Infrared Organization and Critical Cognitive Field Formation in Transformer Dynamics

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arXiv:2607.10923v3 Announce Type: replace Abstract: Large language models exhibit remarkable emergent behaviors, yet the physical mechanism governing their collective dynamics remains poorly understood. Cognitive Field Theory predicts that learning reorganizes the collective relaxation spectrum through the infrared accumulation of slow relaxation modes, thereby enhancing memory self-energy, long-memory dynamics, and collective susceptibility. Here we test this framework directly in Transformer dynamics. Using publicly available Pythia language models, we extract relaxation spectra from layer Jacobians throughout training, prompt ensembles, network depth, and model scale, allowing the collective observables of Cognitive Field Theory to be measured quantitatively. The measurements reveal pronounced infrared reorganization of the relaxation spectrum. Slow relaxation modes progressively accumulate toward the infrared, producing an approximately flat time-scale density of states, \( \rho(\lambda)\sim\lambda^\beta,\ \beta\simeq-0.1, \) while the corresponding memory kernel exhibits universal scaling, \( K(t)\sim1/t. \) The collective observables further reveal a critical formation process: the memory self-energy reaches a transient maximum during early training before relaxing toward a metastable near-critical regime. Prompt-resolved and token-subspace measurements show that distinct local Jacobians converge toward the same normalized infrared TDOS, consistent with an infrared fixed-point organization under coarse graining. The reproducibility of the same infrared organization …

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