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Dynamical phase selection controls compute scaling in looped transformers — arXiv:2608.26556

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.26556
License (as archived): CC0-1.0
Archived: 2026-10-17T16:15:50.265Z
SHA-256 of the archived text: 0fac6dd5ad3a8c8fc2bc035934f6a7d9d08735629d61bda6349976c8be981104
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Dynamical phase selection controls compute scaling in looped transformers — arXiv:2608.26556 — arXiv (en), https://arxiv.org/abs/2608.26556 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_0bef467abc2a (Metraipolis archive dc_0bef467abc2a, sha256 0fac6dd5ad3a8c8fc2bc035934f6a7d9d08735629d61bda6349976c8be981104)

BibTeX

@misc{dc0bef467abc2a,
  title = {Dynamical phase selection controls compute scaling in looped transformers — arXiv:2608.26556},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.26556},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_0bef467abc2a; sha256 0fac6dd5ad3a8c8fc2bc035934f6a7d9d08735629d61bda6349976c8be981104},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.26556. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A looped transformer performs inference by iterating a weight-tied map, making its computation a dynamical process whose cost is set by the resulting inference dynamics. Here we show that networks with identical architecture and objective, trained to identical accuracy, nevertheless realize distinct dynamical phases depending strongly on initialization, and that the bifurcation defining each phase determines how test-time compute scales. The phases are distinguished by their bifurcation mechanisms, including a saddle-node fold and a Neimark-Sacker-type transition to bounded nonstationary motion. In the fold phase, a one-dimensional normal-form reduction predicts both the relaxation-time and spectral-gap amplitudes from local derivatives of the trained map, yielding the parameter-free relation $\tau(\varepsilon)[1-\lambda_{\max}(-\varepsilon)]\to\pi$. Composed with a regular distribution of problem difficulty, the same critical slowing down produces the workload-level tail $P(\tau>N)\sim N^{-2}$. In the Neimark--Sacker phase, the fold scaling law disappears rather than merely changing its prefactor. Thus, test-time compute is not determined by architecture alone. It is governed by the dynamical phase of the solution found by training.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-08-28 in cs.LG).
Categorie arXiv: Disordered Systems and Neural Networks (cond-mat.dis-nn) ; Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2608.26556 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T15:34:49.992Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-08-28?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).