On the Statistical Mechanics of Attention

arXiv:2610.17347v1 Announce Type: new Abstract: We revisit the statistical mechanics of Transformer attention via modern Hopfield models. We present a free-energy formalism to characterize parameter regimes and critical thresholds for robust attention inference. The resulting free-energy landscape incorporates randomness in query states and attention weights. Attention then emerges as the equation of motion of the corresponding statistical-mechanical system (i.e., modern Hopfield model) through the standard free-energy minimization principle. This allows us to identify first-order phase transitions in attention between glassy and robust-inference phases. We further extend to attentions with stochastic queries and keys. Together, our results provide a rigorous statistical-mechanics framework for characterizing phase structure and inference reliability across a family of Transformer attention mechanisms.

Source: arXiv cs.LG | 2026-10-14