Transformer-based models have demonstrated exceptional performance across diverse domains, becoming the state-of-the-art solution for addressing sequential machine learning problems. Even though we have a general understanding of the fundamental components in the transformer architecture, little is known about how they operate or what are their expected dynamics. Recently, there has been an increasing interest in exploring the relationship between attention mechanisms and Hopfield networks, promising to shed light on the statistical physics of transformer networks. However, to date, the dynamical regimes of transformer-like models have not been studied in depth. In this paper, we address this gap by using methods for the study of asymmetric Hopfield networks in nonequilibrium regimes --namely path integral methods over generating functionals, yielding dynamics governed by concurrent mean-field variables. Assuming 1-bit tokens and weights, we derive analytical approximations for the behavior of large self-attention neural networks coupled to a softmax output, which become exact in the large limit size. Our findings reveal nontrivial dynamical phenomena, including nonequilibrium phase transitions associated with chaotic bifurcations, even for very simple configurations with a few encoded features and a very short context window. Finally, we discuss the potential of our analytic approach to improve our understanding of the inner workings of transformer models, potentially reducing computational training costs and enhancing model interpretability.

使用非平衡Hopfield网络的路径积分方法研究了变压器网络的动力学规律，发现了与混沌分叉相关的非平衡相变等非平凡的动力学现象，并讨论了这种分析方法改善对变压器模型内部运作理解的潜力。

自注意力神经网络的动力学平均场理论