11 citations · 48 across the 10 of their papers we have counts for
10 papers
Relu and softplus neural nets as zero-sum turn-based games
Stephane Gaubert, Yiannis Vlassopoulos
We show that the output of a ReLU neural network can be interpreted as the value of a zero-sum, turn-based, stopping game, which we call the ReLU net game. The game runs in the dir…
Directed Metric Structures arising in Large Language Models
Stéphane Gaubert, Yiannis Vlassopoulos
Large Language Models are transformer neural networks which are trained to produce a probability distribution on the possible next words to given texts in a corpus, in such a way t…
Smooth Calabi-Yau structures and the noncommutative Legendre transform
Maxim Kontsevich, Alex Takeda, Yiannis Vlassopoulos
We elucidate the relation between smooth Calabi-Yau structures and pre-Calabi-Yau structures. We show that, from a smooth Calabi-Yau structure on an -category , one ca…
Pre-Calabi-Yau algebras and topological quantum field theories
Maxim Kontsevich, Alex Takeda, Yiannis Vlassopoulos
We introduce a notion generalizing Calabi-Yau structures on A-infinity algebras and categories, which we call pre-Calabi-Yau structures. This notion does not need either one of the…
An enriched category theory of language: from syntax to semantics
Tai-Danae Bradley, John Terilla, Yiannis Vlassopoulos
State of the art language models return a natural language text continuation from any piece of input text. This ability to generate coherent text extensions implies significant sop…
Homologies of monomial operads and algebras
Natalia Iyudu, Ioannis Vlassopoulos
We consider the bar complex of a monomial non-unital associative algebra . It splits as a direct sum of complexes , defined for any fixe…
Language Modeling with Reduced Densities
Tai-Danae Bradley, Yiannis Vlassopoulos
This work originates from the observation that today's state-of-the-art statistical language models are impressive not only for their performance, but also - and quite crucially -…
Language as a matrix product state
Vasily Pestun, John Terilla, Yiannis Vlassopoulos
We propose a statistical model for natural language that begins by considering language as a monoid, then representing it in complex matrices with a compatible translation invarian…
Tensor network language model
Vasily Pestun, Yiannis Vlassopoulos
We propose a new statistical model suitable for machine learning of systems with long distance correlations such as natural languages. The model is based on directed acyclic graph…
Quantum Cohomology and Morse Theory on the Loop Space of Toric Varieties
Yiannis Vlassopoulos
On a symplectic manifold , the quantum product defines a complex, one parameter family of flat connections called the A-model or Dubrovin connections. Let denote the par…