Stochastic Scaling Limits and Synchronization by Noise in Deep Transformer Models
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917447776337920 |
|---|---|
| author | Agazzi, Andrea Bruno, Giuseppe García, Eloy Mosig Saviozzi, Samuele Romito, Marco |
| author_facet | Agazzi, Andrea Bruno, Giuseppe García, Eloy Mosig Saviozzi, Samuele Romito, Marco |
| contents | We prove pathwise convergence of the layerwise evolution of tokens in a finite-depth, finite-width transformer model with MultiLayer Perceptron (MLP) blocks to a continuous-time stochastic interacting particle system. We also identify the stochastic partial differential equation describing the evolution of the tokens' distribution in this limit and prove propagation of chaos when the number of such tokens is large. The bounds we establish are quantitative and the limits we consider commute. We further prove that the limiting stochastic model displays synchronization by noise and establish exponential dissipation of the interaction energy on average, provided that the common noise is sufficiently coercive relative to the deterministic self-attention drift. We finally characterize the activation functions satisfying the former condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26898 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic Scaling Limits and Synchronization by Noise in Deep Transformer Models Agazzi, Andrea Bruno, Giuseppe García, Eloy Mosig Saviozzi, Samuele Romito, Marco Probability Machine Learning We prove pathwise convergence of the layerwise evolution of tokens in a finite-depth, finite-width transformer model with MultiLayer Perceptron (MLP) blocks to a continuous-time stochastic interacting particle system. We also identify the stochastic partial differential equation describing the evolution of the tokens' distribution in this limit and prove propagation of chaos when the number of such tokens is large. The bounds we establish are quantitative and the limits we consider commute. We further prove that the limiting stochastic model displays synchronization by noise and establish exponential dissipation of the interaction energy on average, provided that the common noise is sufficiently coercive relative to the deterministic self-attention drift. We finally characterize the activation functions satisfying the former condition. |
| title | Stochastic Scaling Limits and Synchronization by Noise in Deep Transformer Models |
| topic | Probability Machine Learning |
| url | https://arxiv.org/abs/2604.26898 |