Related papers: Falsifiable implies Learnable

There is a strong consensus that combining the versatility of machine learning with the assurances given by formal verification is highly desirable. It is much less clear what verified machine learning should mean exactly. We consider this…

Building on the view of machine learning as search, we demonstrate the necessity of bias in learning, quantifying the role of bias (measured relative to a collection of possible datasets, or more generally, information resources) in…

The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…

Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…

Learning and the ability to learn are important factors in development and evolutionary processes [1]. Depending on the level, the complexity of learning can strongly vary. While associative learning can explain simple learning behaviour…

Computer algebra systems are really good at factoring polynomials, i.e. writing f as a product of irreducible factors. It is relatively easy to verify that we have a factorisation, but verifying that these factors are irreducible is a much…

When two different parties use the same learning rule on their own data, how can we test whether the distributions of the two outcomes are similar? In this paper, we study the similarity of outcomes of learning rules through the lens of the…

We provide a full characterization of the concept classes that are optimistically universally online learnable with $\{0, 1\}$ labels. The notion of optimistically universal online learning was defined in [Hanneke, 2021] in order to…

Machine unlearning aims to remove points from the training dataset of a machine learning model after training: e.g., when a user requests their data to be deleted. While many unlearning methods have been proposed, none of them enable users…

We formulate the machine unlearning problem as a general constrained optimization problem. It unifies the first-order methods from the approximate machine unlearning literature. This paper then introduces the concept of feasible updates as…

The usual reading of logical implication "A implies B" as "if A then B" fails in intuitionistic logic: there are formulas A and B such that "A implies B" is not provable, even though B is provable whenever A is provable. Intuitionistic…

In this paper, we make the case that a scientific theory of deep learning is emerging. By this we mean a theory which characterizes important properties and statistics of the training process, hidden representations, final weights, and…

Some of the most obviously correct physical theories - namely string theory and the multiverse - make no testable predictions, leading many to question whether we should accept something as scientific even if it makes no testable…

A new derivative, called deformable derivative, is introduced here which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach like that of ordinary one but with…

Self-supervised learning is an empirically successful approach to unsupervised learning based on creating artificial supervised learning problems. A popular self-supervised approach to representation learning is contrastive learning, which…

We study several questions in the reliable agnostic learning framework of Kalai et al. (2009), which captures learning tasks in which one type of error is costlier than others. A positive reliable classifier is one that makes no false…

Transparency is an essential requirement of machine learning based decision making systems that are deployed in real world. Often, transparency of a given system is achieved by providing explanations of the behavior and predictions of the…

As machine learning systems become ubiquitous, there has been a surge of interest in interpretable machine learning: systems that provide explanation for their outputs. These explanations are often used to qualitatively assess other…

Machine learning is the science of discovering statistical dependencies in data, and the use of those dependencies to perform predictions. During the last decade, machine learning has made spectacular progress, surpassing human performance…

To cope with real-world dynamics, an intelligent system needs to incrementally acquire, update, accumulate, and exploit knowledge throughout its lifetime. This ability, known as continual learning, provides a foundation for AI systems to…