Conservation Laws for Modern Neural Architectures
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Computer Science > Machine Learning
Title:Conservation Laws for Modern Neural Architectures
Abstract:Understanding gradient descent dynamics is key to explaining the success of over-parameterized models, where implicit bias manifests through conservation laws in gradient flow. While such laws are well understood for linear and ReLU networks, they remain largely unexplored for modern architectures. This work develops a unified framework to characterize conservation laws for contemporary models, including feedforward networks with GELU, SiLU, and SwiGLU activations, multihead attention with sinusoidal and rotary positional encodings, and Mixture-of-Experts architectures under diverse gating designs. Our theoretical findings are supported by experiments that validate the predicted invariants.
| Comments: | Published at the International Conference on Machine Learning (ICML 2026) |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2606.17816 [cs.LG] |
| (or arXiv:2606.17816v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.17816
arXiv-issued DOI via DataCite (pending registration)
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