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

It is shown that the isomorphism relation between continuous t-norms is Borel bireducible with the relation of order isomorphism between linear orders on the set of natural numbers, and therefore, it is a Borel complete equivalence…

We continue the work of [1, 2, 3] by analyzing the equivalence relation of bi-embeddability on various classes of countable planes, most notably the class of countable non-Desarguesian projective planes. We use constructions of the second…

We determine, up to the equivalence of first-order interdefinability, all structures which are first-order definable in the random partial order. It turns out that these structures fall into precisely five equivalence classes. We achieve…

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…

While the successes of transformers across many domains are indisputable, accurate understanding of the learning mechanics is still largely lacking. Their capabilities have been probed on benchmarks which include a variety of structured and…

Statistical learning theory chiefly studies restricted hypothesis classes, particularly those with finite Vapnik-Chervonenkis (VC) dimension. The fundamental quantity of interest is the sample complexity: the number of samples required to…

We consider probabilistic topic models and more recent word embedding techniques from a perspective of learning hidden semantic representations. Inspired by a striking similarity of the two approaches, we merge them and learn probabilistic…

We consider multi-class classification where the predictor has a hierarchical structure that allows for a very large number of labels both at train and test time. The predictive power of such models can heavily depend on the structure of…

In the classical herding model, asymptotic learning refers to situations where individuals eventually take the correct action regardless of their private information. Classical results identify classes of information structures for which…

Recombining known primitive concepts into larger novel combinations is a quintessentially human cognitive capability. Whether large neural models in NLP can acquire this ability while learning from data is an open question. In this paper,…

The vital role of analogical reasoning in human cognition allows us to grasp novel concepts by linking them with familiar ones through shared relational structures. Despite the attention previous research has given to word analogies, this…

We present a model-theoretic property of finite structures, that can be seen to be a finitary analogue of the well-studied downward L\"owenheim-Skolem property from classical model theory. We call this property as the…

Coupled learning is a contrastive scheme for tuning the properties of individual elements within a network in order to achieve desired functionality of the system. It takes advantage of physics both to learn using local rules and to…

We make progress on two important problems regarding attribute efficient learnability. First, we give an algorithm for learning decision lists of length $k$ over $n$ variables using $2^{\tilde{O}(k^{1/3})} \log n$ examples and time…

We consider an old question of Slaman and Steel: whether Turing equivalence is an increasing union of Borel equivalence relations none of which contain a uniformly computable infinite sequence. We show this question is deeply connected to…

We study the ability of foundation models to learn representations for classification that are transferable to new, unseen classes. Recent results in the literature show that representations learned by a single classifier over many classes…

In order to model an efficient learning paradigm, iterative learning algorithms access data one by one, updating the current hypothesis without regress to past data. Past research on iterative learning analyzed for example many important…

Learning of continuous exponential family distributions with unbounded support remains an important area of research for both theory and applications in high-dimensional statistics. In recent years, score matching has become a widely used…

Answer selection aims at identifying the correct answer for a given question from a set of potentially correct answers. Contrary to previous works, which typically focus on the semantic similarity between a question and its answer, our…

We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…