Generative-model compressed sensing requires at least Ω(k log L) measurements for L-Lipschitz models and Ω(kd log w / log n) for ReLU networks, matching prior upper bounds up to small gaps.
Information- theoretically optimal compressed sensing via spatial coupling and ap- proximate message passing,
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Information-Theoretic Lower Bounds for Compressive Sensing with Generative Models
Generative-model compressed sensing requires at least Ω(k log L) measurements for L-Lipschitz models and Ω(kd log w / log n) for ReLU networks, matching prior upper bounds up to small gaps.