22 citations · 61 across the 9 of their papers we have counts for
9 papers
Entropy as a Topological Operad Derivation
Tai-Danae Bradley
We share a small connection between information theory, algebra, and topology - namely, a correspondence between Shannon entropy and derivations of the operad of topological simpli…
Probabilistic Graphical Models and Tensor Networks: A Hybrid Framework
Jacob Miller, Geoffrey Roeder, Tai-Danae Bradley
We investigate a correspondence between two formalisms for discrete probabilistic modeling: probabilistic graphical models (PGMs) and tensor networks (TNs), a powerful modeling fra…
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…
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 -…
At the Interface of Algebra and Statistics
Tai-Danae Bradley
This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from…
Modeling Sequences with Quantum States: A Look Under the Hood
Tai-Danae Bradley, E. Miles Stoudenmire, John Terilla
Classical probability distributions on sets of sequences can be modeled using quantum states. Here, we do so with a quantum state that is pure and entangled. Because it is entangle…
Translating and Evolving: Towards a Model of Language Change in DisCoCat
Tai-Danae Bradley, Martha Lewis, Jade Master +1
The categorical compositional distributional (DisCoCat) model of meaning developed by Coecke et al. (2010) has been successful in modeling various aspects of meaning. However, it f…
What is Applied Category Theory?
Tai-Danae Bradley
This is a collection of introductory, expository notes on applied category theory, inspired by the 2018 Applied Category Theory Workshop, and in these notes we take a leisurely str…
On the Distribution of the Greatest Common Divisor of Gaussian Integers
Tai-Danae Bradley, Yin Choi Cheng, Yan Fei Luo
For a pair of random Gaussian integers chosen uniformly and independently from the set of Gaussian integers of norm or less as goes to infinity, we find asymptotics for the…