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Port-Hamiltonian Latent Deliberation: Mitigating the Deliberation Drift Cliff in Test-Time Compute Scaling — arXiv:2609.37351

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.37351
License (as archived): CC0-1.0
Archived: 2026-10-07T16:27:11.067Z
SHA-256 of the archived text: 80c63898a515988f52c1807a103873402837fe55cdd052fec5750b056ef82d25
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How to cite

Port-Hamiltonian Latent Deliberation: Mitigating the Deliberation Drift Cliff in Test-Time Compute Scaling — arXiv:2609.37351 — arXiv (en), https://arxiv.org/abs/2609.37351 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_68fcd004ecab (Metraipolis archive dc_68fcd004ecab, sha256 80c63898a515988f52c1807a103873402837fe55cdd052fec5750b056ef82d25)

BibTeX

@misc{dc68fcd004ecab,
  title = {Port-Hamiltonian Latent Deliberation: Mitigating the Deliberation Drift Cliff in Test-Time Compute Scaling — arXiv:2609.37351},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.37351},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_68fcd004ecab; sha256 80c63898a515988f52c1807a103873402837fe55cdd052fec5750b056ef82d25},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.37351. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Test-time compute scaling has emerged as a cornerstone of advanced machine reasoning, yet performing iterative deliberation directly within continuous latent representation spaces reveals a catastrophic pathology: the Deliberation Drift Cliff. While unconstrained recurrent latent models achieve initial reasoning gains at short horizons (K <= 4), their reasoning collapses when extrapolated to deeper thinking steps (K >= 16), dropping by 22% to 62% across standard logical benchmarks. We resolve the trilemma among expressivity, Lyapunov stability, and computational efficiency in test-time latent reasoning through a 22-round empirical and theoretical investigation. We demonstrate that strictly conservative scalar potential gradient flows suppress long-range drift (cliff 3.40%) but bottleneck peak reasoning accuracy at 32.73%, whereas unconstrained rotational flows achieve high symbolic expressivity (82.33%) but suffer a severe 36.87% drift cliff. To resolve this geometric duality, we establish Port-Hamiltonian Latent Deliberation (PH-LD) and propose the Direct-Gradient Pure-Tensor Helmholtz-Hodge Decomposition (DG-HHD). DG-HHD parameterizes the attracting flow as a tangent projection tensor network while orthogonally decoupling non-zero circulation (Hodge machine error 1.65e-17, contraction error 5.55e-17), eliminating runtime autograd dependencies to achieve 1.84x vector field and 2.09x RK45 rollout speedups. In a 15-arm symmetrical Pareto benchmark, DG-HHD achieves 58.67% peak accuracy (+25.94% absolute gain over conservative HHD) and retains 35.27% at K=32. Transferred to small language model (SLM) multi-hop causal reasoning, DG-HHD delivers monotonic compute scaling (49.33% to 51.56%) and suppresses out-of-distribution drift (cliff -0.66%). All 30 Level 0 deterministic invariants are certified.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-30 in cs.AI).
Categorie arXiv: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI); Computation and Language (cs.CL).
Pagina del lavoro: https://arxiv.org/abs/2609.37351 — 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 2026-10-07T15:54:53.973Z dalla pagina https://arxiv.org/catchup/cs.AI/2026-09-30?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).