On the Statistical Mechanics of Attention
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 re...
| Authors | Jerry Yao-Chieh Hu, Yu-An Chen, Maojiang Su et al. |
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| Primary category | cs.LG |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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