On Parameter Symmetries and Conservation Laws in Gradient Flow
Parameter space symmetries and conservation laws play an important role in understanding the loss landscapes and implicit biases of neural networks. Inspired by Noether's theorem in physics, prior works have sought to derive conservation laws under gradient flow from parameter symmetries, but the scope and limitations of this connection remain unclear. We develop a unified geometric framework that clarifies the precise relationship between the two notions, including the conditions under which symmetries correspond to conservation laws. We introduce a notion of compositional identifiability and use it to establish a general inheritance principle for complete characterizations of symmetries...
| Authors | Khang Nguyen, Guido Montúfar |
|---|---|
| Primary category | cs.LG |
| Published | 28 September 2026 |
| Last updated at source | 28 September 2026 |
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