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The Asymmetric Maximum Margin Bias of Quasi-Homogeneous Neural Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use quasi-homogeneous parameterization instead of homogeneous parameterization | Linear classifier on two dense balls · Two-ball binary classification | robustness: l(w_hom) = 1 - r; l(w_quasi-hom)=sqrt(1- r^{-2}rho_mu^2)(sqrt(1- rho_mu^2) - sqrt(r^2-rho_mu^2)) | Hurt |
| Use quasi-homogeneous parameterization with highest-rate parameters | Linear classifier on two dense balls · Two-ball binary classification, r = ρμ = 0.5 | robustness: r = ρμ = 0.5 | Hurt |
| Minimize only the highest-rate parameter seminorm | Quasi-homogeneous networks trained by gradient flow · Separable training data | maximum-margin objective | Helped |
| Remove the conditional separability requirement | Quasi-homogeneous networks · Linear classifier on two dense balls | higher-rate parameter magnitude: r ≤ 0.5; r = 0.25 | Mixed |
| Apply last-hidden-layer normalization and sufficient expressivity | Multiclass neural networks with cross-entropy loss · Neural Collapse | Neural Collapse properties | Helped |
Closest papers by meaning
- Implicit Bias of Gradient Descent for Non-Homogeneous Deep Networks (ICML 2025 · similarity 0.91)
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- Large Stepsize Gradient Descent for Non-Homogeneous Two-Layer Networks: Margin Improvement and Fast Optimization (NeurIPS 2024 · similarity 0.88)
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