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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.07095 |
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| _version_ | 1866917195778359296 |
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| author | Wadayama, Tadashi Takahashi, Takumi |
| author_facet | Wadayama, Tadashi Takahashi, Takumi |
| contents | We propose score-based VAMP (SC-VAMP), a variant of vector approximate message passing (VAMP) in which the Onsager correction is expressed and computed via conditional Fisher information, thereby enabling a Jacobian-free implementation. Using learned score functions, SC-VAMP constructs nonlinear MMSE estimators through Tweedie's formula and derives the corresponding Onsager terms from the score-norm statistics, avoiding the need for analytical derivatives of the prior or likelihood. When combined with random orthogonal/unitary mixing to mitigate non-ideal, structured or correlated sensing settings, the proposed framework extends VAMP to complex black-box inference problems where explicit modeling is intractable. Finally, by leveraging the entropic CLT, we provide an information-theoretic perspective on the Gaussian approximation underlying SE, offering insight into the decoupling principle beyond idealized i.i.d. settings, including nonlinear regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07095 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Score-Based VAMP with Fisher-Information-Based Onsager Correction Wadayama, Tadashi Takahashi, Takumi Information Theory We propose score-based VAMP (SC-VAMP), a variant of vector approximate message passing (VAMP) in which the Onsager correction is expressed and computed via conditional Fisher information, thereby enabling a Jacobian-free implementation. Using learned score functions, SC-VAMP constructs nonlinear MMSE estimators through Tweedie's formula and derives the corresponding Onsager terms from the score-norm statistics, avoiding the need for analytical derivatives of the prior or likelihood. When combined with random orthogonal/unitary mixing to mitigate non-ideal, structured or correlated sensing settings, the proposed framework extends VAMP to complex black-box inference problems where explicit modeling is intractable. Finally, by leveraging the entropic CLT, we provide an information-theoretic perspective on the Gaussian approximation underlying SE, offering insight into the decoupling principle beyond idealized i.i.d. settings, including nonlinear regimes. |
| title | Score-Based VAMP with Fisher-Information-Based Onsager Correction |
| topic | Information Theory |
| url | https://arxiv.org/abs/2601.07095 |