[
    {
        "id": "osp-20569",
        "type": "article-journal",
        "title": "Port-Hamiltonian Latent Deliberation: Mitigating the Deliberation Drift Cliff in Test-Time Compute Scaling",
        "author": [
            {
                "family": "Jia",
                "given": "Zeyu"
            }
        ],
        "URL": "https://omanscience.com/en/articles/port-hamiltonian-latent-deliberation-mitigating-the-deliberation-drift-cliff-in-test-time-compute-scaling",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "abstract": "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 = 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."
    }
]