Research map / Learning theory and algorithms / Prediction and decision losses
Are deep ResNets provably better than linear predictors?
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a one-block ResNet instead of a fully-connected ReLU network | Models on the six-point synthetic dataset · Six-point synthetic dataset, squared error, ρ ≤ √(5/4) | empirical risk at local minima relative to the best linear predictor: ≥ 8ρ^2/15 for fully-connected local minima; the ResNet has a local minimum < 8ρ^2/15 | Helped |
| Add a residual block with the specified parameters | One-block ResNet · Six-point synthetic dataset, squared error, ρ ∈ (0,√(5/4)] | empirical risk relative to the best linear predictor: \frac{\rho^2 (12 \rho^2+82 \rho + 215)}{21 \rho^2+ 156 \rho + 420} < 8\rho^2/15 | Helped |
| Add multiple chained skip-connections, subject to representation and parameter coverage | Deep ResNet critical points · General data distributions with convex twice-differentiable loss | risk relative to best linear predictor or Hessian curvature: risk ≤ best linear predictor, or Hessian has a strictly negative eigenvalue | Helped |
| Constrain residual blocks to be near identity, with each Lipschitz constant O(1/L) | Deep ResNet · General data distributions with near-identity residual blocks | risk bound at critical points: the additive term is size-independent | Helped |
| Constrain residual blocks to be near identity, with each Lipschitz constant o(1/L) | Deep ResNet · General data distributions with near-identity residual blocks | risk bound at critical points: the additive term diminishes to zero as the network gets deeper | Helped |
| Use norm-bounded residual layers with M_l = O(1/√L) | Deep ResNet · Bounded-input sample S | empirical Rademacher complexity bound: size-independent | Helped |
| Use a two-block ResNet whose first block maps X to H1 | Three-point synthetic dataset · Linear fit using representation H1 versus raw input X | minimum mean squared error: 0.3205 -> 0.3810 | Hurt |
| Add the second residual block, mapping H1 to H2 | Two-block ResNet · Three-point synthetic dataset | minimum mean squared error of linear fit: 0.3810 -> 0 | Helped |
Closest papers by meaning
- Are ResNets Provably Better than Linear Predictors? (NeurIPS 2018 · similarity 0.95)
- Towards Understanding the Importance of Shortcut Connections in Residual Networks (NeurIPS 2019 · similarity 0.90)
- Residual Connections Encourage Iterative Inference (ICLR 2018 · similarity 0.90)
- On global convergence of ResNets: From finite to infinite width using linear parameterization (NeurIPS 2022 · similarity 0.90)
- Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers (NeurIPS 2025 · similarity 0.87)
- Generalization of Scaled Deep ResNets in the Mean-Field Regime (ICLR 2024 · similarity 0.87)
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