提出可验证稳定性的动态内部场，用以调控Transformer计算，而非提升认知能力。
Can a Dynamic Internal Field Govern a Transformer's Cognition? Certifiability, not Superiority, in Homeostatic Compute Control
- 设计基于图拉普拉斯PDE的低维动态场，通过可证稳定性控制计算深度
- 实验证明该场能有效调控计算，但不提升模型性能（ΔAUC=+0.0007）
- 关键突破：无需交换假设的离散Schur-Cohn准则，实现精确运行时稳定性检验
智能系统不仅推理，还应自主调控推理过程——决定计算量、停止时机与模块激活。本文探索一种低维内源性稳态场（具有明确物理机制和可证稳定性）是否可作为认知的调控者，而非执行者。该场定义在模块图上，由一组作用于图拉普拉斯的偏微分方程驱动，配合自适应深度推理器。我们证明了整个家族积分器的稳定性——获得一个积分器证书（非闭环证书）。首次建立含速度耦合的Verlet方法的离散Schur-Cohn准则，对每个特征根均必要且充分，无需交换假设。实验结果三重回答：认知能力无提升（物质层面否），结构部分影响（如第二阶效应在某一族中显著，+0.087 [0.042, 0.132], t=4.0），但并非因顺序差异；另一族未检测到（+0.014 [-0.013, +0.040]，不显著）。匹配接口的GRU在两组中表现相近，甚至略优（-0.035 [-0.067, -0.002]）。真正的区别在于其一步算子具备精确运行时稳定性检验能力——这是性质之别，而非存在之别。学习型递归同样拥有足够且保守的证书。对照实验显示，该场并非证据积累器（ΔAUC +0.0007 [-0.0065, +0.0079]，低于0.03阈值）。结论：动态内部场是可行的可证计算控制器，但非认知增强器，仅调节不思考。
原文摘要 · Abstract (English)
An intelligent system does not merely reason: it governs its own reasoning - how much to compute, when to stop, which module to activate. Can that role be played by a dynamic internal field - a low-dimensional homeostatic state with explicit physics and certified stability - that modulates cognition without performing it? Ours is a field on the module graph governed by a family of PDEs on the graph Laplacian, advancing with an adaptive-depth reasoner. We certify the stability of the integrator of the whole family - an integrator certificate, not a closed-loop one. New, and proved here: a discrete Schur-Cohn criterion for Verlet with velocity coupling, necessary and sufficient per latent root, with no commutation hypothesis. The answer is threefold: substance no, structure only in part, certifiability yes. The type of the field's physics is irrelevant for accuracy: wave, diffusion, gated mixtures and a 2D Navier-Stokes substrate tie. A twenty-seed preregistered deconfounding campaign bounds the structural claim: at equalized caps the second-order effect is strong in one family (+0.087 [+0.042, +0.132], t=4.0) but is not detected in the other (+0.014 [-0.013, +0.040], n.s.), so part of the original contrast was capacity, not order; and a matched-interface GRU is indistinguishable in the first and nominally exceeds the field in the second (-0.035 [-0.067, -0.002]). What distinguishes the field is not capability but that its one-step operator admits an exact runtime stability check - a difference of kind, not of existence: learned recurrences carry certificates too, sufficient and conservative ones. A kill-gate with a positive control finds no evidence for the field as evidence accumulator (Delta AUC +0.0007 [-0.0065, +0.0079] vs a 0.03 threshold). A dynamic internal field is a viable, certifiable compute governor, but not an enhancer of cognition: it modulates, it does not think.
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