Related papers: Learnability and Positive Equivalence Relations

What can large language models learn? By definition, language models (LM) are distributions over strings. Therefore, an intuitive way of addressing the above question is to formalize it as a matter of learnability of classes of…

In this article, we investigate the arithmetical hierarchy from the perspective of realizability theory. An experimental observation in classical computability theory is that the notion of degrees of unsolvability for natural arithmetical…

We define a sequence of positive integers recursively, where each term is determined as follows: starting with a given positive integer, if the term is odd, the next is the sum of its positive divisors; if the term is even, the subsequent…

We study the interaction of views, queries, and background knowledge in the form of existential rules. The motivating questions concern monotonic determinacy of a query using views w.r.t. rules, which refers to the ability to recover the…

We continue the research on the generative capacity of contextual grammars where contexts are adjoined around whole words (externally) or around subwords (internally) which belong to special regular selection languages. All languages…

We introduce the notions of u-amenability and hyper-u-amenability for countable Borel equivalence relations, strong forms of amenability that are implied by hyperfiniteness. We show that treeable, hyper-u-amenable countable Borel…

In contrast with standard classification tasks, strategic classification involves agents strategically modifying their features in an effort to receive favorable predictions. For instance, given a classifier determining loan approval based…

Owing much to the revolution of information technology, the recent progress of deep learning benefits incredibly from the vastly enhanced access to data available in various digital formats. However, in certain scenarios, people may not…

Recursion is the nature of human natural language. Since Chomsky proposed generative grammar, many scholars have studied recursion either theoretically or empirically. However, by observing children's acquisition of tail recursion…

We introduce an analog of the theory of Borel equivalence relations in which we study equivalence relations that are decidable by an infinite time Turing machine. The Borel reductions are replaced by the more general class of infinite time…

Transformation-based learning has been successfully employed to solve many natural language processing problems. It has many positive features, but one drawback is that it does not provide estimates of class membership probabilities. In…

In this paper we consider a general way of constructing profinite struc- tures based on a given framework - a countable family of objects and a countable family of recognisers (e.g. formulas). The main theorem states: A subset of a family…

In Team Semantics, a dependency notion is strongly first order if every sentence of the logic obtained by adding the corresponding atoms to First Order Logic is equivalent to some first order sentence. In this work it is shown that all…

Typical arguments for results like Kleene's Second Recursion Theorem and the existence of self-writing computer programs bear the fingerprints of equational reasoning and combinatory logic. In fact, the connection of combinatory logic and…

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…

A supervised learning algorithm has access to a distribution of labeled examples, and needs to return a function (hypothesis) that correctly labels the examples. The hypothesis of the learner is taken from some fixed class of functions…

Recent advancements in cognitive science and multi-round reasoning techniques for Large Language Models (LLMs) suggest that iterative thinking processes improve problem-solving performance in complex tasks. Inspired by this, approaches like…

The paper demonstrates that falsifiability is fundamental to learning. We prove the following theorem for statistical learning and sequential prediction: If a theory is falsifiable then it is learnable -- i.e. admits a strategy that…

Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of…

This paper focuses on the relation between computational learning theory and resource-bounded dimension. We intend to establish close connections between the learnability/nonlearnability of a concept class and its corresponding size in…