相关论文: On the learning power of Friedman-Stanley jumps

We develop a theory of high-arity PAC learning, which is statistical learning in the presence of "structured correlation". In this theory, hypotheses are either graphs, hypergraphs or, more generally, structures in finite relational…

Analogical reasoning depends fundamentally on the ability to learn and generalize about relations between objects. We develop an approach to relational learning which, given a set of pairs of objects…

Continual learning is the ability to sequentially learn over time by accommodating knowledge while retaining previously learned experiences. Neural networks can learn multiple tasks when trained on them jointly, but cannot maintain…

Given a countable structure $\mathcal{A}$, the degree spectrum of $\mathcal{A}$ is the set of all Turing degrees which can compute an isomorphic copy of $\mathcal{A}$. One of the major programs in computable structure theory is to determine…

We present a type of epistemic logics that encapsulates both the dynamics of acquiring knowledge (knowing) and losing information (forgetting), alongside the integration of group knowledge concepts. Our approach is underpinned by a system…

There is a fascinating interplay and overlap between recursion theory and descriptive set theory. A particularly beautiful source of such interaction has been Martin's conjecture on Turing invariant functions. This longstanding open problem…

This paper describes a family of probabilistic architectures designed for online learning under the logarithmic loss. Rather than relying on non-linear transfer functions, our method gains representational power by the use of data…

The cut pseudo-metric on the space of graph limits induces an equivalence relation. The quotient space obtained by collapsing each equivalence class to a point is a metric space with appealing analytic properties. We show that the…

Lifted Relational Neural Networks (LRNNs) describe relational domains using weighted first-order rules which act as templates for constructing feed-forward neural networks. While previous work has shown that using LRNNs can lead to…

Learning performed over finite time is inherently irreversible. In Part~I of this series, we modeled learning as a transport process in the space of parameter distributions and derived the Epistemic Speed Limit (ESL), which lower-bounds…

We introduce new combinatorial quantities for concept classes, and prove lower and upper bounds for learning complexity in several models of query learning in terms of various combinatorial quantities. Our approach is flexible and powerful…

We study the complexity of isomorphism of classes of metric structures using methods from infinitary continuous logic. For Borel classes of locally compact structures, we prove that if the equivalence relation of isomorphism is potentially…

We consider the relationship between learnability of a "base class" of functions on a set $X$, and learnability of a class of statistical functions derived from the base class. For example, we refine results showing that learnability of a…

Let $F_{\omega_1}$ be the countable admissible ordinal equivalence relation defined on ${}^\omega 2$ by $x \ F_{\omega_1} \ y$ if and only if $\omega_1^x = \omega_1^y$. It will be shown that $F_{\omega_1}$ is classifiable by countable…

We use a formal correspondence between thermodynamics and inference, where the number of samples can be thought of as the inverse temperature, to study a quantity called ``learning capacity'' which is a measure of the effective…

Word Embeddings are used widely in multiple Natural Language Processing (NLP) applications. They are coordinates associated with each word in a dictionary, inferred from statistical properties of these words in a large corpus. In this paper…

The notion of computable reducibility between equivalence relations on the natural numbers provides a natural computable analogue of Borel reducibility. We investigate the computable reducibility hierarchy, comparing and contrasting it with…

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 define and study expansion problems on countable structures in the setting of descriptive combinatorics. We consider both expansions on countable Borel equivalence relations and on countable groups, in the Borel, measure and category…

Can we effectively learn a nonlinear representation in time comparable to linear learning? We describe a new algorithm that explicitly and adaptively expands higher-order interaction features over base linear representations. The algorithm…