Research map / Learning theory and algorithms / Sample complexity
On the Power of Compressed Sensing with Generative Models
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Lower bound on measurements for compressed sensing with L-Lipschitz generative models (Theorem 1.1), showing the Bora et al. 2017 bound m=O(k + k log(Lr/δ)) is tight | Lipschitz generative model compressed sensing · theoretical (non-uniform recovery, l2 and l1 guarantees) | measurements m needed | No clear effect |
| Additive error δ is necessary for Lipschitz generative model recovery; with δ=0 recovery needs m=Ω(n) | Lipschitz generative model recovery · theoretical | measurements m needed | No clear effect |
| ReLU network with 2 hidden layers and width O(nk) whose range is exactly the k-sparse vectors (generative models generalize sparsity) | generative representation of sparse structure · theoretical | range equals k-sparse vectors | No clear effect |
| Low-width 2-hidden-layer ReLU generator (width O(n)) whose range is all k-sparse vectors, via randomized construction | sparsity-producing generator · theoretical | network width | Helped |
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