发表机构
University of Almería; Research Centre CIAIMBITAL（阿尔梅里亚大学; CIAIMBITAL研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究探究动态内部场能否调控Transformer认知，证明其具有可认证的运行时稳定性，虽未提升认知能力，但可作为可行的计算调控器。
AI 中文摘要
智能系统不仅进行推理，还会调控自身的推理过程——计算量多少、何时停止、激活哪个模块。动态内部场（一种具有明确物理特性和可认证稳定性的低维稳态状态，可在不执行认知任务的情况下对认知进行调制）能否承担这一角色？我们的场是模块图上的场，由图拉普拉斯算子上的一族偏微分方程（PDE）控制，并与自适应深度推理器协同推进。我们证明了该族积分器的稳定性，这是一种积分器证书，而非闭环证书。本文还提出并证明了一项新成果：针对带速度耦合的Verlet方法，提出了离散Schur-Cohn准则，该准则对每个潜根而言是充分必要条件，且无需交换性假设。答案分为三个层面：本质层面不行，结构层面部分可行，可认证性层面可行。该场的物理类型对准确性无关紧要：波动、扩散、门控混合以及二维Navier-Stokes基底均能适用。一项包含20个种子的预注册混杂控制实验对结构层面的主张进行了限定：在同等容量上限下，某一族的二阶效应较强（+0.087 [+0.042, +0.132]，t=4.0），但另一族中未检测到该效应（+0.014 [-0.013, +0.040]，无统计学意义），因此原对比中的部分差异源于容量而非阶数；匹配接口的GRU在第一族中表现无差异，在第二族中名义上超过该场（-0.035 [-0.067, -0.002]）。该场的区别不在于能力，而在于其单步算子可进行精确的运行时稳定性检查——这是一种本质差异，而非存在性差异：学习到的循环也带有充分且保守的证书。带有正控制的终止门未发现该场作为证据累加器的证据（Delta AUC +0.0007 [-0.0065, +0.0079]，对比阈值为0.03）。动态内部场是一种可行的、可认证的计算调控器，但并非认知增强器：它进行调制，而非思考。
英文摘要
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.
Comments22 pages, 4 figures. Companion paper: "Where Cognition Lives" (arXiv:2608.22347). Code, preregistrations and results: https://github.com/fmarrabal/miuracognitive
