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A view of mini-batch SGD via generating functions: conditions of convergence, phase transitions, benefit from negative momenta.
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| adding momentum beta>0 to SGD in the signal-dominated regime | mini-batch SGD with momentum · MNIST / CIFAR10 (signal-dominated) | loss convergence | Helped |
| using negative momentum (beta<0) instead of positive momentum | mini-batch SGD in noise-dominated phase · synthetic power-law problems (noise-dominated) | loss at late time | Helped |
| increasing the SGD batch noise (decreasing batch size) to enter noise-dominated regime | mini-batch SGD · power-law spectral distributions | convergence regime | Hurt |
| removing the sampling noise (gamma to 0), i.e., full-batch GD, versus SGD: effective learning rate bound | SGD vs full-batch GD · non-strongly convex quadratic problems | stability of effective learning rate | Hurt |
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