Related papers: Learnability and Positive Equivalence Relations

The rankability of data is a recently proposed problem that considers the ability of a dataset, represented as a graph, to produce a meaningful ranking of the items it contains. To study this concept, a number of rankability measures have…

We find all finite Ockham algebras that admit only finitely many compatible relations (modulo a natural equivalence). Up to isomorphism and symmetry, these Ockham algebras form two countably infinite families: one family consists of the…

We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain. Data values can be compared wrt.\ equality. As the satisfiability problem for this logic is undecidable in…

We show that the automorphism groups of countably categorical linear orders are extremely amenable. Using methods of Kechris, Pestov, and Todorcevic, we use this fact to derive a structural Ramsey theorem for certain families of finite…

The success of neural networks comes hand in hand with a desire for more interpretability. We focus on text classifiers and make them more interpretable by having them provide a justification, a rationale, for their predictions. We approach…

Large Language Models (LLMs) have demonstrated impressive generalization capabilities across various tasks, but their claim to practical relevance is still mired by concerns on their reliability. Recent works have proposed examining the…

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…

A relational structure ${\mathbb X}$ is said to be reversible iff every bijective endomorphism $f:X\rightarrow X$ is an automorphism. We define a sequence of non-zero cardinals $\langle \kappa_i :i\in I\rangle$ to be reversible iff each…

A real \alpha is called recursively enumerable ("r.e." for short) if there exists a computable, increasing sequence of rationals which converges to \alpha. It is known that the randomness of an r.e. real \alpha can be characterized in…

Strategic classification studies learning settings in which individuals can modify their features, at a cost, in order to influence the classifier's decision. A central question is how the sample complexity of the induced (strategic)…

The theory of two binary relations has the strong amalgamation property when the first relation is assumed to be coarser than the second relation, and each relation satisfies a chosen set of properties from the following list: transitivity,…

We aim at enforcing hard constraints to impose a global structure on sequences generated from Markov models. In this report, we study the complexity of sampling Markov sequences under two classes of constraints: Binary Equalities and…

One of the well-known results in concurrency theory concerns the relationship between event structures and occurrence nets: an occurrence net can be associated with a prime event structure, and vice versa. More generally, the relationships…

We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories are known to be conservative extensions of the original…

Svenonius theorem reduces the problem of first-order definability to the problem of relationship between groups of permutations. In the present paper we use this approach to describe the lattice of definable relations for the structure of…

The tendency of repeating past choices more often than expected from the history of outcomes has been repeatedly empirically observed in reinforcement learning experiments. It can be explained by at least two computational processes:…

Grammatical relationships (GRs) form an important level of natural language processing, but different sets of GRs are useful for different purposes. Therefore, one may often only have time to obtain a small training corpus with the desired…

A relationally exchangeable structure is a random combinatorial structure whose law is invariant with respect to relabeling its relations, as opposed to its elements. Aside from exchangeable random partitions, examples include edge…

Existential positive formulas form a fragment of first-order logic that includes and is semantically equivalent to unions of conjunctive queries, one of the most important and well-studied classes of queries in database theory. We consider…

Teachers intentionally pick the most informative examples to show their students. However, if the teacher and student are neural networks, the examples that the teacher network learns to give, although effective at teaching the student, are…