Research map / Optimization / Implicit bias and generalization
How Much Over-parameterization Is Sufficient to Learn Deep ReLU Networks?
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed deep-network GD analysis under data separation | Deep ReLU network trained with GD · Data separation | over-parameterization condition: \tilde \Omega(\epsilon^{-14})\cdot e^{\Omega(L)} -> \text{polylog}(n,\epsilon^{-1})\cdot\text{poly}(L) | Helped |
| Use the proposed deep-network SGD analysis under data separation | Deep ReLU network trained with SGD · Data separation | sample complexity: \tilde \cO(\epsilon^{-2})\cdot\text{poly}(L) -> \tilde \cO(\epsilon^{-1})\cdot \text{poly}(L) | Helped |
| Use a constant-bounded linear approximation error rather than requiring it to be as small as the target loss | Deep ReLU network optimization analysis · NTRF reference class | required network width: m=\tilde\Omega(1) | Helped |
| Allow a small fraction of training examples to be misclassified by the NTRF separator | Deep ReLU networks under data separation · Data separation | data-separation requirement: 1-\rho | Helped |
| Use the class-dependent nondegeneration assumption | Deep ReLU network trained with GD · Class-dependent data nondegeneration | over-parameterization condition: m=\tilde \Omega\big(n^{14}L^{16}\phi^{-4}+n^{12}L^{16}\phi^{-4}\epsilon^{-1}\big) -> m=\tilde \Omega\big(L^{22}n^{12}\ph | Helped |
Closest papers by meaning
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- A NON-PARAMETRIC REGRESSION VIEWPOINT : GENERALIZATION OF OVERPARAMETRIZED DEEP RELU NETWORK UNDER NOISY OBSERVATIONS (ICLR 2022 · similarity 0.91)
- Optimal Rates for Generalization of Gradient Descent for Deep ReLU Classification (NeurIPS 2025 · similarity 0.89)
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- Stable Minima Cannot Overfit in Univariate ReLU Networks: Generalization by Large Step Sizes (NeurIPS 2024 · similarity 0.88)
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