Four Dynamical Regimes in large Language Models : An Empirical Phase Map
We introduce ct_t = delta_t × curvature_t, a token-level instability metric computed from L2-normalised hidden states of large language models, and ratio_norm = max(ct_t) / mean(ct_t) as a scalar regime indicator. Evaluated across 10 open-source models (158 runs), four dynamical regimes emerge consistently: UNDERACTIVE (ratio 1.55-1.70), ADAPTIVE (2.27-2.92), TRANSITION (~2.97), and CHAOTIC (4.42-35.55). The Qwen family is the only family observed in the ADAPTIVE zone in this panel. The ordering is robust across temperature (0.1-1.0) and token budget […]