Research map / Optimization / Implicit bias and generalization
On the Explicit Role of Initialization on the Convergence and Implicit Bias of Overparametrized Linear Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| increase level of initialization imbalance c while keeping end-to-end matrix fixed (ablation) | single-hidden-layer linear network under gradient descent · synthetic regression with Σx=I | convergence rate of loss | Helped |
| balanced initialization instead of imbalanced (ablation) | single-hidden-layer linear network · synthetic regression with Σx=I | convergence rate of loss | Hurt |
| wide width with random N(0,h^-2α) initialization (adding width h) | single-hidden-layer linear network · regression, min-norm distance | distance to min-norm solution ||UV^T - Θ_hat||_F | Helped |
| proper orthogonal initialization (V(0)U2(0)^T=0, U1(0)U2(0)^T=0) enforced | single-hidden-layer linear network · theoretical (Proposition 1) | convergence to min-norm solution | Helped |
| zero initialization V(0)=0, U(0)=0 instead of orthogonal initialization | single-hidden-layer linear network · theoretical discussion | convergence to min-norm solution | Hurt |
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