally‑invariant data.

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