Stochastic Scaling Limits and Synchronization by Noise in Deep Transformer Models
arXiv stat.ML / 4/30/2026
💬 OpinionIdeas & Deep AnalysisModels & Research
Key Points
- The paper shows that, under stochastic scaling, the token dynamics across layers in a finite transformer with MLP blocks converge (pathwise) to a continuous-time stochastic interacting particle system.
- It derives the specific stochastic partial differential equation (SPDE) that governs how the token distribution evolves in the limiting model.
- The authors prove propagation of chaos, establishing that as the number of tokens grows large, tokens behave increasingly independently while still following the same limiting law.
- The study demonstrates “synchronization by noise,” meaning the limiting stochastic system exhibits exponential decay of interaction energy on average when common noise is strong enough relative to the deterministic self-attention drift.
- It also characterizes which activation functions satisfy the coercivity condition required for the noise-driven synchronization results.
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