Related papers: Induction, Popper, and machine learning
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…
Sound deductive reasoning -- the ability to derive new knowledge from existing facts and rules -- is an indisputably desirable aspect of general intelligence. Despite the major advances of AI systems in areas such as math and science,…
The progress of machine learning over the past decade is undeniable. In retrospect, it is both remarkable and unsettling that this progress was achievable with little to no rigorous theory to guide experimentation. Despite this fact,…
The advent of Generative Artificial Intelligence (GAI) has heralded an inflection point that changed how society thinks about knowledge acquisition. While GAI cannot be fully trusted for decision-making, it may still provide valuable…
Mathematical induction is a fundamental tool in computer science and mathematics. Henkin initiated the study of formalization of mathematical induction restricted to the setting when the base case B is set to singleton set containing 0 and…
The first decade of this century has seen the nascency of the first mathematical theory of general artificial intelligence. This theory of Universal Artificial Intelligence (UAI) has made significant contributions to many theoretical,…
Solomonoff Induction is an optimal-in-the-limit unbounded algorithm for sequence prediction, representing a Bayesian mixture of every computable probability distribution and performing close to optimally in predicting any computable…
The human brain is the substrate for human intelligence. By simulating the human brain, artificial intelligence builds computational models that have learning capabilities and perform intelligent tasks approaching the human level. Deep…
The two most important algorithms in artificial intelligence are backpropagation and belief propagation. In spite of their importance, the connection between them is poorly characterized. We show that when an input to backpropagation is…
This paper shows that the common method used for making predictions under uncertainty in A1 and science is in error. This method is to use currently available data to select the best model from a given class of models-this process is called…
The idea that the brain is a probabilistic (Bayesian) inference machine, continuously trying to figure out the hidden causes of its inputs, has become very influential in cognitive (neuro)science over recent decades. Here I present a…
Chaitin's work, in its depth and breadth, encompasses many areas of scientific and philosophical interest. It helped establish the accepted mathematical concept of randomness, which in turn is the basis of tools that I have developed to…
Meta-learning has emerged as a powerful approach to train neural networks to learn new tasks quickly from limited data. Broad exposure to different tasks leads to versatile representations enabling general problem solving. But, what are the…
Current discussions of "Explainable AI" (XAI) do not much consider the role of abduction in explanatory reasoning (see Mueller, et al., 2018). It might be worthwhile to pursue this, to develop intelligent systems that allow for the…
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…
Hybrid learning methods use theoretical knowledge of a domain and a set of classified examples to develop a method for classification. Methods that use domain knowledge have been shown to perform better than inductive learners. However,…
A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we…
The Bayesian framework is ideally suited for induction problems. The probability of observing $x_t$ at time $t$, given past observations $x_1...x_{t-1}$ can be computed with Bayes' rule if the true distribution $\mu$ of the sequences…
We are at the cusp of a transition from "learning from data" to "learning what data to learn from" as a central focus of artificial intelligence (AI) research. While the first-order learning problem is not completely solved, large models…
The ability to generalise from a small number of examples is a fundamental challenge in machine learning. To tackle this challenge, we introduce an inductive logic programming (ILP) approach that combines negation and predicate invention.…