Generative-model compressed sensing requires at least 惟(k log L) measurements for L-Lipschitz models and 惟(kd log w / log n) for ReLU networks, matching prior upper bounds up to small gaps.
Sharp thresholds for high-dimensional and noisy sparsity recovery using 饾搧1-constrained quadratic programming (Lasso),
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Information-Theoretic Lower Bounds for Compressive Sensing with Generative Models
Generative-model compressed sensing requires at least 惟(k log L) measurements for L-Lipschitz models and 惟(kd log w / log n) for ReLU networks, matching prior upper bounds up to small gaps.