Low-dimensional topology of deep neural networks
We study layered models, including feedforward networks, ResNets, and transformers, by limiting each layer to a width of $d = 3$, i.e., $\mathbb{R}^3$ as representation space. This allows us to track how a neural network changes low-dimensional topological invariants through its layers. Just about any topological structure may be simplified or even trivialized by simply increasing dimension; e.g., any knot is equivalent to an unknot in $\mathbb{R}^4$. By restricting to $\mathbb{R}^3$, we not only isolate the effects of activation and depth from that of width, we work in a space that lends itself to easy visualization. We focus on linking number here, deferring other invariants like link g...
| Authors | Junyu Ren, Lek-Heng Lim |
|---|---|
| Primary category | cs.LG |
| Published | 30 June 2026 |
| Last updated at source | 18 August 2026 |
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