A score-matching procedure driven by state evolution trains a neural network to replace the analytically intractable MMSE denoiser, allowing Bayes-GAMP to achieve its asymptotic optimality for arbitrary complex nonlinear observation mappings under ideal training.
Optimal errors and phase transitions in hig h- dimensional generalized linear models,
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State-Evolution-based Score Matching for Generalized Approximate Message Passing
A score-matching procedure driven by state evolution trains a neural network to replace the analytically intractable MMSE denoiser, allowing Bayes-GAMP to achieve its asymptotic optimality for arbitrary complex nonlinear observation mappings under ideal training.