端口-哈密顿潜在深思：缓解测试时计算扩展中的深思漂移悬崖
Port-Hamiltonian Latent Deliberation: Mitigating the Deliberation Drift Cliff in Test-Time Compute Scaling
- Tianjin Medical University（天津医科大学）
- Tianjin University（天津大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
针对测试时计算扩展中潜在深思的漂移悬崖问题，提出端口-哈密顿潜在深思（PH-LD）与DG-HHD分解，在保持高表达性的同时抑制漂移，实现峰值准确率58.67%并提升计算效率。
中文摘要 AI 辅助
测试时计算扩展已成为先进机器推理的基石，然而直接在连续潜在表示空间中进行迭代深思却揭示了一种灾难性病理：深思漂移悬崖。虽然无约束的循环潜在模型在短视界（K≤4）内取得了初步推理增益，但当外推到更深的思考步骤（K≥16）时，其推理能力崩溃，在标准逻辑基准上下降22%至62%。我们通过22轮实证与理论调查，解决了测试时潜在推理中表达性、李雅普诺夫稳定性与计算效率之间的三难问题。我们证明，严格保守的标量势梯度流抑制了长程漂移（悬崖3.40%），但将峰值推理准确率瓶颈限制在32.73%；而无约束的旋转流实现了高符号表达性（82.33%），却遭受了36.87%的严重漂移悬崖。为解决这一几何二元性，我们建立了端口-哈密顿潜在深思（PH-LD），并提出了直接梯度纯张量亥姆霍兹-霍奇分解（DG-HHD）。DG-HHD将吸引流参数化为切投影张量网络，同时正交解耦非零环量（霍奇机误差1.65e-17，收缩误差5.55e-17），消除了运行时自动微分依赖，实现了1.84倍向量场和2.09倍RK45滚动加速。在15臂对称帕累托基准中，DG-HHD实现了58.67%的峰值准确率（较保守HHD绝对增益+25.94%），并在K=32时保持35.27%。迁移到小语言模型（SLM）多跳因果推理中，DG-HHD提供了单调计算扩展（49.33%至51.56%），并抑制了分布外漂移（悬崖-0.66%）。所有30个Level 0确定性不变量均已认证。
英文摘要
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.
