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Deep learning versus kernel learning: an empirical study of loss landscape geometry and the time evolution of the Neural Tangent Kernel
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train the full network for 3 to 4 epochs before switching to linearized training | ResNet20 · CIFAR10 and CIFAR100 | performance relative to the initial NTK: outperform the standard initial NTK by a factor of 3 | Helped |
| Train the full network for 30 to 90 epochs before switching to linearized training | ResNet20 · CIFAR10 and CIFAR100 | performance relative to full network training: 30 to 90 epochs; 15\% to 45\% of training | Helped |
| Vary the child spawn time from early to later training (ablation) | ResNet20 · CIFAR10 and CIFAR100 | error barrier between children: within 2-3 epochs | Helped |
| Use constant learning rate instead of learning rate drops (ablation) | ResNet20 · CIFAR10 | early error-barrier reduction and later kernel evolution: 200 epochs | No clear effect |
| Use very low learning-rate nonlinear training instead of linearized training (ablation) | ResNet20 · CIFAR10 and CIFAR100 | test error during the early chaotic phase | Helped |
| Use very low learning-rate nonlinear training instead of linearized training after the early chaotic phase (ablation) | ResNet20 · CIFAR10 and CIFAR100 | test error | No clear effect |
| Use a second-order Taylor expansion instead of a first-order expansion (ablation) | Taylorized ResNet20 · CIFAR10 and CIFAR100 | error | Helped |
| Remove batch normalization (ablation) | ResNet20 · CIFAR10 | relationship between nonlinear advantage and error barrier | No clear effect |
| Use WideResNet-16-4 instead of ResNet20 (ablation) | WideResNet-16-4 · CIFAR10 and CIFAR100 | data-dependent linearized model error as training progresses | Mixed |
Closest papers by meaning
- Neural (Tangent Kernel) Collapse (NeurIPS 2023 · similarity 0.91)
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- Understanding the Evolution of the Neural Tangent Kernel at the Edge of Stability (NeurIPS 2025 · similarity 0.89)
- The Surprising Effectiveness of Infinite-Width NTKs for Characterizing and Improving Model Training (AAAI 2025 · similarity 0.88)
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