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Understanding Edge-of-Stability Training Dynamics with a Minimalist Example
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the coupled 4-scalar degree-4 objective and fixed-step gradient descent | 4-scalar degree-4 model · Local initialization region | final sharpness: (2/η - 20/3 η, 2/η) | Helped |
| Vary the step size from a shared initialization | 4-scalar degree-4 model · Different learning rates | final sharpness: 2/η | Helped |
| Use rank-1 isotropic matrix factorization with a multiplicative perturbation | Rank-1 isotropic matrix factorization · Random spherical initializations satisfying the theorem conditions | final norm squared sum: (1/η - 10/3 η, 1/η) | Helped |
| Train a 5-layer ELU network on a small binary CIFAR-10 subset | 5-layer ELU FC network · CIFAR-10 50-sample binary subset | sharpness: 199.97; 2/η=200 | Helped |
| Use a degree-2 scalar objective instead of the degree-4 model | Scalar network gradient descent · 2-layer scalar network | sharpness concentration | Hurt |
| Use degree-2 scalar factorization rather than the degree-4 model | Scalar factorization gradient descent · 2-component scalar factorization | final sharpness relative to 2/η | Hurt |
| Consider different EoS minima in the degree-3 scalar network | 3-layer scalar network · EoS minima with small single entry versus small duplicated entries | sharpness concentration | Mixed |
| Add a multiplicative perturbation to the vector factor | Rank-1 isotropic matrix factorization · Avoiding convergence to unstable points | convergence to an EoS minimum: 1+2K^{-1} | Helped |
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