12 papers · 1 filter
Measure-to-measure Regression with Transformers
Matthew Vandergrift, Martha White, Yury Polyanskiy +2
Many learning problems require predicting how populations evolve under an unknown transformation. A natural representation for such populations is a probability measure, with point…
Propagation of Chaos in Contextual Flow Maps
Shi Chen, Zhengjiang Lin, Kaizhao Liu +1
We develop a quantitative statistical theory of transformers in the large-context regime by adopting the abstraction of contextual flow maps (CFMs): dynamical systems that evolve a…
Scaling Limits of Long-Context Transformers
Giuseppe Bruno, Shi Chen, Zhengjiang Lin +2
We study the long-context limit of softmax self-attention with a fixed query and a random context of i.i.d. keys on the sphere, viewing the inverse temperature as the sc…
Quantitative Clustering in Mean-Field Transformer Models
Shi Chen, Zhengjiang Lin, Yury Polyanskiy +1
The evolution of tokens through deep transformer models can be modeled as an interacting particle system that has been shown to exhibit an asymptotic clustering behavior akin to th…
YuriiFormer: A Suite of Nesterov-Accelerated Transformers
Aleksandr Zimin, Yury Polyanskiy, Philippe Rigollet
We propose a variational framework that interprets transformer layers as iterations of an optimization algorithm acting on token embeddings. In this view, self-attention implements…
The Mean-Field Dynamics of Transformers
Philippe Rigollet
We develop a mathematical framework that interprets Transformer attention as an interacting particle system and studies its continuum (mean-field) limits. By idealizing attention o…