Research map / Optimization / Implicit bias and generalization
SGD Learns One-Layer Networks in WGANs
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a quadratic discriminator to match second-order moments instead of a linear discriminator | WGAN with a one-layer generator · Joint distribution learning | covariance recovery | Helped |
| Train the proposed WGAN with stochastic gradient descent-ascent | One-layer generator with quadratic discriminator · Realizable target distribution | covariance recovery error: \|A^{(T)}(A^{(T)})^\top - Z^*\|_F\leq \Ocal(\epsilon) | Helped |
| Increase the observed sample size (ablation) | Stochastic gradient descent-ascent WGAN · Synthetic recovery experiments | relative parameter estimation error | Helped |
| Increase the output dimension (ablation) | Stochastic gradient descent-ascent WGAN · Synthetic recovery experiments | relative parameter estimation error | Hurt |
| Use leaky ReLU rather than tanh (ablation) | Stochastic gradient descent-ascent WGAN · Synthetic recovery, k=1 and d=2 | parameter recovery | No clear effect |
| Use tanh rather than leaky ReLU (ablation) | Stochastic gradient descent-ascent WGAN · Synthetic recovery, k=1 and d=2 | parameter recovery | No clear effect |
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