Research map / Learning theory and algorithms / Sample complexity
Robust One-Bit Recovery via ReLU Generative Networks: Near-Optimal Statistical Rate and Global Landscape Analysis
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use an unconstrained ERM with uniform dithering and a ReLU generative prior | one-bit compressed sensing with mean-zero, isotropic sub-exponential measurements · Uniform recovery over G(R^k) ∩ B₂ᵈ(R) | sample complexity: \widetilde{\mathcal{O}}(kn \log d /\varepsilon^2) | Helped |
| Use the proposed generative-prior recovery framework for shallow networks | one-bit compressed sensing · Shallow ReLU networks, k ≪ d | sample complexity: at least \Omega \big( k \log(d/k)/\varepsilon^2 \big); matches the information-theoretic lower bound up to logarithm fac | Helped |
| Use ReLU weights satisfying WDC and the stated further assumptions | the proposed empirical risk · Dithered one-bit recovery | global minimizer location | Helped |
| Use ReLU weights satisfying WDC | the proposed empirical risk · Dithered one-bit recovery | stationary-point landscape | Helped |
| Replace Gaussian or sub-Gaussian measurement assumptions with mean-zero, isotropic sub-exponential measurements | uniform one-bit recovery with a ReLU generative prior · Uniform recovery over G(R^k) ∩ B₂ᵈ(R) | measurement-distribution generality | Helped |
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