Layer-Wise Analysis Reveals Universal Discrete Emergence Across Large Language Model Architectures

The mechanisms underlying capability emergence in large language models remain poorly characterized. This study conducts system atic layer-by-layer probing across seven architecturally diverse models spanning three orders of magnitude in size, testing mathematical rea soning, logical inference, commonsense reasoning, and language under standing. Nearly all model task combinations exhibit abrupt accuracy transitions at speci c network depths rather than gradual improve ment, providing strong evidence for discrete phase changes in capabil ity formation. Post-emergence performance converges to remarkably consistent levels across all tested conditions, suggesting binary com petence states in which abilities are either absent or fully expressed. The analysis reveals robust task-dependent emergence ordering, with linguistically simpler capabilities crystallizing in shallower layers while abstract reasoning requires deeper computation. This hierarchy proves consistent across all tested architectures, indicating universal orga nizing principles independent of model family or training procedure. Size-dependent e ects appear complex and non-monotonic, with some larger models exhibiting earlier emergence while others show delayed capability formation, suggesting that architectural details modulate pure scaling e ects. These ndings establish a quantitative framework for understanding neural network capability formation, with implica tions for safety through predictability, interpretability through mech anistic localization, and architecture design through principled opti mization of emergence properties.