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Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use modified gradient flow instead of ordinary gradient flow to model finite learning-rate updates | Gradient descent trajectories · Quadratic loss | trajectory agreement with discrete updates | Helped |
| Use symmetry-based dynamics with modified gradient flow to predict parameter combinations | VGG-16 · Tiny ImageNet | agreement between predicted and empirical parameter dynamics | Helped |
| Add weight decay to symmetry-constrained dynamics | Parameters with translation symmetry · VGG-16 on Tiny ImageNet | translation-symmetry parameter sum | Mixed |
| Add finite learning-rate discretization to scale-symmetry dynamics | Parameters with scale symmetry · VGG-16 on Tiny ImageNet | squared parameter norm | Mixed |
| Include weight decay and finite learning-rate effects in rescale-symmetry dynamics | Parameters with rescale symmetry · VGG-16 on Tiny ImageNet | difference in squared parameter norms | Mixed |
| Increase momentum enough to enter the underdamped regime | SGD dynamics · VGG-16 on Tiny ImageNet | translation-symmetry parameter sum | Mixed |
| Add momentum under standard hyperparameter choices | SGD dynamics · VGG-16 on Tiny ImageNet | agreement with first-order solutions | No clear effect |
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