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Adaptive depth

Two-Scale Latent Dynamics

Two-Scale Latent Dynamics for Recurrent-Depth Transformers

Francesco Pappone, Donato Crisostomi, Emanuele Rodolà

Describes recurrent-depth iterates as small refinements within a looped block and larger drift across blocks; loop steps grow smaller and more mutually orthogonal over training. This motivates an early exit based on the second-order difference of step size.

Inside the method

[ Looped block ] × r → exit when second-order step-size difference is small

Simplified conceptual schematic. Consult the paper for the complete architecture.

Recurrence family
Adaptive depth
Depth control
Early exit from latent geometry
KV / state strategy
See paper

Reading note

The second-order exit beats Huginn's KL-divergence exit and a first-order variant in performance, stability and time efficiency.

Sources checked 2026-10-28. This catalog does not imply independent reproduction.

Related works

Cite this work

@misc{twoscalelatentdynamics2025,
  title = {Two-Scale Latent Dynamics for Recurrent-Depth Transformers},
  author = {Francesco Pappone and Donato Crisostomi and Emanuele Rodolà},
  year = {2025},
  eprint = {2509.23314},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2509.23314}
}

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