Related papers: Thin Coalgebraic Behaviours Are Inductive
We combine computable structure theory and algorithmic learning theory to study learning of families of algebraic structures. Our main result is a model-theoretic characterization of the class $\mathbf{InfEx}_{\cong}$, consisting of the…
For every smooth projective variety, we construct an action of the Heisenberg algebra on the direct sum of the Grothendieck groups of all the symmetric quotient stacks which contains the Fock space as a subrepresentation. The action is…
In this thesis, we try to build a connection between the two schools by introducing syntactic inductive biases for deep learning models. We propose two families of inductive biases, one for constituency structure and another one for…
Coinductive definitions, such as that of an infinite stream, may often be described by elegant logic programs, but ones for which SLD-refutation is of no value as SLD-derivations fall into infinite loops. Such definitions give rise to…
We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
Thin coverings are a method of constructing graded-simple modules from simple (ungraded) modules. After a general discussion, we classify the thin coverings of (quasifinite) simple modules over associative algebras graded by finite abelian…
We propound the thesis that there is a limitation to the number of possible structures which are axiomatically endowed with identities involving operations. In the case of algebras with a binary operation satisfying a formally reducible (to…
For endofunctors of varieties preserving intersections, a new description of the final coalgebra and the initial algebra is presented: the former consists of all well-pointed coalgebras. These are the pointed coalgebras having no proper…
A Bialgebra is a module over a ring that is both an associative algebra and a co-associative coalgebra with the product and coproduct additionally satisfying an appropriate commutative relationship. One application of Bialgebras is in the…
We construct a wide subcategory of the category of finite association schemes with a collection of desirable properties. Our subcategory has a first isomorphism theorem analogous to that of groups. Also, standard constructions taking…
Language theory, symbolic dynamics, modelisation of viral insertion into the genetic code of a host cell motivate the introduction of new types of bialgebras whose coalgebra parts are not necessarily coassociative. One of the aim of this…
To every minimal model of a complete local isolated cDV singularity Donovan--Wemyss associate a finite dimensional symmetric algebra known as the contraction algebra. We construct the first known standard derived equivalences between these…
A substantial thread of recent work on latent tree learning has attempted to develop neural network models with parse-valued latent variables and train them on non-parsing tasks, in the hope of having them discover interpretable tree…
In this article, we combine Sweedler's classic theory of measuring coalgebras -- by which $k$-algebras are enriched in $k$-coalgebras for $k$ a field -- with the theory of W-types -- by which the categorical semantics of inductive data…
We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the…
The partition algebra is an associative algebra with a basis of set-partition diagrams and multiplication given by diagram concatenation. It contains as subalgebras a large class of diagram algebras including the Brauer, planar partition,…
Simple function classes have emerged as toy problems to better understand in-context-learning in transformer-based architectures used for large language models. But previously proposed simple function classes like linear regression or…
Analytic combinatorics studies the asymptotic behaviour of sequences through the analytic properties of their generating functions. This article provides effective algorithms required for the study of analytic combinatorics in several…
The modelling, specification and study of the semantics of concurrent reactive systems have been interesting research topics for many years now. The aim of this thesis is to exploit the strengths of the (co)algebraic framework in modelling…