Transformers converge pathwise to a stochastic particle system and SPDE in the scaling limit, exhibiting synchronization by noise and exponential energy dissipation when common noise is coercive relative to self-attention drift.
Topics in propagation of chaos.Ecole d’été de probabilités de Saint- Flour XIX—1989, 1464:165–251
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Stochastic Scaling Limits and Synchronization by Noise in Deep Transformer Models
Transformers converge pathwise to a stochastic particle system and SPDE in the scaling limit, exhibiting synchronization by noise and exponential energy dissipation when common noise is coercive relative to self-attention drift.