Emergence of Fibrations, Compression, and Symmetry Breaking in Artificial Neural Networks
Artificial neural networks are often regarded as powerful yet opaque black boxes. Here, we demonstrate that learning in deep neural networks generates local symmetries known in graph theory as fibrations and coverings. We prove that covering symmetries are stable attractors of stochastic gradient descent. Consistent with this theory, we report the emergence of covering symmetries across major network architectures, including multilayer, convolutional, recurrent, and transformer networks. Exploiting these symmetries enables drastic model compression - reducing networks to 17% of their original size without sacrificing performance. Furthermore, controlled breaking of covering symmetry overc...
| Authors | Osvaldo M Velarde, Lucas C Parra, Alireza Hashemi et al. |
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| Primary category | cs.LG |
| Published | 1 September 2026 |
| Last updated at source | 1 September 2026 |
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