Related papers: Learning Theory in the Arithmetic Hierarchy
Attempts of learning from hierarchical taxonomies in computer vision have been mostly focusing on image classification. Though ways of best harvesting learning improvements from hierarchies in classification are far from being solved, there…
Many learning algorithms are known to converge to an equilibrium for specific classes of games if the same learning algorithm is adopted by all agents. However, when the agents are self-interested, a natural question is whether agents have…
We investigate enumerability properties for classes of sets which permit recursive, lexicographically increasing approximations, or left-r.e. sets. In addition to pinpointing the complexity of left-r.e. Martin-L\"{o}f, computably, Schnorr,…
Curriculum learning--ordering training examples in a sequence to aid machine learning--takes inspiration from human learning, but has not gained widespread acceptance. Static strategies for scoring item difficulty rely on indirect proxy…
Most models of machine teaching and learning assume the learner makes no errors in its internal deductive inference. However, humans and large language models in few-shot learning regimes are two important examples of learners where this…
We study the matrix completion problem that leverages hierarchical similarity graphs as side information in the context of recommender systems. Under a hierarchical stochastic block model that well respects practically-relevant social…
G. Edelman, O. Sporns, and G. Tononi have introduced the neural complexity of a family of random variables, defining it as a specific average of mutual information over subfamilies. We show that their choice of weights satisfies two natural…
An important result from psycholinguistics (Griffiths & Kalish, 2005) states that no language can be learned iteratively by rational agents in a self-sustaining manner. We show how to modify the learning process slightly in order to achieve…
We study the stochastic noisy bandit problem with an unknown reward function $f^*$ in a known function class $\mathcal{F}$. Formally, a model $M$ maps arms $\pi$ to a probability distribution $M(\pi)$ of reward. A model class $\mathcal{M}$…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
Automata over infinite alphabets have emerged as a convenient computational model for processing structures involving data, such as nonces in cryptographic protocols or data values in XML documents. We introduce active learning methods for…
Gathering training data is a key step of any supervised learning task, and it is both critical and expensive. Critical, because the quantity and quality of the training data has a high impact on the performance of the learned function.…
We study the problem of learning overcomplete HMMs---those that have many hidden states but a small output alphabet. Despite having significant practical importance, such HMMs are poorly understood with no known positive or negative results…
Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify…
Continual learning with an increasing number of classes is a challenging task. The difficulty rises when each example is presented exactly once, which requires the model to learn online. Recent methods with classic parameter optimization…
Probabilistic logical models are a core component of neurosymbolic AI and are important in their own right for tasks that require high explainability. Unlike neural networks, logical theories that underlie the model are often handcrafted…
We investigate how different learning restrictions reduce learning power and how the different restrictions relate to one another. We give a complete map for nine different restrictions both for the cases of complete information learning…
We propose a learning setting in which unlabeled data is free, and the cost of a label depends on its value, which is not known in advance. We study binary classification in an extreme case, where the algorithm only pays for negative…
We consider a problem of learning kernels for use in SVM classification in the multi-task and lifelong scenarios and provide generalization bounds on the error of a large margin classifier. Our results show that, under mild conditions on…
The structure of knowledge is commonly described as a network of key concepts and semantic relations between them. A learner of a particular domain can discover this network by navigating the nodes and edges presented by instructional…