A new mathematical framework for analyzing Transformers has been presented, focusing on their interpretation as interacting particle systems. The study reveals that Transformers are flow maps on the space of probability measures over a d-dimensional real vector space. It shows how self-attention leads to token clustering and potential deterministic outcomes. This sheds light on the building blocks of most AI engineering today, providing insight into their functioning and evolution.
Transformers are in fact flow maps on P(R^d), the space of probability measures over R^d. Transformers evolve a mean-field interacting particle system. Every particle follows the flow of a vector field which depends on the empirical measure of all particles.
Discover the new mathematical framework for Transformers, revealing how self-attention leads to token clustering and potential deterministic outcomes: https://t.co/0vG3JSEu5p
Transformers are the building blocks of most AI engineering today, but what even are they?? We wrote about it below (🧵) so you don’t have to gain the intuition yourself 🫶 https://t.co/Rtxqg3GDzb
[LG] A mathematical perspective on Transformers https://t.co/KHMefoPWmU A Mathematical Perspective on Transformers: This paper presents a mathematical framework for analyzing Transformers, focusing on their interpretation as interacting particle systems. The study reveals… https://t.co/rD9rjNl6Ct
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