Research map / Optimization / Implicit bias and generalization
A Diffusion Theory For Deep Learning Dynamics: Stochastic Gradient Descent Exponentially Favors Flat Minima
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Model minibatch gradient noise covariance as Hessian-dependent and inversely proportional to batch size | SGD dynamics near minima · MNIST; Avila | SGN covariance-Hessian relationship: $0.999$ Pearson correlation; Avila: $1.004 \frac{H}{B}$ | Helped |
| Increase minima sharpness | SGD · Styblinski-Tang Function; real-world datasets | escape rate | Hurt |
| Increase batch size | SGD · Styblinski-Tang Function; real-world datasets | escape rate | Hurt |
| Decrease learning rate | SGD · Styblinski-Tang Function; real-world datasets | escape rate | Hurt |
| Replace minibatch SGD noise with injected isotropic Gaussian noise | Gradient descent (SGLD) · Styblinski-Tang Function; neural network | flat-minimum preference as sharpness changes | Mixed |
| Use minibatch SGD noise rather than injected white noise | Gradient descent dynamics · Minima selection | flat-minimum preference | Helped |
| Increase injected diffusion coefficient | SGLD · Styblinski-Tang Function; neural network | escape rate | Hurt |
| Increase Hessian determinant | SGLD · Styblinski-Tang Function; neural network | escape rate | Helped |
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