Infrared Organization and Critical Cognitive Field Formation in Transformer Dynamics

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Original 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 time-scale density of states (TDOS) through the infrared accumulation of slow relaxation modes, thereby enhancing the memory self-energy, reducing the cognitive forgetting gap, and strengthening the collective susceptibility. Using publicly available Pythia language models, we extract relaxation spectra directly from Transformer layer Jacobians throughout training, network depth, and model scale, allowing the TDOS, memory self-energy, forgetting gap, memory kernel, and infrared critical exponent to be measured quantitatively. The measurements reveal progressive infrared accumulation of slow relaxation modes, producing an approximately flat infrared TDOS with \( ρ(λ)\simλ^{-0.1} \) and scale-free memory kernels \( K(t)\sim t^{-1}. \) The memory self-energy exhibits a pronounced transient maximum during early optimization before relaxing toward a metastable near-critical regime, corresponding to the smallest cognitive forgetting gap and the largest collective susceptibility predicted by Cognitive Field Theory. These observations provide quantitative experimental evidence that Transformer dynamics are governed by infrared collective organization. The reproducibility of the same dynamical behavior across training, network depth, and model scales suggests that infrared slow-mode organization represents a universal collective principle of Transformer dynamics.

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