Related papers: Evolutionary Foundations of Mathematics
Inspired by empirical work in neuroscience for Bayesian approaches to brain function, we give a unified probabilistic account of various types of symbolic reasoning from data. We characterise them in terms of formal logic using the…
We demonstrate with a thought experiment that fitness-based population dynamical approaches to evolution are not able to make quantitative, falsifiable predictions about the long-term behavior of evolutionary systems. A key characteristic…
Biological evolution is realised through the same mechanisms of birth and death that underlie change in population density. The deep interdependence between ecology and evolution is well-established, and recent models focus on integrating…
Here we postulate three laws which form a mathematical framework to capture the essence of Darwinian evolutionary dynamics. The second law is most quantitative and is explicitly expressed by a unique form of stochastic differential…
This paper describes a process for combining patterns and features, to guide a search process and make predictions. It is based on the functionality that a human brain might have, which is a highly distributed network of simple neuronal…
In this report, a novel approach to intelligence and learning is introduced, this approach is based on what we call 'perception logic'. Based on this logic, a computing mechanism and automata are introduced. Multi-resolution analysis of…
The use of multiple Decision Models (DMs) enables to enhance the accuracy in decisions and at the same time allows users to evaluate the confidence in decision making. In this paper we explore the ability of multiple DMs to learn from a…
Recently, it has been proven that evolutionary algorithms produce good results for a wide range of combinatorial optimization problems. Some of the considered problems are tackled by evolutionary algorithms that use a representation which…
In a seminal paper, Valiant (2006) introduced a computational model for evolution to address the question of complexity that can arise through Darwinian mechanisms. Valiant views evolution as a restricted form of computational learning,…
Machine learning has made major advances in categorizing objects in images, yet the best algorithms miss important aspects of how people learn and think about categories. People can learn richer concepts from fewer examples, including…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
Statistical learning and logical reasoning are two major fields of AI expected to be unified for human-like machine intelligence. Most existing work considers how to combine existing logical and statistical systems. However, there is no…
Human language acquisition is an efficient, supervised, and continual process. In this work, we took inspiration from how human babies acquire their first language, and developed a computational process for word acquisition through…
Darwin claims in the {\em Origin} that similarity is evidence for common ancestry, but that adaptive similarities are "almost valueless" as evidence. This claim seems reasonable for some adaptive similarities but not for others. Here we…
A simple relation of the order of $n$ abstract objects generates an $n-2$ dimensional basis of three dimensional vectors. A cellular automaton-like model of evolution of this system is postulated. During this evolution, some quantities…
Object recognition has become a crucial part of machine learning and computer vision recently. The current approach to object recognition involves Deep Learning and uses Convolutional Neural Networks to learn the pixel patterns of the…
We show that evolutionarily stable states in general (nonlinear) population games (which can be viewed as continuous vector fields constrained on a polytope) are asymptotically stable under a multiplicative weights dynamic (under…
Attention endows animals an ability to concentrate on the most relevant information among a deluge of distractors at any given time, either through volitionally 'top-down' biasing, or driven by automatically 'bottom-up' saliency of stimuli,…
Mechanistic modelling of animal movement is often formulated in discrete time despite problems with scale invariance, such as handling irregularly timed observations. A natural solution is to formulate in continuous time, yet uptake of this…
The inheritance of characteristics induced by the environment has often been opposed to the theory of evolution by natural selection. Yet, while evolution by natural selection requires new heritable traits to be produced and transmitted, it…