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The ways in which natural selection can allow the proliferation of cooperative behavior have long been seen as a central problem in evolutionary biology. Most of the literature has focused on interactions between pairs of individuals and on linear public goods games. This emphasis has led to the conclusion that even modest levels of migration would pose a serious problem to the spread of altruism through population viscosity in group structured populations. Here we challenge this conclusion, by analyzing evolution in a framework which allows for complex group interactions and random migration among groups. We conclude that contingent forms of strong altruism that benefits equally all group members, regardless of kinship and without greenbeard effects, can spread when rare under realistic group sizes and levels of migration, due to the assortment of genes resulting only from population viscosity. Our analysis combines group-centric and gene-centric perspectives, allows for arbitrary strength of selection, and leads to extensions of Hamilton’s rule for the spread of altruistic alleles, applicable under broad conditions.

We study the online dynamics of learning in fully connected soft committee machines in the student-teacher scenario. The locally optimal modulation function, which determines the learning algorithm, is obtained from a variational argument in such a manner as to maximise the average generalisation error decay per example. Simulations results for the resulting algorithm are presented for a few cases. The symmetric phase plateaux are found to be vastly reduced in comparison to those found when online backpropagation algorithms are used. A discussion of the implementation of these ideas as practical algorithms is given.Key words: neural networks, generalisation, backpropagation, learning algorithms . PACS. #: 87.10.e+10, 05.90.+m, 64.60.Cn Learning how learning occurs in artificial systems has caught the attention of the Statistical Mechanics community in the last decade. This interest was ignited by several reasons, among them, the invention of efficient learning-from-examples methods such as backpropagation, that permit learning in computationally complex machines, to the realisation that ideas from disordered systems, in particular spin glasses, could be applied to the study of attractor as well as feedforward neural networks and to the generalised interest in complex systems with rugged energy landscapes.The main results from the Statistical Mechanics (see e.g. [1-3] ) approach have almost invariantly been obtained in the thermodynamic limit and have benefited from the powerful techniques used to calculate the averages over the disorder introduced by the random nature of the examples.Among several possible approaches to machine learning, online learning [4] has been the subject of an intense research effort due to several factors. In this scheme, examples are used only once, thereby avoiding the need for expensive memory resources, typical of offline methods. This, however, doesn't translate necessarily into poor performance since efficient methods can be devised that have performance comparable to the memory based ones. Furthermore, learning sequentially from single examples has a greater biological flavor than offline processing. While efficiency, computational economy and biological relevance may be the most relevant factors, the theoretical possibility of rather complete analytical studies has also played an important role. If each one of these factors is, by itself, sufficiently important to make online learning an attractive scheme, together they combine to give a most compelling argument for its thorough study.In this letter we present results of the optimisation of online supervised learning in a model consisting of a fully connected multilayer feedforward neural network, in what has become known as the student-teacher scenario. The type of result we present here brings together two separate lines of research that have been recently pursued by several groups.The study of online backpropagation as put forward by Biehl and Schwarze [5] and later developed in [6,7] has permitted the analytical understand...

The moral foundations theory supports that people, across cultures, tend to consider a small number of dimensions when classifying issues on a moral basis. The data also show that the statistics of weights attributed to each moral dimension is related to self-declared political affiliation, which in turn has been connected to cognitive learning styles by recent literature in neuroscience and psychology. Inspired by these data, we propose a simple statistical mechanics model with interacting neural networks classifying vectors and learning from members of their social neighborhood about their average opinion on a large set of issues. The purpose of learning is to reduce dissension among agents even when disagreeing. We consider a family of learning algorithms parametrized by δ, that represents the importance given to corroborating (same sign) opinions. We define an order parameter that quantifies the diversity of opinions in a group with homogeneous learning style. Using Monte Carlo simulations and a mean field approximation we find the relation between the order parameter and the learning parameter δ at a temperature we associate with the importance of social influence in a given group. In concordance with data, groups that rely more strongly on corroborating evidence sustains less opinion diversity. We discuss predictions of the model and propose possible experimental tests.