Research map / Optimization / Implicit bias and generalization
When Expressivity Meets Trainability: Fewer than $n$ Neurons Can Work
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed constrained training regime with PGD, mirrored initialization, and pairwise outer weights instead of regular training | Narrow neural networks · Synthetic regression dataset | training error | Helped |
| Use the proposed training regime instead of regular training | ResNet-18 · R-ImageNet | test accuracy | Helped |
| Use the proposed training regime at width 64 rather than regular training | ResNet-18 · R-ImageNet | test accuracy | Helped |
| Use the proposed training regime at width 64 rather than width 512 | ResNet-18 · R-ImageNet | test accuracy | No clear effect |
| Add a hidden-weight constraint to regular training without changing initialization or network structure (ablation) | Regular training regime · Synthetic regression dataset | training error | Hurt |
| Use regular unconstrained training rather than the proposed constrained regime (ablation) | Narrow neural networks · Synthetic regression dataset | training error | Hurt |
| Search only around regular LeCun initialization instead of mirrored LeCun initialization (ablation) | Narrow neural networks · Synthetic regression dataset | training error | Hurt |
| Remove the mirrored initialization and pairwise outer-weight structure while retaining the hidden-weight constraint and PGD (ablation) | Proposed training regime · Synthetic regression dataset | training error | Hurt |
| Allow unconstrained hidden-weight movement by setting ε=1000 (ablation) | Proposed training regime · Synthetic regression dataset | training error | Hurt |
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