Related papers: G\"odel Incompleteness Theorem for PAC Learnable T…

In 1931, G\"odel presented in K\"onigsberg his famous Incompleteness Theorem, stating that some true mathematical statements are unprovable. Yet, this result gives us no idea about those independent (that is, true and unprovable)…

Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…

Algorithmic interpretability is necessary to build trust, ensure fairness, and track accountability. However, there is no existing formal measurement method for algorithmic interpretability. In this work, we build upon programming language…

A new viewpoint of the G\"odel's incompleteness theorem be given in this article which reveals the deep relationship between the logic and computation. Upon the results of these studies, an algorithm be given which shows how to search a…

The standard definition of PAC learning (Valiant 1984) requires learners to succeed under all distributions -- even ones that are intractable to sample from. This stands in contrast to samplable PAC learning (Blum, Furst, Kearns, and Lipton…

In this paper we prove Chaitin's ``heuristic principle'', {\it the theorems of a finitely-specified theory cannot be significantly more complex than the theory itself}, for an appropriate measure of complexity. We show that the measure is…

We demonstrate a compactness result holding broadly across supervised learning with a general class of loss functions: Any hypothesis class $H$ is learnable with transductive sample complexity $m$ precisely when all of its finite…

The lack of interpretability has hindered the large-scale adoption of AI technologies. However, the fundamental idea of interpretability, as well as how to put it into practice, remains unclear. We provide notions of interpretability based…

The goal of a learning algorithm is to receive a training data set as input and provide a hypothesis that can generalize to all possible data points from a domain set. The hypothesis is chosen from hypothesis classes with potentially…

We informally call a stochastic process learnable if it admits a generalization error approaching zero in probability for any concept class with finite VC-dimension (IID processes are the simplest example). A mixture of learnable processes…

As artificial intelligence is increasingly affecting all parts of society and life, there is growing recognition that human interpretability of machine learning models is important. It is often argued that accuracy or other similar…

In recent years, machine learning researchers have focused on methods to construct flexible and interpretable prediction models. However, an interpretability evaluation, a relationship between generalization performance and an…

Understanding is a crucial yet elusive concept in artificial intelligence (AI). This work proposes a framework for analyzing understanding based on the notion of composability. Given any subject (e.g., a person or an AI), we suggest…

Probably Approximately Correct (i.e., PAC) learning is a core concept of sample complexity theory, and efficient PAC learnability is often seen as a natural counterpart to the class P in classical computational complexity. But while the…

Interpretability is a pressing issue for machine learning. Common approaches to interpretable machine learning constrain interactions between features of the input, rendering the effects of those features on a model's output comprehensible…

Hilbert and Ackermann asked for a method to consistently extend incomplete theories to complete theories. G\"odel essentially proved that any theory capable of encoding its own statements and their proofs contains statements that are true…

We study computable PAC (CPAC) learning as introduced by Agarwal et al. (2020). First, we consider the main open question of finding characterizations of proper and improper CPAC learning. We give a characterization of a closely related…

The tension between deduction and induction is perhaps the most fundamental issue in areas such as philosophy, cognition and artificial intelligence. In an influential paper, Valiant recognised that the challenge of learning should be…

This paper argues that interpretability research in Artificial Intelligence (AI) is fundamentally ill-posed as existing definitions of interpretability fail to describe how interpretability can be formally tested or designed for. We posit…

We study a recent model of collaborative PAC learning where $k$ players with $k$ different tasks collaborate to learn a single classifier that works for all tasks. Previous work showed that when there is a classifier that has very small…