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On the State Evolution of Approximate Message Passing with Discontinuous Denoisers — arXiv:2610.08256

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.08256
License (as archived): CC0-1.0
Archived: 2026-10-07T12:10:21.921Z
SHA-256 of the archived text: 92286054a1af7c92410a0026bf212334289d91f3707079a12497cb6ef11740a0
Stable URL of this page: https://metraipolis.com/documento/dc_aa2eadd8dcc4

How to cite

On the State Evolution of Approximate Message Passing with Discontinuous Denoisers — arXiv:2610.08256 — arXiv (en), https://arxiv.org/abs/2610.08256 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_aa2eadd8dcc4 (Metraipolis archive dc_aa2eadd8dcc4, sha256 92286054a1af7c92410a0026bf212334289d91f3707079a12497cb6ef11740a0)

BibTeX

@misc{dcaa2eadd8dcc4,
  title = {On the State Evolution of Approximate Message Passing with Discontinuous Denoisers — arXiv:2610.08256},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.08256},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_aa2eadd8dcc4; sha256 92286054a1af7c92410a0026bf212334289d91f3707079a12497cb6ef11740a0},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.08256. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We consider approximate message passing (AMP) with discontinuous denoisers, such as hard slicers, quantizers and hard thresholding, for which the classical state evolution (SE) analysis does not apply. It is first shown that the standard Onsager coefficient; i.e., the average pointwise derivative of the denoiser, misses a boundary term, namely, the sum over the jumps of the jump size times the density of the denoiser input at the jump. Then, for real independent and identically distributed (i.i.d.) Gaussian matrices, a positive noise variance, a fixed number of iterations and a prior with finite second moment, we transfer the Lipschitz SE theorem directly to denoisers, fixed in advance, that are continuously differentiable with bounded derivative except at finitely many jumps, by bounding the distance between the iterates of AMP and of AMP on Lipschitz ramps of the denoisers through the fraction of inputs that cross a jump. It is thereby proven that AMP follows SE, also for test functions such as symbol errors, if its Onsager coefficient contains the boundary term, evaluated either along SE or, as we propose, at the noise level estimated from the residual, with the density computed from the known prior. Simulation results with 4- and 8-level pulse amplitude modulation (PAM) demonstrate that AMP with a hard slicer, whose standard coefficient is identically zero, fails with this coefficient, while with the proposed one, it follows SE and comes close to Bayes-optimal AMP.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.IT, nuovi lavori del giorno).
Categorie arXiv: Information Theory (cs.IT).
Pagina del lavoro: https://arxiv.org/abs/2610.08256 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T11:42:17.271Z dalla pagina https://arxiv.org/list/math.IT/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).