On Parameter Symmetries and Conservation Laws in Gradient Flow

arXiv:2609.34549 · cs.LG, math.OC · Submitted 2026-09-28 · Read on arXiv

cs.LG, math.OC

Submitted: 2026-09-28

Updated: 2026-09-28

Code: https://github.com/karpathy/nanoGPT

Terminology

• Conservation Laws — 1× in this paper · explained in 3 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes

Sources

• Noether: The More Things Change, the More Stay the Same
• The Symmetries of Three-Layer ReLU Networks
• Conservation Laws from Data Symmetry in Neural Networks
• Subdifferentiation with symmetry
• Attention Is All You Need
• Regularization Implies balancedness in the deep linear network
• Going Deeper with Convolutions

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