Related papers: Universal Learning Theory
Lately there has been a lot of discussion about why deep learning algorithms perform better than we would theoretically suspect. To get insight into this question, it helps to improve our understanding of how learning works. We explore the…
Knowledge is a central concept within both Bayesian inference and the mathematical and philosophical program of logic and semiotics initiated by Charles Sanders Peirce and further developed by George Spencer-Brown and Louis Kauffman. The…
Solomonoff's central result on induction is that the posterior of a universal semimeasure M converges rapidly and with probability 1 to the true sequence generating posterior mu, if the latter is computable. Hence, M is eligible as a…
Learning to transfer considers learning solutions to tasks in a such way that relevant knowledge can be transferred from known task solutions to new, related tasks. This is important for general learning, as well as for improving the…
This paper briefly reviews the history of meta-learning and describes its contribution to general AI. Meta-learning improves model generalization capacity and devises general algorithms applicable to both in-distribution and…
This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like…
Brief Description: The book provides a unique highly self-contained text introducing the reader to the classical and modern theory of polyanalytic functions and their generalizations. This is a subbranch of complex analysis of several…
This is a gentle introduction to Colombeau nonlinear generalized functions, a generalization of the concept of distributions such that distributions can freely be multiplied. It is intended to physicists and applied mathematicians who…
Bayesian methods since the time of Laplace have been understood by their practitioners as closely aligned to the scientific method. Indeed a recent champion of Bayesian methods, E. T. Jaynes, titled his textbook on the subject Probability…
We introduce and study a learning theory which is roughly automatic, that is, it does not require but a minimum of initial programming, and is based on the potential computational phenomenon of self-reference, (i.e. the potential ability of…
I review our current understanding of the Worldformula, M theory, focusing on themes from the work of Heisenberg.
Michael Kinyon's 2005 open problem, based on the universality of Osborn loops is solved. It is shown that not every Osborn loop is universal.
Shepard's universal law of generalization is a remarkable hypothesis about how intelligent organisms should perceive similarity. In its broadest form, the universal law states that the level of perceived similarity between a pair of stimuli…
The theory of equidistribution is about hundred years old, and has been developed primarily by number theorists and theoretical computer scientists. A motivated uninitiated peer could encounter difficulties perusing the literature, due to…
Neural networks (NNs) are known for their high predictive accuracy in complex learning problems. Beside practical advantages, NNs also indicate favourable theoretical properties such as universal approximation (UA) theorems. Binarized…
It has been demonstrated earlier that universal computation is 'almost surely' chaotic. Machine learning is a form of computational fixed point iteration, iterating over the computable function space. We showcase some properties of this…
In 1993, just about a century after the epoch of Classical Invariant Theory and almost 30 years after Mumford's seminal book on Geometric Invariant Theory, Bernd Sturmfels approached the subject from a new, algorithmic perspective in his…
Understanding when learning is possible is a fundamental task in the theory of machine learning. However, many characterizations known from the literature deal with abstract learning as a mathematical object and ignore the crucial question:…
Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain…
We study and compare the learning dynamics of two universal learning algorithms, one based on Bayesian learning and the other on prediction with expert advice. Both approaches have strong asymptotic performance guarantees. When confronted…