Research map / Learning theory and algorithms / Matrix and tensor methods
Constant-Expansion Suffices for Compressed Sensing with Generative Priors
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace the standard Lipschitz net argument with parameter-dependent pseudo-balls | Uniform concentration used to establish WDC for Gaussian matrices · Gaussian matrices for WDC | minimum aspect ratio for WDC: n ≥ c k log k -> n ≥ c · k · ε^{-2} log(1/ε) | Helped |
| Allow constant rather than logarithmic expansion at each layer | Compressed sensing with a random neural network prior · Compressed sensing with generative priors | minimum layer expansion: n_i ≥ c n_{i-1} log n_{i-1} -> n_i ≥ n_{i-1} · poly(d) | Helped |
| Use constant expansion for Gaussian weight matrices | Gaussian-noise compressed sensing with generative priors · Gaussian noise | required layer expansion: logarithmic expansion -> constant expansion | Helped |
| Use constant expansion for Gaussian weight matrices | One-bit recovery with a generative prior · One-bit recovery | required layer expansion: logarithmic expansion -> constant expansion | Helped |
| Use constant expansion for Gaussian weight matrices | Phase retrieval with a generative prior · Phase retrieval | required layer expansion: logarithmic expansion -> constant expansion | Helped |
| Use constant expansion for Gaussian weights | Two-layer deconvolutional prior · Deconvolutional neural networks | required expansion: logarithmic expansion -> constant expansion | Helped |
| Use constant expansion for Gaussian weight matrices | Generative-prior low-rank matrix recovery · Low-rank matrix recovery | required layer expansion: logarithmic expansion -> constant expansion | Helped |
| Reduce one-layer expansion below 2 | Inversion of a one-layer ReLU network · Inversion without compression or noise | injectivity: m ≤ 2k - 1 | Hurt |
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