Functorial Question Answering

Abstract

We study the relational variant of the categorical compositional distributional (DisCoCat) models of Coecke et al. [1], where we replace vector spaces and linear maps by sets and relations. We show that RelCoCat models factorise through Cartesian bicategories, as a corollary we get logspace reductions from semantics and entailment to evaluation and containment of conjunctive queries respectively.Finally, we de ne question answering as an NP − complete problem.

Functorial Language Models

“…The idea of functorial learning is to take a training set of pairs ⊆ (G) × (Vect) of diagrams ∈ (G) and vectors ∈ (Vect), and learn a functor such that ( ) = . In practice, this exact functor may not exist thus we fix a loss : ∈N R × R → R + and a regularisation : R → R + then using gradient-based methods we approximate: Then the functor may be seen as a DisCoCat model for question-answering, see (de Felice et al, 2019). This model has been deployed on quantum hardware, see (Meichanetzidis et al, 2020a,b;Coecke et al, 2020).…”

“…On the other hand, categorical compositional distributional (DisCoCat) models (Clark et al, 2008(Clark et al, , 2010 use grammatical structure to compose the distributional meaning of words together into a meaning for the sentence. Grammar is explicitly represented as string diagrams, which allow formal reasoning about natural language semantics, for example analysing ambiguity (Kartsaklis et al, 2013(Kartsaklis et al, , 2014Piedeleu et al, 2015) and entailment (Sadrzadeh et al, 2018a;de Felice et al, 2019).…”

Grammar-aware sentence classification on quantum computers

“…This supervised learning task of binary classification for sentences is a special case of question answering (QA) [48][49][50]. Questions are posed as statements and the truth labels are the answers.…”