6 citations · 10 across the 19 of their papers we have counts for
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 sca…
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…
Normalization in Attention Dynamics
Nikita Karagodin, Shu Ge, Yury Polyanskiy +1
We study the effect of normalization schemes on token representations in deep transformers. Modeling their evolution as interacting particles on the sphere, we show that normalizat…
Critical attention scaling in long-context transformers
Shi Chen, Zhengjiang Lin, Yury Polyanskiy +1
As large language models scale to longer contexts, attention layers suffer from a fundamental pathology: attention scores collapse toward uniformity as context length increases…
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…
Residual connections provably mitigate oversmoothing in graph neural networks
Ziang Chen, Zhengjiang Lin, Shi Chen +2
Graph neural networks (GNNs) have achieved remarkable empirical success in processing and representing graph-structured data across various domains. However, a significant challeng…
Clustering in Causal Attention Masking
Nikita Karagodin, Yury Polyanskiy, Philippe Rigollet
This work presents a modification of the self-attention dynamics proposed by Geshkovski et al. (arXiv:2312.10794) to better reflect the practically relevant, causally masked attent…
Dynamic metastability in the self-attention model
Borjan Geshkovski, Hugo Koubbi, Yury Polyanskiy +1
We consider the self-attention model - an interacting particle system on the unit sphere, which serves as a toy model for Transformers, the deep neural network architecture behind…
A mathematical perspective on Transformers
Borjan Geshkovski, Cyril Letrouit, Yury Polyanskiy +1
Transformers play a central role in the inner workings of large language models. We develop a mathematical framework for analyzing Transformers based on their interpretation as int…