Related papers: Model Equivalences
In English semantic similarity tasks, classic word embedding-based approaches explicitly model pairwise "interactions" between the word representations of a sentence pair. Transformer-based pretrained language models disregard this notion,…
We show pro-definability of spaces of definable types in various classical complete first order theories, including complete o-minimal theories, Presburger arithmetic, $p$-adically closed fields, real closed and algebraically closed valued…
One of the longstanding problems in universal algebra is the question of which finite lattices are isomorphic to the congruence lattices of finite algebras. This question can be phrased as which finite lattices can be represented as…
We give a self-contained introduction to accessible categories and how they shed light on both model- and set-theoretic questions. We survey for example recent developments on the study of presentability ranks, a notion of cardinality…
Model theoretic internality provides conditions under which the group of automorphisms of a model over a reduct is itself a definable group. In this paper we formulate a categorical analogue of the condition of internality, and prove an…
We introduce a basic model for contracts. Our model extends event structures with a new relation, which faithfully captures the circular dependencies among contract clauses. We establish whether an agreement exists which respects all the…
We survey current developments in the approximation theory of sequence modelling in machine learning. Particular emphasis is placed on classifying existing results for various model architectures through the lens of classical approximation…
One of the most remarkable properties of word embeddings is the fact that they capture certain types of semantic and syntactic relationships. Recently, pre-trained language models such as BERT have achieved groundbreaking results across a…
In this paper we give a small review of some recent results of elementary equivalence of linear and algebraic groups and our last new results of elementary equivalence of categories of modules, endomorphism rings of modules, lattices of…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
Inferential relations govern our concept use. In order to understand a concept it has to be located in a space of implications. There are different kinds of conditions for statements, i.e. that the conditions represent different kinds of…
We consider a school choice matching model where the priorities for schools are represented by binary relations that may not be weak order. We focus on the (total order) extensions of the binary relations. We introduce a class of algorithms…
While important properties of word vector representations have been studied extensively, far less is known about the properties of sentence vector representations. Word vectors are often evaluated by assessing to what degree they exhibit…
In this article, we introduce a notion of an exponential matrix, which is a polynomial matrix with exponential properties, and a notion of an equivalence relation of two exponential matrices, and then we initiate to study classifying…
It is well-known that biological phenomena are emergent. Emergent phenomena are quite interesting and amazing. However, they are difficult to be understood. Due to this difficulty, we propose a theory to describe emergence based on a…
Debate about fairness in machine learning has largely centered around competing definitions of what fairness or nondiscrimination between groups requires. However, little attention has been paid to what precisely a group is. Many recent…
We consider a class of linear ODEs of second order with variable coefficients and construct its Lie algebra of Lie group of equivalence transformations. Further we find invariants and differential invariants of this Lie algebra and by using…
We use model theoretic techniques to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation is given by inclusion, and existing meets and joins of…
As AI systems develop in complexity it is becoming increasingly hard to ensure non-discrimination on the basis of protected attributes such as gender, age, and race. Many recent methods have been developed for dealing with this issue as…
Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…