Asymptotic Analysis of Discrete-Time Self-Attention Dynamics in Transformers
In machine learning, a self-attention dynamics describes the attention mechanism of transformers, and is obtained treating the layer index of a transformer as time index. Even though naturally discrete-time, this dynamical system is most often studied in continuous-time. Scope of this paper is to provide a thorough investigation of the discrete-time version of the self-attention dynamics: a complete classification of its equilibria is given, and their stability properties are studied, in both the single-head and the multihead case. We show that in both cases the main attractor of the dynamics is a consensus equilibrium aligned with the principal eigenvector of the value matrix (in the sin...
| Authors | Claudio Altafini |
|---|---|
| Primary category | math.DS |
| Published | 9 October 2026 |
| Last updated at source | 9 October 2026 |
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