mlsanityData to 14 Oct 2026

Can a Dynamic Internal Field Govern a Transformer's Cognition? Certifiability, not Superiority, in Homeostatic Compute Control

arXiv 2608.24319 ↗First posted 25 Aug 2026cs.AI cs.LG cs.SYcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 33 of its 56 references that are in the map. First posted on arXiv 25 Aug 2026.

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33 of 56 references.

References · 33

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2014Neural Turing Machinescited by 644
  3. 2016Adaptive Computation Time for Recurrent Neural Networkscited by 506
  4. 2022Transformers Learn Shortcuts to Automatacited by 268
  5. 2021GRAND: Graph Neural Diffusioncited by 258
  6. 2024Mixture-of-Depths: Dynamically allocating compute in transformer-based language modelscited by 258
  7. 2023Looped Transformers as Programmable Computerscited by 237
  8. 2019Depth-Adaptive Transformercited by 236
  9. 2022Exploring Length Generalization in Large Language Modelscited by 206
  10. 2022The Parallelism Tradeoff: Limitations of Log-Precision Transformerscited by 193
  11. 2024The Illusion of State in State-Space Modelscited by 187
  12. 2021PonderNet: Learning to Pondercited by 168
21 more
  1. 2020The Right Tool for the Job: Matching Model and Instance Complexitiescited by 126
  2. 2022Graph-Coupled Oscillator Networkscited by 124
  3. 2019AntisymmetricRNN: A Dynamical System View on Recurrent Neural Networkscited by 112
  4. 2020Learning Stable Deep Dynamics Modelscited by 111
  5. 2021PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equationscited by 106
  6. 2024Looped Transformers for Length Generalizationcited by 99
  7. 2020Lipschitz Recurrent Neural Networkscited by 89
  8. 2018Differentiable plasticity: training plastic neural networks with backpropagationcited by 84
  9. 2020Coupled Oscillatory Recurrent Neural Network (coRNN): An accurate and (gradient) stable architecture for learning long time dependenciescited by 82
  10. 2023Length Generalization in Arithmetic Transformerscited by 66
  11. 2022Anti-Symmetric DGN: a stable architecture for Deep Graph Networkscited by 60
  12. 2021UnICORNN: A recurrent model for learning very long time dependenciescited by 56
  13. 2021Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustnesscited by 45
  14. 2020Backpropamine: training self-modifying neural networks with differentiable neuromodulated plasticitycited by 41
  15. 2024Oscillatory State-Space Modelscited by 39
  16. 2020On the stability properties of Gated Recurrent Units neural networkscited by 19
  17. 2018Introducing Neuromodulation in Deep Neural Networks to Learn Adaptive Behaviourscited by 16
  18. 2025Learning to Dissipate Energy in Oscillatory State-Space Modelscited by 9
  19. 2024Input-to-State Stable Coupled Oscillator Networks for Closed-form Model-based Control in Latent Spacecited by 7
  20. 2022Need is All You Need: Homeostatic Neural Networks Adapt to Concept Shiftcited by 6
  21. 2026Where Cognition Lives: Dissecting Emergent from Computed Function in a Minimal Complete Cognitive Architecturecited by 1

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