Related papers: Bounds in Query Learning
Database theory is exciting because it studies highly general and practically useful abstractions. Conjunctive query (CQ) evaluation is a prime example: it simultaneously generalizes graph pattern matching, constraint satisfaction, and…
Substructural logics are formal logical systems that omit familiar structural rules of classical and intuitionistic logic such as contraction, weakening, exchange (commutativity), and associativity. This leads to a resource-sensitive…
In this paper the problem of {\em learning} appropriate domain-specific bias is addressed. It is shown that this can be achieved by learning many related tasks from the same domain, and a theorem is given bounding the number tasks that must…
The authors describe their approach to teaching a course on finite fields and combinatorial applications, including block designs and error-correcting codes, using a hybrid of lectures and active learning. Under the discussed classroom…
We build a theoretical framework for designing and understanding practical meta-learning methods that integrates sophisticated formalizations of task-similarity with the extensive literature on online convex optimization and sequential…
We examine the complexity of inference in Bayesian networks specified by logical languages. We consider representations that range from fragments of propositional logic to function-free first-order logic with equality; in doing so we cover…
The degree of a polynomial representing (or approximating) a function f is a lower bound for the number of quantum queries needed to compute f. This observation has been a source of many lower bounds on quantum algorithms. It has been an…
Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency list-like array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity,…
This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error…
In this paper, a progressive learning technique for multi-class classification is proposed. This newly developed learning technique is independent of the number of class constraints and it can learn new classes while still retaining the…
Learning arguably involves the discovery and memorization of abstract rules. The aim of this paper is to study associative memory mechanisms. Our model is based on high-dimensional matrices consisting of outer products of embeddings, which…
Artificial intelligence (AI) systems, and Large Language Models (LLMs) in particular, are increasingly employed for creative tasks like scientific idea generation, constituting a form of generalization from training data unaddressed by…
We present a unifying picture of PAC-Bayesian and mutual information-based upper bounds on the generalization error of randomized learning algorithms. As we show, Tong Zhang's information exponential inequality (IEI) gives a general recipe…
Deep learning has yielded extraordinary results in vision and natural language processing, but this achievement comes at a cost. Most models require enormous resources during training, both in terms of computation and in human labeling…
We consider the problem of sequential prediction and provide tools to study the minimax value of the associated game. Classical statistical learning theory provides several useful complexity measures to study learning with i.i.d. data. Our…
Online learning is the process of answering a sequence of questions based on the correct answers to the previous questions. It is studied in many research areas such as game theory, information theory and machine learning. There are two…
Understanding the power of quantum data in machine learning is central to many proposed applications of quantum technologies. While access to quantum data can offer exponential advantages for carefully designed learning tasks and often…
We study online learnability of a wide class of problems, extending the results of (Rakhlin, Sridharan, Tewari, 2010) to general notions of performance measure well beyond external regret. Our framework simultaneously captures such…
The rapidly growing ecosystem of Large Language Models (LLMs) makes it increasingly challenging to manage and utilize the vast and dynamic pool of models effectively. We propose LOCUS, a method that produces low-dimensional vector…
Large language models (LLMs) have shown impressive prowess in solving a wide range of tasks with world knowledge. However, it remains unclear how well LLMs are able to perceive their factual knowledge boundaries, particularly under…