Research map / Optimization / Implicit bias and generalization
Gradient Descent Provably Optimizes Over-parameterized Neural Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use sufficiently large width with random initialization and a constant step size | Gradient descent on a two-layer ReLU network with fixed output layer · Empirical risk minimization (quadratic loss) | squared training error: \norm{\vect{u}(k)-\vect{y}}_2^2 \le \left(1-\frac{\eta \lambda _0}{2}\right)^{k}\norm{\vect{u}(0)-\vect{y}}_2^2 | Helped |
| Use sufficiently large width and random initialization | Gradient flow on a two-layer ReLU network with fixed output layer · Empirical risk minimization (quadratic loss) | squared training error: \norm{\vect{u}(t)-\vect{y}}_2^2 \le \exp(-\lambda_0 t)\norm{\vect{u}(0)-\vect{y}}_2^2 | Helped |
| Train both layers jointly rather than fixing the output layer | Gradient flow on a two-layer ReLU network · Empirical risk minimization (quadratic loss) | squared training error: \norm{\vect{u}(t)-\vect{y}}_2^2 \le \exp(-\lambda_0 t)\norm{\vect{u}(0)-\vect{y}}_2^2 | Helped |
| Increase the hidden-layer width | Gradient descent on synthetic data · Synthetic data; n=1000, d=1000 | convergence rate | Helped |
| Increase the hidden-layer width | Gradient descent on synthetic data · Synthetic data; n=1000, d=1000 | percent of activation-pattern changes | Helped |
| Increase the hidden-layer width | Gradient descent on synthetic data · Synthetic data; n=1000, d=1000 | maximum distance of weights from initialization | Helped |
Closest papers by meaning
- Fast Convergence of Natural Gradient Descent for Over-Parameterized Neural Networks (NeurIPS 2019 · similarity 0.93)
- A Convergence Analysis of Gradient Descent for Deep Linear Neural Networks (ICLR 2019 · similarity 0.93)
- On the Proof of Global Convergence of Gradient Descent for Deep ReLU Networks with Linear Widths (ICML 2021 · similarity 0.92)
- Convex Relaxations of ReLU Neural Networks Approximate Global Optima in Polynomial Time (ICML 2024 · similarity 0.90)
- Compelling ReLU Networks to Exhibit Exponentially Many Linear Regions at Initialization and During Training (ICML 2025 · similarity 0.90)
- Simplicity Bias and Optimization Threshold in Two-Layer ReLU Networks (ICML 2025 · similarity 0.90)
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