Related papers: Learning Equivalence Relations on Polish Spaces
In the last years there has been a growing interest in the study of learning problems associated with algebraic structures. The framework we use models the scenario in which a learner is given larger and larger fragments of a structure from…
Algorithmic learning theory traditionally studies the learnability of effective infinite binary sequences (reals), while recent work by [Vitanyi and Chater, 2017] and [Bienvenu et al., 2014] has adapted this framework to the study of…
We demonstrate that a wide array of machine learning algorithms are specific instances of one single paradigm: reciprocal learning. These instances range from active learning over multi-armed bandits to self-training. We show that all these…
Conversation is like an intricate partner dance and behavioral convergence, or the similarity in observable behaviors of partners over time, can lead to shared understanding, changed beliefs and increased rapport. This article describes a…
We associate to every action of a Polish group on a standard probability space a Polish group that we call the orbit full group. For discrete groups, we recover the well-known full groups of pmp equivalence relations equipped with the…
In this paper we further develop the theory of canonical approximations of Polishable subgroups of Polish groups, building on previous work of Solecki and Farah--Solecki. In particular, we obtain a characterization of such canonical…
We study the class of Borel equivalence relations under continuous reducibility. In particular , we characterize when a Borel equivalence relation with countable equivalence classes is $\Sigma$ 0 $\xi$ (or $\Pi$ 0 $\xi$). We characterize…
Working in the framework of Borel reducibility, we study various notions of embeddability between groups. We prove that the embeddability between countable groups, the topological embeddability between (discrete) Polish groups, and the…
Attributes of words and relations between two words are central to numerous tasks in Artificial Intelligence such as knowledge representation, similarity measurement, and analogy detection. Often when two words share one or more attributes…
We provide a complete classification, up to order-isomorphism, of all possible Wadge hierarchies on zero-dimensional Polish spaces using (essentially) countable ordinals as complete invariants. We also observe that although our assignment…
Human-centered environments are rich with a wide variety of spatial relations between everyday objects. For autonomous robots to operate effectively in such environments, they should be able to reason about these relations and generalize…
A variation of the Scott analysis of countable structures is applied to actions of non-Archimedean TSI Polish groups acting continuously on a Polish spaces. We give results on the potential Borel complexity spectrum of such groups, and…
The ability for autonomous agents to learn and conform to human norms is crucial for their safety and effectiveness in social environments. While recent work has led to frameworks for the representation and inference of simple social rules,…
When robots learn reward functions using high capacity models that take raw state directly as input, they need to both learn a representation for what matters in the task -- the task ``features" -- as well as how to combine these features…
We develop a unified framework for locating natural properties of algebraic and analytic structures within the Borel hierarchy. Objects are presented as quotients of a universal generator and definability is read directly from the quotient…
Learning With Opponent-Learning Awareness (LOLA) (Foerster et al. [2018a]) is a multi-agent reinforcement learning algorithm that typically learns reciprocity-based cooperation in partially competitive environments. However, LOLA often…
In language learning in the limit we investigate computable devices (learners) learning formal languages. Through the years, many natural restrictions have been imposed on the studied learners. As such, monotonic restrictions always enjoyed…
Grammatical features across human languages show intriguing correlations often attributed to learning biases in humans. However, empirical evidence has been limited to experiments with highly simplified artificial languages, and whether…
Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…
While most research in Gold-style learning focuses on learning formal languages, we consider the identification of computable structures, specifically equivalence structures. In our core model the learner gets more and more information…