Attention is Just Another Name for Coupling? A Fast-Slow ODE Perspective on Hierarchical Pretraining
We re-interpret Transformer pretraining as a fast-slow, singularly perturbed flow along depth, with untied weights as its non-autonomous feature. The linearised dynamics is a depth-ordered product of layer maps. Along a token-homogeneous reference trajectory, the linearised layer factorises along the eigenbasis of a frozen attention kernel. Past a computable saturation depth, the flow factors through the block coarse-graining -- in other words, running the layers is running the coarse variable, dually. Weight perturbations supported on the decaying bundle move neither the persistent component of the distinguished trajectory nor the frozen kernel to first order, so the framework partitions...
| Authors | Zhengyuan Gao |
|---|---|
| Primary category | stat.ML |
| Published | 15 June 2026 |
| Last updated at source | 6 July 2026 |
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